idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
51,401 | Is R output reliable (specially IRT package ltm) [duplicate] | R is widely used in scientific circles for published papers. R stores your data in RAM, so either it will be able to process your data set or it won't -- depending on whether the data and processing fit in memory -- there is no degraded mode where you get results but they are less accurate. (Technically, there are pack... | Is R output reliable (specially IRT package ltm) [duplicate] | R is widely used in scientific circles for published papers. R stores your data in RAM, so either it will be able to process your data set or it won't -- depending on whether the data and processing f | Is R output reliable (specially IRT package ltm) [duplicate]
R is widely used in scientific circles for published papers. R stores your data in RAM, so either it will be able to process your data set or it won't -- depending on whether the data and processing fit in memory -- there is no degraded mode where you get res... | Is R output reliable (specially IRT package ltm) [duplicate]
R is widely used in scientific circles for published papers. R stores your data in RAM, so either it will be able to process your data set or it won't -- depending on whether the data and processing f |
51,402 | Is R output reliable (specially IRT package ltm) [duplicate] | If you, or anyone else, has a question about the results of an analysis in R you/they can always look at the source code to see exactly what computations are being made. With any proprietary software you have to take their word that it is doing the correct things.
> library(fortunes)
> fortune(102)
Mingzhai Sun: Wh... | Is R output reliable (specially IRT package ltm) [duplicate] | If you, or anyone else, has a question about the results of an analysis in R you/they can always look at the source code to see exactly what computations are being made. With any proprietary software | Is R output reliable (specially IRT package ltm) [duplicate]
If you, or anyone else, has a question about the results of an analysis in R you/they can always look at the source code to see exactly what computations are being made. With any proprietary software you have to take their word that it is doing the correct t... | Is R output reliable (specially IRT package ltm) [duplicate]
If you, or anyone else, has a question about the results of an analysis in R you/they can always look at the source code to see exactly what computations are being made. With any proprietary software |
51,403 | Is R output reliable (specially IRT package ltm) [duplicate] | I might add that in recent IRT work I am undertaking, when all specifications are made the same, I have found IRT results (2PLM) from the ltm package to map on to the same analyses conducted in the Mplus statistical package extremely well, including model solution indices as well as parameter estimates. | Is R output reliable (specially IRT package ltm) [duplicate] | I might add that in recent IRT work I am undertaking, when all specifications are made the same, I have found IRT results (2PLM) from the ltm package to map on to the same analyses conducted in the Mp | Is R output reliable (specially IRT package ltm) [duplicate]
I might add that in recent IRT work I am undertaking, when all specifications are made the same, I have found IRT results (2PLM) from the ltm package to map on to the same analyses conducted in the Mplus statistical package extremely well, including model sol... | Is R output reliable (specially IRT package ltm) [duplicate]
I might add that in recent IRT work I am undertaking, when all specifications are made the same, I have found IRT results (2PLM) from the ltm package to map on to the same analyses conducted in the Mp |
51,404 | How is CLT related to the condition of data (normality assumption)? | CLT states that if sample is big enough, our data approximates normal distribution
That is false.
If you take a very large sample from a non-normally distributed population, the empirical distribution of the sample has high probability of being close to that of the population, which is not normal. It does not in any w... | How is CLT related to the condition of data (normality assumption)? | CLT states that if sample is big enough, our data approximates normal distribution
That is false.
If you take a very large sample from a non-normally distributed population, the empirical distributio | How is CLT related to the condition of data (normality assumption)?
CLT states that if sample is big enough, our data approximates normal distribution
That is false.
If you take a very large sample from a non-normally distributed population, the empirical distribution of the sample has high probability of being close ... | How is CLT related to the condition of data (normality assumption)?
CLT states that if sample is big enough, our data approximates normal distribution
That is false.
If you take a very large sample from a non-normally distributed population, the empirical distributio |
51,405 | How is CLT related to the condition of data (normality assumption)? | do I even need to check it for normality as CLT states that if sample is big enough, our data approximates normal distribution?
It is wrong that, if the sample is big enough the distribution of the data/population approaches a normal distribution.
Instead, the CLT relates to (the limit of) the mean of samples (or oth... | How is CLT related to the condition of data (normality assumption)? | do I even need to check it for normality as CLT states that if sample is big enough, our data approximates normal distribution?
It is wrong that, if the sample is big enough the distribution of the | How is CLT related to the condition of data (normality assumption)?
do I even need to check it for normality as CLT states that if sample is big enough, our data approximates normal distribution?
It is wrong that, if the sample is big enough the distribution of the data/population approaches a normal distribution.
In... | How is CLT related to the condition of data (normality assumption)?
do I even need to check it for normality as CLT states that if sample is big enough, our data approximates normal distribution?
It is wrong that, if the sample is big enough the distribution of the |
51,406 | How is CLT related to the condition of data (normality assumption)? | As Dave mentioned, a very similar question on this topic was asked about a year ago, which is worth looking over. I happen to be one of the respondents, and you can read my answer here.
The following is going to be in rough terms aimed at making things easily understandable. For more details and technicalities, see my ... | How is CLT related to the condition of data (normality assumption)? | As Dave mentioned, a very similar question on this topic was asked about a year ago, which is worth looking over. I happen to be one of the respondents, and you can read my answer here.
The following | How is CLT related to the condition of data (normality assumption)?
As Dave mentioned, a very similar question on this topic was asked about a year ago, which is worth looking over. I happen to be one of the respondents, and you can read my answer here.
The following is going to be in rough terms aimed at making things... | How is CLT related to the condition of data (normality assumption)?
As Dave mentioned, a very similar question on this topic was asked about a year ago, which is worth looking over. I happen to be one of the respondents, and you can read my answer here.
The following |
51,407 | Regression analysis for a massive dataset | The main thing to keep in mind is that with this amount of data, every coefficient will probably come out as statistically significant.
In order to find out which regressors are really important (as contrasted with statistically significant), I recommend using a holdout sample: fit your model to only 4 million data poi... | Regression analysis for a massive dataset | The main thing to keep in mind is that with this amount of data, every coefficient will probably come out as statistically significant.
In order to find out which regressors are really important (as c | Regression analysis for a massive dataset
The main thing to keep in mind is that with this amount of data, every coefficient will probably come out as statistically significant.
In order to find out which regressors are really important (as contrasted with statistically significant), I recommend using a holdout sample:... | Regression analysis for a massive dataset
The main thing to keep in mind is that with this amount of data, every coefficient will probably come out as statistically significant.
In order to find out which regressors are really important (as c |
51,408 | Regression analysis for a massive dataset | You have 6 variables and 5 milion data points. So your data set would take about half a gigabyte of memory ($\frac{5\cdot 10^6\cdot16}{1024^2}\cdot 6$). So it is not that big for computers which now usually have 4GB RAM as a standard. The point I am trying to make is that although your data is big it is not massive and... | Regression analysis for a massive dataset | You have 6 variables and 5 milion data points. So your data set would take about half a gigabyte of memory ($\frac{5\cdot 10^6\cdot16}{1024^2}\cdot 6$). So it is not that big for computers which now u | Regression analysis for a massive dataset
You have 6 variables and 5 milion data points. So your data set would take about half a gigabyte of memory ($\frac{5\cdot 10^6\cdot16}{1024^2}\cdot 6$). So it is not that big for computers which now usually have 4GB RAM as a standard. The point I am trying to make is that altho... | Regression analysis for a massive dataset
You have 6 variables and 5 milion data points. So your data set would take about half a gigabyte of memory ($\frac{5\cdot 10^6\cdot16}{1024^2}\cdot 6$). So it is not that big for computers which now u |
51,409 | t-test where one sample has zero variance? | This answer doesn't address the issue of why the second group has no variation (and I really do suggest you get to the bottom of that).
If you're comfortable saying the yield of group 2 is definitely known to be 4.0 you can use a one-sample t-test to compare group 1 against that value.
Update
I should clarify some thin... | t-test where one sample has zero variance? | This answer doesn't address the issue of why the second group has no variation (and I really do suggest you get to the bottom of that).
If you're comfortable saying the yield of group 2 is definitely | t-test where one sample has zero variance?
This answer doesn't address the issue of why the second group has no variation (and I really do suggest you get to the bottom of that).
If you're comfortable saying the yield of group 2 is definitely known to be 4.0 you can use a one-sample t-test to compare group 1 against th... | t-test where one sample has zero variance?
This answer doesn't address the issue of why the second group has no variation (and I really do suggest you get to the bottom of that).
If you're comfortable saying the yield of group 2 is definitely |
51,410 | t-test where one sample has zero variance? | It requires a bit of explaining how or why this second sample is so "precise" so to speak. Is this rounding error, or are there accidental replications? There is a lot of science going on, not explained, that would inform which option(s) would or would not work. However, it's not a dead-end. Here are 3 suggestions (non... | t-test where one sample has zero variance? | It requires a bit of explaining how or why this second sample is so "precise" so to speak. Is this rounding error, or are there accidental replications? There is a lot of science going on, not explain | t-test where one sample has zero variance?
It requires a bit of explaining how or why this second sample is so "precise" so to speak. Is this rounding error, or are there accidental replications? There is a lot of science going on, not explained, that would inform which option(s) would or would not work. However, it's ... | t-test where one sample has zero variance?
It requires a bit of explaining how or why this second sample is so "precise" so to speak. Is this rounding error, or are there accidental replications? There is a lot of science going on, not explain |
51,411 | t-test where one sample has zero variance? | One solution is to use a one-sample t-test of the null hypothesis:
$$\text{H}_{0}\text{: }\mu_{1} = 4\text{, with H}_{\text{A}}\text{: }\mu_{1} \ne 4$$
If $n_1=26$, $\bar{x}_1=3.865$ and $s_{1} = .24428$, our test statistic for this null would be:
$$t = \frac{\bar{x}_{1}-4}{\frac{s_{1}}{\sqrt{n_{1}}}} = \frac{3.865-4}{... | t-test where one sample has zero variance? | One solution is to use a one-sample t-test of the null hypothesis:
$$\text{H}_{0}\text{: }\mu_{1} = 4\text{, with H}_{\text{A}}\text{: }\mu_{1} \ne 4$$
If $n_1=26$, $\bar{x}_1=3.865$ and $s_{1} = .244 | t-test where one sample has zero variance?
One solution is to use a one-sample t-test of the null hypothesis:
$$\text{H}_{0}\text{: }\mu_{1} = 4\text{, with H}_{\text{A}}\text{: }\mu_{1} \ne 4$$
If $n_1=26$, $\bar{x}_1=3.865$ and $s_{1} = .24428$, our test statistic for this null would be:
$$t = \frac{\bar{x}_{1}-4}{\f... | t-test where one sample has zero variance?
One solution is to use a one-sample t-test of the null hypothesis:
$$\text{H}_{0}\text{: }\mu_{1} = 4\text{, with H}_{\text{A}}\text{: }\mu_{1} \ne 4$$
If $n_1=26$, $\bar{x}_1=3.865$ and $s_{1} = .244 |
51,412 | t-test where one sample has zero variance? | As others have already said, it would be better to address the issue with rounding to get the original data. However, if you have to work with the data you have here's another fairly simple option that may have some advantages over current answers:
Do a t-test under the assumption of equal variance where the variance i... | t-test where one sample has zero variance? | As others have already said, it would be better to address the issue with rounding to get the original data. However, if you have to work with the data you have here's another fairly simple option tha | t-test where one sample has zero variance?
As others have already said, it would be better to address the issue with rounding to get the original data. However, if you have to work with the data you have here's another fairly simple option that may have some advantages over current answers:
Do a t-test under the assump... | t-test where one sample has zero variance?
As others have already said, it would be better to address the issue with rounding to get the original data. However, if you have to work with the data you have here's another fairly simple option tha |
51,413 | How to plot $x^{1700}(1-x)^{300}$? | Stephan's answer about floating point is correct. As a work-around, you could plot the data on a logarithmic scale. Instead of plotting
$$
x ^{1700} (1-x)^{300}
$$
you would plot
$$
1700\log(x) + 300\log(1-x)
$$
Working on a logarithmic scale can be nice when it keeps the data in a reasonable range for floating point a... | How to plot $x^{1700}(1-x)^{300}$? | Stephan's answer about floating point is correct. As a work-around, you could plot the data on a logarithmic scale. Instead of plotting
$$
x ^{1700} (1-x)^{300}
$$
you would plot
$$
1700\log(x) + 300\ | How to plot $x^{1700}(1-x)^{300}$?
Stephan's answer about floating point is correct. As a work-around, you could plot the data on a logarithmic scale. Instead of plotting
$$
x ^{1700} (1-x)^{300}
$$
you would plot
$$
1700\log(x) + 300\log(1-x)
$$
Working on a logarithmic scale can be nice when it keeps the data in a re... | How to plot $x^{1700}(1-x)^{300}$?
Stephan's answer about floating point is correct. As a work-around, you could plot the data on a logarithmic scale. Instead of plotting
$$
x ^{1700} (1-x)^{300}
$$
you would plot
$$
1700\log(x) + 300\ |
51,414 | How to plot $x^{1700}(1-x)^{300}$? | That likelihood function is proportional to a beta density with parameters $\alpha=1701, \beta=301$ so can be plotted as a beta density, as a likelihood function is only defined up to proportionality: What does "likelihood is only defined up to a multiplicative constant of proportionality" mean in practice? resulting ... | How to plot $x^{1700}(1-x)^{300}$? | That likelihood function is proportional to a beta density with parameters $\alpha=1701, \beta=301$ so can be plotted as a beta density, as a likelihood function is only defined up to proportionality: | How to plot $x^{1700}(1-x)^{300}$?
That likelihood function is proportional to a beta density with parameters $\alpha=1701, \beta=301$ so can be plotted as a beta density, as a likelihood function is only defined up to proportionality: What does "likelihood is only defined up to a multiplicative constant of proportiona... | How to plot $x^{1700}(1-x)^{300}$?
That likelihood function is proportional to a beta density with parameters $\alpha=1701, \beta=301$ so can be plotted as a beta density, as a likelihood function is only defined up to proportionality: |
51,415 | How to plot $x^{1700}(1-x)^{300}$? | The $y$ value of your maximum (which indeed is at $x=0.85$) is $\exp(-845.42)\approx 10^{-367.16}$. The smallest double numbers R can work with are about $2\times 10^{-308}$. You are simply running out of number space. If you really want to plot this, use a dedicated package for high precision arithmetic. | How to plot $x^{1700}(1-x)^{300}$? | The $y$ value of your maximum (which indeed is at $x=0.85$) is $\exp(-845.42)\approx 10^{-367.16}$. The smallest double numbers R can work with are about $2\times 10^{-308}$. You are simply running ou | How to plot $x^{1700}(1-x)^{300}$?
The $y$ value of your maximum (which indeed is at $x=0.85$) is $\exp(-845.42)\approx 10^{-367.16}$. The smallest double numbers R can work with are about $2\times 10^{-308}$. You are simply running out of number space. If you really want to plot this, use a dedicated package for high ... | How to plot $x^{1700}(1-x)^{300}$?
The $y$ value of your maximum (which indeed is at $x=0.85$) is $\exp(-845.42)\approx 10^{-367.16}$. The smallest double numbers R can work with are about $2\times 10^{-308}$. You are simply running ou |
51,416 | How to plot $x^{1700}(1-x)^{300}$? | You can plot this curve accurately, on a linear scale.
Let $a=1700$ and $b=300$ be the parameters.
The largest value of $f(x)=x^a(1-x)^b$ for $0\lt x \lt 1$ is attained at $x_m=(a-1)/(a+b-2)$ (the mode of the corresponding Beta$(a,b)$ distribution). There,
$$y_m = \log f(x_m) = a \log(x_m) + b \log(1-x_m)$$
is the log... | How to plot $x^{1700}(1-x)^{300}$? | You can plot this curve accurately, on a linear scale.
Let $a=1700$ and $b=300$ be the parameters.
The largest value of $f(x)=x^a(1-x)^b$ for $0\lt x \lt 1$ is attained at $x_m=(a-1)/(a+b-2)$ (the mod | How to plot $x^{1700}(1-x)^{300}$?
You can plot this curve accurately, on a linear scale.
Let $a=1700$ and $b=300$ be the parameters.
The largest value of $f(x)=x^a(1-x)^b$ for $0\lt x \lt 1$ is attained at $x_m=(a-1)/(a+b-2)$ (the mode of the corresponding Beta$(a,b)$ distribution). There,
$$y_m = \log f(x_m) = a \lo... | How to plot $x^{1700}(1-x)^{300}$?
You can plot this curve accurately, on a linear scale.
Let $a=1700$ and $b=300$ be the parameters.
The largest value of $f(x)=x^a(1-x)^b$ for $0\lt x \lt 1$ is attained at $x_m=(a-1)/(a+b-2)$ (the mod |
51,417 | How to calculate the 4th quartile from median and IQR? | Note: In the following answer I assume that you only know the quantiles you mentioned and you do not know anything else about the distribution, for instance you do not know whether the distribution is symmetric or what its pdf or its (centralized) moments are.
It is not possible to calculate the 4th quartile, if you h... | How to calculate the 4th quartile from median and IQR? | Note: In the following answer I assume that you only know the quantiles you mentioned and you do not know anything else about the distribution, for instance you do not know whether the distribution is | How to calculate the 4th quartile from median and IQR?
Note: In the following answer I assume that you only know the quantiles you mentioned and you do not know anything else about the distribution, for instance you do not know whether the distribution is symmetric or what its pdf or its (centralized) moments are.
It ... | How to calculate the 4th quartile from median and IQR?
Note: In the following answer I assume that you only know the quantiles you mentioned and you do not know anything else about the distribution, for instance you do not know whether the distribution is |
51,418 | How to calculate the 4th quartile from median and IQR? | @Ferdi is correct, but I think that you are asking the wrong question. I think you are confused because "quartile" seems to mean "4 of something". There are, indeed, 4 groups. But that means there are 3 divisions and, at least in what I've read, the term 4th quartile (as a number) is not used at all. If you do calcul... | How to calculate the 4th quartile from median and IQR? | @Ferdi is correct, but I think that you are asking the wrong question. I think you are confused because "quartile" seems to mean "4 of something". There are, indeed, 4 groups. But that means there a | How to calculate the 4th quartile from median and IQR?
@Ferdi is correct, but I think that you are asking the wrong question. I think you are confused because "quartile" seems to mean "4 of something". There are, indeed, 4 groups. But that means there are 3 divisions and, at least in what I've read, the term 4th quar... | How to calculate the 4th quartile from median and IQR?
@Ferdi is correct, but I think that you are asking the wrong question. I think you are confused because "quartile" seems to mean "4 of something". There are, indeed, 4 groups. But that means there a |
51,419 | How to calculate the 4th quartile from median and IQR? | The first quartile has 25% of the data below it, 2nd quartile = median has 50% of data below it, third quartile has 75% data below and 25% above. IQR = 3rd quartile - 1st quartile. A fourth quartile would be the maximum, which you can't get from the median and IQR. IQR and median tell you very little about the shape of... | How to calculate the 4th quartile from median and IQR? | The first quartile has 25% of the data below it, 2nd quartile = median has 50% of data below it, third quartile has 75% data below and 25% above. IQR = 3rd quartile - 1st quartile. A fourth quartile w | How to calculate the 4th quartile from median and IQR?
The first quartile has 25% of the data below it, 2nd quartile = median has 50% of data below it, third quartile has 75% data below and 25% above. IQR = 3rd quartile - 1st quartile. A fourth quartile would be the maximum, which you can't get from the median and IQR.... | How to calculate the 4th quartile from median and IQR?
The first quartile has 25% of the data below it, 2nd quartile = median has 50% of data below it, third quartile has 75% data below and 25% above. IQR = 3rd quartile - 1st quartile. A fourth quartile w |
51,420 | Why does dbeta not sum to 1? | The relevant property of a probability density is not that it sums (for evaluation on some particular $x$ values) to one, but that it integrates to one.
If you evaluate a density $f$ at $x$ values that form a regular grid with grid width $\Delta x$, then you have very approximately
$$ \int_{-\infty}^\infty f(x)\,dx \ap... | Why does dbeta not sum to 1? | The relevant property of a probability density is not that it sums (for evaluation on some particular $x$ values) to one, but that it integrates to one.
If you evaluate a density $f$ at $x$ values tha | Why does dbeta not sum to 1?
The relevant property of a probability density is not that it sums (for evaluation on some particular $x$ values) to one, but that it integrates to one.
If you evaluate a density $f$ at $x$ values that form a regular grid with grid width $\Delta x$, then you have very approximately
$$ \int_... | Why does dbeta not sum to 1?
The relevant property of a probability density is not that it sums (for evaluation on some particular $x$ values) to one, but that it integrates to one.
If you evaluate a density $f$ at $x$ values tha |
51,421 | Why does dbeta not sum to 1? | d* functions represent proportions only with a discrete response. In fact, your dnorm example just happens to sum to one, but
> sum(dnorm(seq(-10, 30, by = 0.01), mean = 10, sd = 2, log = FALSE))
[1] 100
is 100! The normal and beta distributions are continuous, not discrete. Therefore, instead of summing to 1, they mu... | Why does dbeta not sum to 1? | d* functions represent proportions only with a discrete response. In fact, your dnorm example just happens to sum to one, but
> sum(dnorm(seq(-10, 30, by = 0.01), mean = 10, sd = 2, log = FALSE))
[1] | Why does dbeta not sum to 1?
d* functions represent proportions only with a discrete response. In fact, your dnorm example just happens to sum to one, but
> sum(dnorm(seq(-10, 30, by = 0.01), mean = 10, sd = 2, log = FALSE))
[1] 100
is 100! The normal and beta distributions are continuous, not discrete. Therefore, ins... | Why does dbeta not sum to 1?
d* functions represent proportions only with a discrete response. In fact, your dnorm example just happens to sum to one, but
> sum(dnorm(seq(-10, 30, by = 0.01), mean = 10, sd = 2, log = FALSE))
[1] |
51,422 | Why does dbeta not sum to 1? | dpois is the probability mass function (pmf) a discrete Poisson distribution that can take integer values in $(0, \infty)$. If you sum over the probabilities for all integers, you should indeed get 1.
dnorm is the probability density function (pdf) for the normal distribution over the real numbers in $(\infty, \infty)$... | Why does dbeta not sum to 1? | dpois is the probability mass function (pmf) a discrete Poisson distribution that can take integer values in $(0, \infty)$. If you sum over the probabilities for all integers, you should indeed get 1. | Why does dbeta not sum to 1?
dpois is the probability mass function (pmf) a discrete Poisson distribution that can take integer values in $(0, \infty)$. If you sum over the probabilities for all integers, you should indeed get 1.
dnorm is the probability density function (pdf) for the normal distribution over the real ... | Why does dbeta not sum to 1?
dpois is the probability mass function (pmf) a discrete Poisson distribution that can take integer values in $(0, \infty)$. If you sum over the probabilities for all integers, you should indeed get 1. |
51,423 | Examples for Type I and Type II errors | A picture is worth a thousand words. Null hypothesis: patient is not pregnant.
Image via Paul Ellis. | Examples for Type I and Type II errors | A picture is worth a thousand words. Null hypothesis: patient is not pregnant.
Image via Paul Ellis. | Examples for Type I and Type II errors
A picture is worth a thousand words. Null hypothesis: patient is not pregnant.
Image via Paul Ellis. | Examples for Type I and Type II errors
A picture is worth a thousand words. Null hypothesis: patient is not pregnant.
Image via Paul Ellis. |
51,424 | Examples for Type I and Type II errors | Let's say you are testing a new drug for some disease. In a test of its effectiveness, a type I error would be to say it has an effect when it does not; a type II error would be to say it has no effect when it does. | Examples for Type I and Type II errors | Let's say you are testing a new drug for some disease. In a test of its effectiveness, a type I error would be to say it has an effect when it does not; a type II error would be to say it has no effec | Examples for Type I and Type II errors
Let's say you are testing a new drug for some disease. In a test of its effectiveness, a type I error would be to say it has an effect when it does not; a type II error would be to say it has no effect when it does. | Examples for Type I and Type II errors
Let's say you are testing a new drug for some disease. In a test of its effectiveness, a type I error would be to say it has an effect when it does not; a type II error would be to say it has no effec |
51,425 | Examples for Type I and Type II errors | Type I error /false positive: is same as rejecting the null when it is true.
Few Examples:
(With the null hypothesis that the person is innocent), convicting an innocent person
(With the null hypothesis that e-mail is non-spam), non-spam mail is sent to spam box
(With the null hypothesis that there is no metal prese... | Examples for Type I and Type II errors | Type I error /false positive: is same as rejecting the null when it is true.
Few Examples:
(With the null hypothesis that the person is innocent), convicting an innocent person
(With the null hypot | Examples for Type I and Type II errors
Type I error /false positive: is same as rejecting the null when it is true.
Few Examples:
(With the null hypothesis that the person is innocent), convicting an innocent person
(With the null hypothesis that e-mail is non-spam), non-spam mail is sent to spam box
(With the null ... | Examples for Type I and Type II errors
Type I error /false positive: is same as rejecting the null when it is true.
Few Examples:
(With the null hypothesis that the person is innocent), convicting an innocent person
(With the null hypot |
51,426 | Examples for Type I and Type II errors | The boy who cried wolf.
I am not sure who is who in the fable but the basic idea is that the two types of errors (Type I and Type II) are timely ordered in the famous fable.
Type I: villagers (scientists) believe there is a wolf (effect in population), since the boy cried wolf, but in reality there is not any.
Type II:... | Examples for Type I and Type II errors | The boy who cried wolf.
I am not sure who is who in the fable but the basic idea is that the two types of errors (Type I and Type II) are timely ordered in the famous fable.
Type I: villagers (scienti | Examples for Type I and Type II errors
The boy who cried wolf.
I am not sure who is who in the fable but the basic idea is that the two types of errors (Type I and Type II) are timely ordered in the famous fable.
Type I: villagers (scientists) believe there is a wolf (effect in population), since the boy cried wolf, bu... | Examples for Type I and Type II errors
The boy who cried wolf.
I am not sure who is who in the fable but the basic idea is that the two types of errors (Type I and Type II) are timely ordered in the famous fable.
Type I: villagers (scienti |
51,427 | Examples for Type I and Type II errors | Null hypothesis is: "Today is not my friends birthday."
Type I error: My friend does not have birthday today but I will wish her happy birthday.
Type II error: My friend has birthday today but I don't wish her happy birthday. | Examples for Type I and Type II errors | Null hypothesis is: "Today is not my friends birthday."
Type I error: My friend does not have birthday today but I will wish her happy birthday.
Type II error: My friend has birthday today but I don' | Examples for Type I and Type II errors
Null hypothesis is: "Today is not my friends birthday."
Type I error: My friend does not have birthday today but I will wish her happy birthday.
Type II error: My friend has birthday today but I don't wish her happy birthday. | Examples for Type I and Type II errors
Null hypothesis is: "Today is not my friends birthday."
Type I error: My friend does not have birthday today but I will wish her happy birthday.
Type II error: My friend has birthday today but I don' |
51,428 | Suitable graph to visualize the spread of data | There are numerous possible displays, depending on what more specifically you want.
One example would be a boxplot for each group (A, B, ...) (assuming there are enough values in each group to support one*):
boxplot(len~supp,data=ToothGrowth,horizontal=TRUE,boxwex=.7)
But you might want to look at histograms, ecdfs,... | Suitable graph to visualize the spread of data | There are numerous possible displays, depending on what more specifically you want.
One example would be a boxplot for each group (A, B, ...) (assuming there are enough values in each group to suppor | Suitable graph to visualize the spread of data
There are numerous possible displays, depending on what more specifically you want.
One example would be a boxplot for each group (A, B, ...) (assuming there are enough values in each group to support one*):
boxplot(len~supp,data=ToothGrowth,horizontal=TRUE,boxwex=.7)
B... | Suitable graph to visualize the spread of data
There are numerous possible displays, depending on what more specifically you want.
One example would be a boxplot for each group (A, B, ...) (assuming there are enough values in each group to suppor |
51,429 | Suitable graph to visualize the spread of data | You already got some excellent answers but let me suggest another plot that was not mentioned yet (this is an example that I created to answer another question):
In R, it is available e.g. through stripchart() or ggplot2's geom_point() or geom_jitter(). (Jitter adds a little bit of noise to avoid too much overlap.) Th... | Suitable graph to visualize the spread of data | You already got some excellent answers but let me suggest another plot that was not mentioned yet (this is an example that I created to answer another question):
In R, it is available e.g. through st | Suitable graph to visualize the spread of data
You already got some excellent answers but let me suggest another plot that was not mentioned yet (this is an example that I created to answer another question):
In R, it is available e.g. through stripchart() or ggplot2's geom_point() or geom_jitter(). (Jitter adds a lit... | Suitable graph to visualize the spread of data
You already got some excellent answers but let me suggest another plot that was not mentioned yet (this is an example that I created to answer another question):
In R, it is available e.g. through st |
51,430 | Suitable graph to visualize the spread of data | As mentioned by Glen_b, there are a number of possibilities.
Here is an example of a histogram and density plot using the "lattice" package. I've also provided some sample data.
set.seed(1)
mydf <- data.frame(V1 = sample(LETTERS[1:5], 500, replace = TRUE),
V2 = sample(0:50, 500, replace = TRUE))
hea... | Suitable graph to visualize the spread of data | As mentioned by Glen_b, there are a number of possibilities.
Here is an example of a histogram and density plot using the "lattice" package. I've also provided some sample data.
set.seed(1)
mydf <- d | Suitable graph to visualize the spread of data
As mentioned by Glen_b, there are a number of possibilities.
Here is an example of a histogram and density plot using the "lattice" package. I've also provided some sample data.
set.seed(1)
mydf <- data.frame(V1 = sample(LETTERS[1:5], 500, replace = TRUE),
... | Suitable graph to visualize the spread of data
As mentioned by Glen_b, there are a number of possibilities.
Here is an example of a histogram and density plot using the "lattice" package. I've also provided some sample data.
set.seed(1)
mydf <- d |
51,431 | How to decide between PCA and logistic regression? | The key difference between two approches
PCA will NOT consider the response variable but only the variance of the independent variables.
Logistic Regression will consider how each independent variable impact on response variable.
We can make an example that PCA and logistic regression will have completely different... | How to decide between PCA and logistic regression? | The key difference between two approches
PCA will NOT consider the response variable but only the variance of the independent variables.
Logistic Regression will consider how each independent variab | How to decide between PCA and logistic regression?
The key difference between two approches
PCA will NOT consider the response variable but only the variance of the independent variables.
Logistic Regression will consider how each independent variable impact on response variable.
We can make an example that PCA and... | How to decide between PCA and logistic regression?
The key difference between two approches
PCA will NOT consider the response variable but only the variance of the independent variables.
Logistic Regression will consider how each independent variab |
51,432 | How to decide between PCA and logistic regression? | https://en.wikipedia.org/wiki/Principal_component_analysis
Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.
It does... | How to decide between PCA and logistic regression? | https://en.wikipedia.org/wiki/Principal_component_analysis
Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of pos | How to decide between PCA and logistic regression?
https://en.wikipedia.org/wiki/Principal_component_analysis
Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrela... | How to decide between PCA and logistic regression?
https://en.wikipedia.org/wiki/Principal_component_analysis
Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of pos |
51,433 | How to decide between PCA and logistic regression? | PCA is good at streamlining numerous variables and recombining them into three Mega-variables called Principal Components. PCA by doing so is very good at resolving multicollinearity issues within your numerous variables. Your Principal Components will be the equivalent of indexes that are weighting your variable com... | How to decide between PCA and logistic regression? | PCA is good at streamlining numerous variables and recombining them into three Mega-variables called Principal Components. PCA by doing so is very good at resolving multicollinearity issues within yo | How to decide between PCA and logistic regression?
PCA is good at streamlining numerous variables and recombining them into three Mega-variables called Principal Components. PCA by doing so is very good at resolving multicollinearity issues within your numerous variables. Your Principal Components will be the equival... | How to decide between PCA and logistic regression?
PCA is good at streamlining numerous variables and recombining them into three Mega-variables called Principal Components. PCA by doing so is very good at resolving multicollinearity issues within yo |
51,434 | What sort of GLM should I use if my response variable is colony size? | This is a partial answer only, but the graphical content makes a comment a poor alternative. In a comment, the OP talks about using sqrt(log()) as a transformation.
I'd advise against that on the general grounds that it is a very unusual and idiosyncratic transformation, so you will face puzzlement at all levels up to... | What sort of GLM should I use if my response variable is colony size? | This is a partial answer only, but the graphical content makes a comment a poor alternative. In a comment, the OP talks about using sqrt(log()) as a transformation.
I'd advise against that on the gen | What sort of GLM should I use if my response variable is colony size?
This is a partial answer only, but the graphical content makes a comment a poor alternative. In a comment, the OP talks about using sqrt(log()) as a transformation.
I'd advise against that on the general grounds that it is a very unusual and idiosyn... | What sort of GLM should I use if my response variable is colony size?
This is a partial answer only, but the graphical content makes a comment a poor alternative. In a comment, the OP talks about using sqrt(log()) as a transformation.
I'd advise against that on the gen |
51,435 | What sort of GLM should I use if my response variable is colony size? | There's not enough information to offer a definitive answer.
Colony size would be a count, I gather (rather than say an area, or a mass).
It's better not to think of them as representing an error term but rather the conditional distribution of the response.
Some possible models include negative binomial or log series d... | What sort of GLM should I use if my response variable is colony size? | There's not enough information to offer a definitive answer.
Colony size would be a count, I gather (rather than say an area, or a mass).
It's better not to think of them as representing an error term | What sort of GLM should I use if my response variable is colony size?
There's not enough information to offer a definitive answer.
Colony size would be a count, I gather (rather than say an area, or a mass).
It's better not to think of them as representing an error term but rather the conditional distribution of the re... | What sort of GLM should I use if my response variable is colony size?
There's not enough information to offer a definitive answer.
Colony size would be a count, I gather (rather than say an area, or a mass).
It's better not to think of them as representing an error term |
51,436 | What sort of GLM should I use if my response variable is colony size? | About transformation, see :
O’Hara, Robert B., and D. Johan Kotze. 2010. « Do Not Log-Transform Count Data ». Methods in Ecology and Evolution 1 (2): 118‑22. doi:10.1111/j.2041-210X.2010.00021.x.
Summary :
1. Ecological count data (e.g. number of individuals or species) are often log-transformed to satisfy parametric ... | What sort of GLM should I use if my response variable is colony size? | About transformation, see :
O’Hara, Robert B., and D. Johan Kotze. 2010. « Do Not Log-Transform Count Data ». Methods in Ecology and Evolution 1 (2): 118‑22. doi:10.1111/j.2041-210X.2010.00021.x.
Summ | What sort of GLM should I use if my response variable is colony size?
About transformation, see :
O’Hara, Robert B., and D. Johan Kotze. 2010. « Do Not Log-Transform Count Data ». Methods in Ecology and Evolution 1 (2): 118‑22. doi:10.1111/j.2041-210X.2010.00021.x.
Summary :
1. Ecological count data (e.g. number of in... | What sort of GLM should I use if my response variable is colony size?
About transformation, see :
O’Hara, Robert B., and D. Johan Kotze. 2010. « Do Not Log-Transform Count Data ». Methods in Ecology and Evolution 1 (2): 118‑22. doi:10.1111/j.2041-210X.2010.00021.x.
Summ |
51,437 | Inference to the population when the survey response rate is only 30% | If it is "correct" to do logistic regression with these data depends on the type of non-response you have. Usually, one distinguishes three types of mechanisms for non-response.
Missing completely at random: The non-response does not depend neither on the variable of interest nor the covariates.
Missing at random, gi... | Inference to the population when the survey response rate is only 30% | If it is "correct" to do logistic regression with these data depends on the type of non-response you have. Usually, one distinguishes three types of mechanisms for non-response.
Missing completely a | Inference to the population when the survey response rate is only 30%
If it is "correct" to do logistic regression with these data depends on the type of non-response you have. Usually, one distinguishes three types of mechanisms for non-response.
Missing completely at random: The non-response does not depend neither... | Inference to the population when the survey response rate is only 30%
If it is "correct" to do logistic regression with these data depends on the type of non-response you have. Usually, one distinguishes three types of mechanisms for non-response.
Missing completely a |
51,438 | Inference to the population when the survey response rate is only 30% | If at all possible, be very careful about scaling the results of your analysis. Non-response tends to be related to interest. For example, regardless of demographic match, people who fill out a survey about bus service tend to be people who are more interested in taking the bus than the average person. Therefore, estim... | Inference to the population when the survey response rate is only 30% | If at all possible, be very careful about scaling the results of your analysis. Non-response tends to be related to interest. For example, regardless of demographic match, people who fill out a survey | Inference to the population when the survey response rate is only 30%
If at all possible, be very careful about scaling the results of your analysis. Non-response tends to be related to interest. For example, regardless of demographic match, people who fill out a survey about bus service tend to be people who are more ... | Inference to the population when the survey response rate is only 30%
If at all possible, be very careful about scaling the results of your analysis. Non-response tends to be related to interest. For example, regardless of demographic match, people who fill out a survey |
51,439 | Inference to the population when the survey response rate is only 30% | Ignore it (at your risk). (30% is probably an excellent return rate by most standards.)
Resample some of the non-responders (with a slightly different survey, and perhaps some "teasers" to gain interest), and see if they respond differently from the original sample (bearing in mind that you will get an even poorer res... | Inference to the population when the survey response rate is only 30% | Ignore it (at your risk). (30% is probably an excellent return rate by most standards.)
Resample some of the non-responders (with a slightly different survey, and perhaps some "teasers" to gain inter | Inference to the population when the survey response rate is only 30%
Ignore it (at your risk). (30% is probably an excellent return rate by most standards.)
Resample some of the non-responders (with a slightly different survey, and perhaps some "teasers" to gain interest), and see if they respond differently from the... | Inference to the population when the survey response rate is only 30%
Ignore it (at your risk). (30% is probably an excellent return rate by most standards.)
Resample some of the non-responders (with a slightly different survey, and perhaps some "teasers" to gain inter |
51,440 | Inference to the population when the survey response rate is only 30% | Here is a simple element of answer
A simple way to decide whether or not having filled in the form is related to explanatory variables is to perform a logistic regression where the binary response variable is 1 if the person answered and 0 otherwise. If it turns out that having filled in the form is not related to expl... | Inference to the population when the survey response rate is only 30% | Here is a simple element of answer
A simple way to decide whether or not having filled in the form is related to explanatory variables is to perform a logistic regression where the binary response var | Inference to the population when the survey response rate is only 30%
Here is a simple element of answer
A simple way to decide whether or not having filled in the form is related to explanatory variables is to perform a logistic regression where the binary response variable is 1 if the person answered and 0 otherwise.... | Inference to the population when the survey response rate is only 30%
Here is a simple element of answer
A simple way to decide whether or not having filled in the form is related to explanatory variables is to perform a logistic regression where the binary response var |
51,441 | Inference to the population when the survey response rate is only 30% | Hmm, I analyse data like this all the time. I know it's very naughty but I figure it's better than having no analysis.
The best I've ever come up with is to compare your sample with what you know about the population of interest. Are there more people from white backgrounds in the sample? Are there more women in the sa... | Inference to the population when the survey response rate is only 30% | Hmm, I analyse data like this all the time. I know it's very naughty but I figure it's better than having no analysis.
The best I've ever come up with is to compare your sample with what you know abou | Inference to the population when the survey response rate is only 30%
Hmm, I analyse data like this all the time. I know it's very naughty but I figure it's better than having no analysis.
The best I've ever come up with is to compare your sample with what you know about the population of interest. Are there more peopl... | Inference to the population when the survey response rate is only 30%
Hmm, I analyse data like this all the time. I know it's very naughty but I figure it's better than having no analysis.
The best I've ever come up with is to compare your sample with what you know abou |
51,442 | Inference to the population when the survey response rate is only 30% | Dealing with response rates gets less quantitative and more qualitative, as there are no statistical tests to compare the respondents and non-respondents. You can find some guidelines to computing and generally dealing with (low) response rates at http://www.aapor.org/Content/aapor/Resources/PollampSurveyFAQ1/DoRespons... | Inference to the population when the survey response rate is only 30% | Dealing with response rates gets less quantitative and more qualitative, as there are no statistical tests to compare the respondents and non-respondents. You can find some guidelines to computing and | Inference to the population when the survey response rate is only 30%
Dealing with response rates gets less quantitative and more qualitative, as there are no statistical tests to compare the respondents and non-respondents. You can find some guidelines to computing and generally dealing with (low) response rates at ht... | Inference to the population when the survey response rate is only 30%
Dealing with response rates gets less quantitative and more qualitative, as there are no statistical tests to compare the respondents and non-respondents. You can find some guidelines to computing and |
51,443 | When is a statistic not a statistic? | The statistic is defined as
A statistic is a function $T (X^n )$ of the data.
(Larry Wasserman All of Statistics, p. 137)
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose.
(Wikipedia)
Definition 5.2.1 Let $X_1,\dots,X_n$ be a... | When is a statistic not a statistic? | The statistic is defined as
A statistic is a function $T (X^n )$ of the data.
(Larry Wasserman All of Statistics, p. 137)
A statistic (singular) or sample statistic is any quantity computed from va | When is a statistic not a statistic?
The statistic is defined as
A statistic is a function $T (X^n )$ of the data.
(Larry Wasserman All of Statistics, p. 137)
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose.
(Wikipedia)
Defi... | When is a statistic not a statistic?
The statistic is defined as
A statistic is a function $T (X^n )$ of the data.
(Larry Wasserman All of Statistics, p. 137)
A statistic (singular) or sample statistic is any quantity computed from va |
51,444 | When is a statistic not a statistic? | This answer is a theoretical supplement to Tim's more practical answer (+1).
There is an axiomatic and mathematical side of statistics. Random variables are measurable functions on the outcome space $\Omega$ of a probability space $(\Omega, \mathcal{F}, P)$. Data are modelled to be instances of random variables, that i... | When is a statistic not a statistic? | This answer is a theoretical supplement to Tim's more practical answer (+1).
There is an axiomatic and mathematical side of statistics. Random variables are measurable functions on the outcome space $ | When is a statistic not a statistic?
This answer is a theoretical supplement to Tim's more practical answer (+1).
There is an axiomatic and mathematical side of statistics. Random variables are measurable functions on the outcome space $\Omega$ of a probability space $(\Omega, \mathcal{F}, P)$. Data are modelled to be ... | When is a statistic not a statistic?
This answer is a theoretical supplement to Tim's more practical answer (+1).
There is an axiomatic and mathematical side of statistics. Random variables are measurable functions on the outcome space $ |
51,445 | Does rnorm produce numbers with replacement/without replacement? | Both the normal and uniform distributions are continuous; ie, any particular value has probability of zero. Obviously there is numerical precision and other considerations involved with a machine-specific implementation but for all intents and purposes, you can suppose that $\mathbb P(X = x) = 0$ for any particular $x$... | Does rnorm produce numbers with replacement/without replacement? | Both the normal and uniform distributions are continuous; ie, any particular value has probability of zero. Obviously there is numerical precision and other considerations involved with a machine-spec | Does rnorm produce numbers with replacement/without replacement?
Both the normal and uniform distributions are continuous; ie, any particular value has probability of zero. Obviously there is numerical precision and other considerations involved with a machine-specific implementation but for all intents and purposes, y... | Does rnorm produce numbers with replacement/without replacement?
Both the normal and uniform distributions are continuous; ie, any particular value has probability of zero. Obviously there is numerical precision and other considerations involved with a machine-spec |
51,446 | Does rnorm produce numbers with replacement/without replacement? | For "with replacement" and "without replacement" to be distinct, you'd need a finite population. If you have a finite population, you don't have a normal distribution (nor any other continuous distribution).
[Implementation wise, however, there's only a finite number of different values that it's possible to generate o... | Does rnorm produce numbers with replacement/without replacement? | For "with replacement" and "without replacement" to be distinct, you'd need a finite population. If you have a finite population, you don't have a normal distribution (nor any other continuous distrib | Does rnorm produce numbers with replacement/without replacement?
For "with replacement" and "without replacement" to be distinct, you'd need a finite population. If you have a finite population, you don't have a normal distribution (nor any other continuous distribution).
[Implementation wise, however, there's only a f... | Does rnorm produce numbers with replacement/without replacement?
For "with replacement" and "without replacement" to be distinct, you'd need a finite population. If you have a finite population, you don't have a normal distribution (nor any other continuous distrib |
51,447 | Neural network vs regression in a small sample | Neural networks, in vast majority of cases, need lots of data. If you have 20 observations, neural network is clearly a bad choice. With that small sample size, network would easily memorize the data and overfit. Even cross-validation with that small sample size is disputable, because you'd be validating the results on... | Neural network vs regression in a small sample | Neural networks, in vast majority of cases, need lots of data. If you have 20 observations, neural network is clearly a bad choice. With that small sample size, network would easily memorize the data | Neural network vs regression in a small sample
Neural networks, in vast majority of cases, need lots of data. If you have 20 observations, neural network is clearly a bad choice. With that small sample size, network would easily memorize the data and overfit. Even cross-validation with that small sample size is disputa... | Neural network vs regression in a small sample
Neural networks, in vast majority of cases, need lots of data. If you have 20 observations, neural network is clearly a bad choice. With that small sample size, network would easily memorize the data |
51,448 | Neural network vs regression in a small sample | In your first case, you will have 30 * 7 + 1 parameters to explain 30 * 20 data points. With such a complex model you are bound to overfit and memorize your training data to a degree.
With such a small sample size, your validation results can also be unreliable and merely due to chance. I would maybe try leave-one-out ... | Neural network vs regression in a small sample | In your first case, you will have 30 * 7 + 1 parameters to explain 30 * 20 data points. With such a complex model you are bound to overfit and memorize your training data to a degree.
With such a smal | Neural network vs regression in a small sample
In your first case, you will have 30 * 7 + 1 parameters to explain 30 * 20 data points. With such a complex model you are bound to overfit and memorize your training data to a degree.
With such a small sample size, your validation results can also be unreliable and merely ... | Neural network vs regression in a small sample
In your first case, you will have 30 * 7 + 1 parameters to explain 30 * 20 data points. With such a complex model you are bound to overfit and memorize your training data to a degree.
With such a smal |
51,449 | Neural network vs regression in a small sample | The sample size is so low and the variables-to-observations ratio is so high that the modeling framework has to be made even more "modest", beyond linear regression. It is quite likely that some form of regularization will improve the performance of the estimated model out of sample. Try lasso, ridge regression or leas... | Neural network vs regression in a small sample | The sample size is so low and the variables-to-observations ratio is so high that the modeling framework has to be made even more "modest", beyond linear regression. It is quite likely that some form | Neural network vs regression in a small sample
The sample size is so low and the variables-to-observations ratio is so high that the modeling framework has to be made even more "modest", beyond linear regression. It is quite likely that some form of regularization will improve the performance of the estimated model out... | Neural network vs regression in a small sample
The sample size is so low and the variables-to-observations ratio is so high that the modeling framework has to be made even more "modest", beyond linear regression. It is quite likely that some form |
51,450 | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | One way to make your mgf approach to the problem easier is to use the power series
$$(1-t^2)^{-1}=\sum_{j=0}^{\infty} t^{2j}$$
Differentiating the rhs repeatedly is much easier than differentiating the lhs. (note this only applies for $|t|<1$ but as you are differentiating at $t=0$ it still works). You should see that ... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | One way to make your mgf approach to the problem easier is to use the power series
$$(1-t^2)^{-1}=\sum_{j=0}^{\infty} t^{2j}$$
Differentiating the rhs repeatedly is much easier than differentiating th | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
One way to make your mgf approach to the problem easier is to use the power series
$$(1-t^2)^{-1}=\sum_{j=0}^{\infty} t^{2j}$$
Differentiating the rhs repeatedly is much easier than differentiating the lhs. (note this only applies for $|... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
One way to make your mgf approach to the problem easier is to use the power series
$$(1-t^2)^{-1}=\sum_{j=0}^{\infty} t^{2j}$$
Differentiating the rhs repeatedly is much easier than differentiating th |
51,451 | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | Hint: This is an example of a probability density function that is symmetric about zero:
$$f_X(0+x) = f_X(0-x)
\quad \quad \quad \text{for all } x \in \mathbb{R}.$$
Visually, this means that the distribution is reflected around the zero line, and is the same on both sides. See if you can use this property to figure ou... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | Hint: This is an example of a probability density function that is symmetric about zero:
$$f_X(0+x) = f_X(0-x)
\quad \quad \quad \text{for all } x \in \mathbb{R}.$$
Visually, this means that the distr | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
Hint: This is an example of a probability density function that is symmetric about zero:
$$f_X(0+x) = f_X(0-x)
\quad \quad \quad \text{for all } x \in \mathbb{R}.$$
Visually, this means that the distribution is reflected around the zero ... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
Hint: This is an example of a probability density function that is symmetric about zero:
$$f_X(0+x) = f_X(0-x)
\quad \quad \quad \text{for all } x \in \mathbb{R}.$$
Visually, this means that the distr |
51,452 | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | If you don't care to do unnecessary calculation, it is convenient to view your distribution as an equal mixture of an Exponential and its negative:
$$\frac{1}{2} e^{-|x|} = \frac{1}{2} e^{-x}\,\mathcal{I}(x\gt 0) + \frac{1}{2} e^{x}\,\mathcal{I}(x \lt 0).$$
Because $((-1)^n + (1)^n)/2$ is either $-1+1=0$ or $(1+1)/2 = ... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | If you don't care to do unnecessary calculation, it is convenient to view your distribution as an equal mixture of an Exponential and its negative:
$$\frac{1}{2} e^{-|x|} = \frac{1}{2} e^{-x}\,\mathca | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
If you don't care to do unnecessary calculation, it is convenient to view your distribution as an equal mixture of an Exponential and its negative:
$$\frac{1}{2} e^{-|x|} = \frac{1}{2} e^{-x}\,\mathcal{I}(x\gt 0) + \frac{1}{2} e^{x}\,\ma... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
If you don't care to do unnecessary calculation, it is convenient to view your distribution as an equal mixture of an Exponential and its negative:
$$\frac{1}{2} e^{-|x|} = \frac{1}{2} e^{-x}\,\mathca |
51,453 | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | Since the OP seems to be having difficulty with the various hints in the comments and the other answers, here is a heuristic method that yields the right answer in this instance.
\begin{align}
E[\exp(tX)] &= E\left[1 + tX + \frac{(tX)^2}{2!} + \frac{(tX)^3}{3!} + \cdots\right]\\
&= 1 + tE[X] + \frac{t^2}{2!}E[X^2] + \f... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | Since the OP seems to be having difficulty with the various hints in the comments and the other answers, here is a heuristic method that yields the right answer in this instance.
\begin{align}
E[\exp( | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
Since the OP seems to be having difficulty with the various hints in the comments and the other answers, here is a heuristic method that yields the right answer in this instance.
\begin{align}
E[\exp(tX)] &= E\left[1 + tX + \frac{(tX)^2}... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
Since the OP seems to be having difficulty with the various hints in the comments and the other answers, here is a heuristic method that yields the right answer in this instance.
\begin{align}
E[\exp( |
51,454 | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | So I calculated the first, second, third, and fourth derivatives. I got $E(X^1)=0$, $E(X^2)=2$, $E(X^3)=0$, and $E(X^4)=12$. These derivatives are quite long to compute at this point, so I m wondering if there is an easier way to go about this to obtain a formula for the evens.
You could use the Taylor series expansio... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$? | So I calculated the first, second, third, and fourth derivatives. I got $E(X^1)=0$, $E(X^2)=2$, $E(X^3)=0$, and $E(X^4)=12$. These derivatives are quite long to compute at this point, so I m wondering | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
So I calculated the first, second, third, and fourth derivatives. I got $E(X^1)=0$, $E(X^2)=2$, $E(X^3)=0$, and $E(X^4)=12$. These derivatives are quite long to compute at this point, so I m wondering if there is an easier way to go abou... | How do I find all even moments (and odd moments) for $f_X(x)=\frac{1}{2}e^{-|x|}$?
So I calculated the first, second, third, and fourth derivatives. I got $E(X^1)=0$, $E(X^2)=2$, $E(X^3)=0$, and $E(X^4)=12$. These derivatives are quite long to compute at this point, so I m wondering |
51,455 | Why are two random variables independent if the Pearson's correlation coefficient equals zero, but the same result does not hold for covariance? | Zero correlation does not imply independence. Either:
There is a typo/mistake and the book is wrong or
The book made additional assumptions previously, for example, that the joint distribution of A and B were bivariate normal. There exist additional conditions such that zero correlation and these conditions would imp... | Why are two random variables independent if the Pearson's correlation coefficient equals zero, but t | Zero correlation does not imply independence. Either:
There is a typo/mistake and the book is wrong or
The book made additional assumptions previously, for example, that the joint distribution of A a | Why are two random variables independent if the Pearson's correlation coefficient equals zero, but the same result does not hold for covariance?
Zero correlation does not imply independence. Either:
There is a typo/mistake and the book is wrong or
The book made additional assumptions previously, for example, that the ... | Why are two random variables independent if the Pearson's correlation coefficient equals zero, but t
Zero correlation does not imply independence. Either:
There is a typo/mistake and the book is wrong or
The book made additional assumptions previously, for example, that the joint distribution of A a |
51,456 | Why are two random variables independent if the Pearson's correlation coefficient equals zero, but the same result does not hold for covariance? | Your book is wrong. Correlation zero is not a sufficient condition for independence. You can have Pearson correlation zero for variables that are not independent.
The independent variables will have both covariance and correlation zero, provided their variances are non-zero. There's no contradiction here. | Why are two random variables independent if the Pearson's correlation coefficient equals zero, but t | Your book is wrong. Correlation zero is not a sufficient condition for independence. You can have Pearson correlation zero for variables that are not independent.
The independent variables will have | Why are two random variables independent if the Pearson's correlation coefficient equals zero, but the same result does not hold for covariance?
Your book is wrong. Correlation zero is not a sufficient condition for independence. You can have Pearson correlation zero for variables that are not independent.
The indepen... | Why are two random variables independent if the Pearson's correlation coefficient equals zero, but t
Your book is wrong. Correlation zero is not a sufficient condition for independence. You can have Pearson correlation zero for variables that are not independent.
The independent variables will have |
51,457 | If two events are not mutually exclusive, does that mean they're independent? | No. You can have dependent events that are not mutually exclusive.
Consider the events:
$A$: The radio traffic report says that traffic is "heavy".
$B$: I am late for work
$B^c$: I am not late for work
Neither $B$ nor $B^c$ are independent of $A$ (since I am more likely to be late when the radio says traffic is heavy t... | If two events are not mutually exclusive, does that mean they're independent? | No. You can have dependent events that are not mutually exclusive.
Consider the events:
$A$: The radio traffic report says that traffic is "heavy".
$B$: I am late for work
$B^c$: I am not late for wor | If two events are not mutually exclusive, does that mean they're independent?
No. You can have dependent events that are not mutually exclusive.
Consider the events:
$A$: The radio traffic report says that traffic is "heavy".
$B$: I am late for work
$B^c$: I am not late for work
Neither $B$ nor $B^c$ are independent of... | If two events are not mutually exclusive, does that mean they're independent?
No. You can have dependent events that are not mutually exclusive.
Consider the events:
$A$: The radio traffic report says that traffic is "heavy".
$B$: I am late for work
$B^c$: I am not late for wor |
51,458 | If two events are not mutually exclusive, does that mean they're independent? | Suppose for your two events $A$ and $B$, $P(A)\ne 0$ and $P(B)\ne 0$.
Now suppose $A$ and $B$ are mutually exclusive
which means $A\cap B =\varnothing$ then $P(A\cap B)=0 \tag{1}$
If $A$ and $B$ are independent then
$P(A\cap B)=P(A)P(B)\ne0 \tag{2}$
since neither $P(A)$ nor $P(B)$ are $0$.
You can see $(1)$ and $(... | If two events are not mutually exclusive, does that mean they're independent? | Suppose for your two events $A$ and $B$, $P(A)\ne 0$ and $P(B)\ne 0$.
Now suppose $A$ and $B$ are mutually exclusive
which means $A\cap B =\varnothing$ then $P(A\cap B)=0 \tag{1}$
If $A$ and $B$ a | If two events are not mutually exclusive, does that mean they're independent?
Suppose for your two events $A$ and $B$, $P(A)\ne 0$ and $P(B)\ne 0$.
Now suppose $A$ and $B$ are mutually exclusive
which means $A\cap B =\varnothing$ then $P(A\cap B)=0 \tag{1}$
If $A$ and $B$ are independent then
$P(A\cap B)=P(A)P(B)\n... | If two events are not mutually exclusive, does that mean they're independent?
Suppose for your two events $A$ and $B$, $P(A)\ne 0$ and $P(B)\ne 0$.
Now suppose $A$ and $B$ are mutually exclusive
which means $A\cap B =\varnothing$ then $P(A\cap B)=0 \tag{1}$
If $A$ and $B$ a |
51,459 | If two events are not mutually exclusive, does that mean they're independent? | Event that can't occur simultaneously are mutually exclusive. Eg. If you toss a coin you will get head or tail, so event of getting head and event of getting tail are mutually exclusive.
If events are independent outcome of one does not affect other event.Eg. 2 different events of tossing two coins are independent as o... | If two events are not mutually exclusive, does that mean they're independent? | Event that can't occur simultaneously are mutually exclusive. Eg. If you toss a coin you will get head or tail, so event of getting head and event of getting tail are mutually exclusive.
If events are | If two events are not mutually exclusive, does that mean they're independent?
Event that can't occur simultaneously are mutually exclusive. Eg. If you toss a coin you will get head or tail, so event of getting head and event of getting tail are mutually exclusive.
If events are independent outcome of one does not affec... | If two events are not mutually exclusive, does that mean they're independent?
Event that can't occur simultaneously are mutually exclusive. Eg. If you toss a coin you will get head or tail, so event of getting head and event of getting tail are mutually exclusive.
If events are |
51,460 | If two events are not mutually exclusive, does that mean they're independent? | Consider this example:
Rolling the dice only once:
Event A: The result is 1 or 6.
Event B: The result is 1 or 3.
Does Event A and Event B mutually Exclusive? No, two events occur simultaneously if the result is 1.
Does Event A and Event B independent? No, because if event A occurs, it increases the chance that event... | If two events are not mutually exclusive, does that mean they're independent? | Consider this example:
Rolling the dice only once:
Event A: The result is 1 or 6.
Event B: The result is 1 or 3.
Does Event A and Event B mutually Exclusive? No, two events occur simultaneously if | If two events are not mutually exclusive, does that mean they're independent?
Consider this example:
Rolling the dice only once:
Event A: The result is 1 or 6.
Event B: The result is 1 or 3.
Does Event A and Event B mutually Exclusive? No, two events occur simultaneously if the result is 1.
Does Event A and Event B ... | If two events are not mutually exclusive, does that mean they're independent?
Consider this example:
Rolling the dice only once:
Event A: The result is 1 or 6.
Event B: The result is 1 or 3.
Does Event A and Event B mutually Exclusive? No, two events occur simultaneously if |
51,461 | Testing significance of overlap in R | If my comment is right, then you can Monte-carlo simulate it:
sim=unlist(lapply(1:10000,
function(i){A=sample(1:27511,23706);B=sample(1:27511,14557);return(sum(A %in% B))}))
hist(sim)
Probably neater ways to do that loop but whatever.
Your 10752 is waaaay over to the left of my histogram, so significantly fewer commo... | Testing significance of overlap in R | If my comment is right, then you can Monte-carlo simulate it:
sim=unlist(lapply(1:10000,
function(i){A=sample(1:27511,23706);B=sample(1:27511,14557);return(sum(A %in% B))}))
hist(sim)
Probably neate | Testing significance of overlap in R
If my comment is right, then you can Monte-carlo simulate it:
sim=unlist(lapply(1:10000,
function(i){A=sample(1:27511,23706);B=sample(1:27511,14557);return(sum(A %in% B))}))
hist(sim)
Probably neater ways to do that loop but whatever.
Your 10752 is waaaay over to the left of my hi... | Testing significance of overlap in R
If my comment is right, then you can Monte-carlo simulate it:
sim=unlist(lapply(1:10000,
function(i){A=sample(1:27511,23706);B=sample(1:27511,14557);return(sum(A %in% B))}))
hist(sim)
Probably neate |
51,462 | Testing significance of overlap in R | A model for this situation is to put 61000 ($n$) balls into an urn, of which 23000 ($n_1$) are labeled "A". 15000 ($k$) of these are drawn randomly without replacement. Of these, $m$ are found to be labeled "A". What is the chance that $m \ge 10000$?
The total number of possible samples equals the number of $k$-elem... | Testing significance of overlap in R | A model for this situation is to put 61000 ($n$) balls into an urn, of which 23000 ($n_1$) are labeled "A". 15000 ($k$) of these are drawn randomly without replacement. Of these, $m$ are found to be | Testing significance of overlap in R
A model for this situation is to put 61000 ($n$) balls into an urn, of which 23000 ($n_1$) are labeled "A". 15000 ($k$) of these are drawn randomly without replacement. Of these, $m$ are found to be labeled "A". What is the chance that $m \ge 10000$?
The total number of possible ... | Testing significance of overlap in R
A model for this situation is to put 61000 ($n$) balls into an urn, of which 23000 ($n_1$) are labeled "A". 15000 ($k$) of these are drawn randomly without replacement. Of these, $m$ are found to be |
51,463 | Testing significance of overlap in R | You have a large enough sample size that a Chi-square test is reasonable. If you are using R, then chisq.test() is the function to utilize; its help page can be found via ?chisq.test. | Testing significance of overlap in R | You have a large enough sample size that a Chi-square test is reasonable. If you are using R, then chisq.test() is the function to utilize; its help page can be found via ?chisq.test. | Testing significance of overlap in R
You have a large enough sample size that a Chi-square test is reasonable. If you are using R, then chisq.test() is the function to utilize; its help page can be found via ?chisq.test. | Testing significance of overlap in R
You have a large enough sample size that a Chi-square test is reasonable. If you are using R, then chisq.test() is the function to utilize; its help page can be found via ?chisq.test. |
51,464 | Testing significance of overlap in R | Well, if nothing else, you can do it by simulation:
Draw 23000 random elements out of 61000 and draw 15000 random elements from the same 61000. Now count the number of overlapped items.
Repeat 100000 times (should not take all too long): now you have an empirical distribution of the number of overlapped items, and you ... | Testing significance of overlap in R | Well, if nothing else, you can do it by simulation:
Draw 23000 random elements out of 61000 and draw 15000 random elements from the same 61000. Now count the number of overlapped items.
Repeat 100000 | Testing significance of overlap in R
Well, if nothing else, you can do it by simulation:
Draw 23000 random elements out of 61000 and draw 15000 random elements from the same 61000. Now count the number of overlapped items.
Repeat 100000 times (should not take all too long): now you have an empirical distribution of the... | Testing significance of overlap in R
Well, if nothing else, you can do it by simulation:
Draw 23000 random elements out of 61000 and draw 15000 random elements from the same 61000. Now count the number of overlapped items.
Repeat 100000 |
51,465 | Testing significance of overlap in R | The correct approach depends on what is fixed. If the size of the 2 sets are "fixed" then this is just done by a chi-squared test of independence where the 2x2 table is "in /not in" each set. If only the total number of items is fixed, then the chi-squared test is not correct. | Testing significance of overlap in R | The correct approach depends on what is fixed. If the size of the 2 sets are "fixed" then this is just done by a chi-squared test of independence where the 2x2 table is "in /not in" each set. If onl | Testing significance of overlap in R
The correct approach depends on what is fixed. If the size of the 2 sets are "fixed" then this is just done by a chi-squared test of independence where the 2x2 table is "in /not in" each set. If only the total number of items is fixed, then the chi-squared test is not correct. | Testing significance of overlap in R
The correct approach depends on what is fixed. If the size of the 2 sets are "fixed" then this is just done by a chi-squared test of independence where the 2x2 table is "in /not in" each set. If onl |
51,466 | What would be a good way to work with a large data set in Excel? | If you feel you may start more of such very large Excel type projects in the future, then you should consider installing and spending 10 hours learning the basics of R (free), which will let you do what you mention in your question, in a much more efficient manner than Excel.
R for Beginners PDF
You can ask questions a... | What would be a good way to work with a large data set in Excel? | If you feel you may start more of such very large Excel type projects in the future, then you should consider installing and spending 10 hours learning the basics of R (free), which will let you do wh | What would be a good way to work with a large data set in Excel?
If you feel you may start more of such very large Excel type projects in the future, then you should consider installing and spending 10 hours learning the basics of R (free), which will let you do what you mention in your question, in a much more efficie... | What would be a good way to work with a large data set in Excel?
If you feel you may start more of such very large Excel type projects in the future, then you should consider installing and spending 10 hours learning the basics of R (free), which will let you do wh |
51,467 | What would be a good way to work with a large data set in Excel? | Although I would always recommend to use R, you could nevertheless achieve what you want with python.
There is at least a package for reading dbf files.
Furthermore, scipy offers a great range of functions for statistical analysis. For example the library ScientifyPython probably contains the functions you need.
The be... | What would be a good way to work with a large data set in Excel? | Although I would always recommend to use R, you could nevertheless achieve what you want with python.
There is at least a package for reading dbf files.
Furthermore, scipy offers a great range of func | What would be a good way to work with a large data set in Excel?
Although I would always recommend to use R, you could nevertheless achieve what you want with python.
There is at least a package for reading dbf files.
Furthermore, scipy offers a great range of functions for statistical analysis. For example the library... | What would be a good way to work with a large data set in Excel?
Although I would always recommend to use R, you could nevertheless achieve what you want with python.
There is at least a package for reading dbf files.
Furthermore, scipy offers a great range of func |
51,468 | What would be a good way to work with a large data set in Excel? | Excel 2010 and 2013 have a free microsoft addin called power pivot which allows you to work with millions of rows. Its a columnar database that is designed for creating pivot tables, subtotals etc and has standard deviation etc predefined. you might also look at other microsoft addins power query (data input), power v... | What would be a good way to work with a large data set in Excel? | Excel 2010 and 2013 have a free microsoft addin called power pivot which allows you to work with millions of rows. Its a columnar database that is designed for creating pivot tables, subtotals etc an | What would be a good way to work with a large data set in Excel?
Excel 2010 and 2013 have a free microsoft addin called power pivot which allows you to work with millions of rows. Its a columnar database that is designed for creating pivot tables, subtotals etc and has standard deviation etc predefined. you might also... | What would be a good way to work with a large data set in Excel?
Excel 2010 and 2013 have a free microsoft addin called power pivot which allows you to work with millions of rows. Its a columnar database that is designed for creating pivot tables, subtotals etc an |
51,469 | How to compute $\eta^2$ in ANOVA by hand? | It rather depends on what you mean by "by hand".
There is more than one way to do it. You can use the residuals:
> etasq(xyaov)
Partial eta^2
x 0.4854899
Residuals NA
> 1 - var(xyaov$residuals)/var(y)
[1] 0.4854899
(You didn't set a seed, so we don't have exactly the same result).
Almo... | How to compute $\eta^2$ in ANOVA by hand? | It rather depends on what you mean by "by hand".
There is more than one way to do it. You can use the residuals:
> etasq(xyaov)
Partial eta^2
x 0.4854899
Residuals NA
| How to compute $\eta^2$ in ANOVA by hand?
It rather depends on what you mean by "by hand".
There is more than one way to do it. You can use the residuals:
> etasq(xyaov)
Partial eta^2
x 0.4854899
Residuals NA
> 1 - var(xyaov$residuals)/var(y)
[1] 0.4854899
(You didn't set a seed, so we... | How to compute $\eta^2$ in ANOVA by hand?
It rather depends on what you mean by "by hand".
There is more than one way to do it. You can use the residuals:
> etasq(xyaov)
Partial eta^2
x 0.4854899
Residuals NA
|
51,470 | How to compute $\eta^2$ in ANOVA by hand? | eta-squared ($\eta^2$), is a measure of effect size for ANOVA models that is analogous to $R^2$. That is, it gives the proportion of the variability in $Y$ that can be accounted for by knowledge of $X$. There is a 'regular' $\eta^2$, and a partial $\eta^2$. This distinction only comes into play when you have an ANOV... | How to compute $\eta^2$ in ANOVA by hand? | eta-squared ($\eta^2$), is a measure of effect size for ANOVA models that is analogous to $R^2$. That is, it gives the proportion of the variability in $Y$ that can be accounted for by knowledge of $ | How to compute $\eta^2$ in ANOVA by hand?
eta-squared ($\eta^2$), is a measure of effect size for ANOVA models that is analogous to $R^2$. That is, it gives the proportion of the variability in $Y$ that can be accounted for by knowledge of $X$. There is a 'regular' $\eta^2$, and a partial $\eta^2$. This distinction ... | How to compute $\eta^2$ in ANOVA by hand?
eta-squared ($\eta^2$), is a measure of effect size for ANOVA models that is analogous to $R^2$. That is, it gives the proportion of the variability in $Y$ that can be accounted for by knowledge of $ |
51,471 | Alternatives to the Baron-Kenny approach to modeling mediation | Baron and Kenny are indeed outdated, though that does not make them wrong in all cases.
The concerns divide into broadly statistical limitations and assumptions which are discussed in the reference your reviewer suggests and in the literature alluded to by @PeterFlom, and broadly non-statistical concerns about the de... | Alternatives to the Baron-Kenny approach to modeling mediation | Baron and Kenny are indeed outdated, though that does not make them wrong in all cases.
The concerns divide into broadly statistical limitations and assumptions which are discussed in the reference | Alternatives to the Baron-Kenny approach to modeling mediation
Baron and Kenny are indeed outdated, though that does not make them wrong in all cases.
The concerns divide into broadly statistical limitations and assumptions which are discussed in the reference your reviewer suggests and in the literature alluded to b... | Alternatives to the Baron-Kenny approach to modeling mediation
Baron and Kenny are indeed outdated, though that does not make them wrong in all cases.
The concerns divide into broadly statistical limitations and assumptions which are discussed in the reference |
51,472 | Alternatives to the Baron-Kenny approach to modeling mediation | This is more a discussion of concerns I have firstly with the approach of Baron and Kenny (which has some bearing on your question), and with a number of more recent papers (I haven't seen them all, so my comments may not apply to everything). It may also relate to the 2011 paper you mention, which I have only had the ... | Alternatives to the Baron-Kenny approach to modeling mediation | This is more a discussion of concerns I have firstly with the approach of Baron and Kenny (which has some bearing on your question), and with a number of more recent papers (I haven't seen them all, s | Alternatives to the Baron-Kenny approach to modeling mediation
This is more a discussion of concerns I have firstly with the approach of Baron and Kenny (which has some bearing on your question), and with a number of more recent papers (I haven't seen them all, so my comments may not apply to everything). It may also r... | Alternatives to the Baron-Kenny approach to modeling mediation
This is more a discussion of concerns I have firstly with the approach of Baron and Kenny (which has some bearing on your question), and with a number of more recent papers (I haven't seen them all, s |
51,473 | Alternatives to the Baron-Kenny approach to modeling mediation | Here are some places to look. I'd especially recommend the work by Kosuke Imai and colleagues.
Bullock, John G., and Shang E. Ha. 2011. Mediation Analysis is Harder Than it Looks. In Cambridge Handbook of Experimental Political Science, ed. James N. Druckman, Donald P. Green, James H. Kuklinski, and Arthur Lupia. New Y... | Alternatives to the Baron-Kenny approach to modeling mediation | Here are some places to look. I'd especially recommend the work by Kosuke Imai and colleagues.
Bullock, John G., and Shang E. Ha. 2011. Mediation Analysis is Harder Than it Looks. In Cambridge Handboo | Alternatives to the Baron-Kenny approach to modeling mediation
Here are some places to look. I'd especially recommend the work by Kosuke Imai and colleagues.
Bullock, John G., and Shang E. Ha. 2011. Mediation Analysis is Harder Than it Looks. In Cambridge Handbook of Experimental Political Science, ed. James N. Druckma... | Alternatives to the Baron-Kenny approach to modeling mediation
Here are some places to look. I'd especially recommend the work by Kosuke Imai and colleagues.
Bullock, John G., and Shang E. Ha. 2011. Mediation Analysis is Harder Than it Looks. In Cambridge Handboo |
51,474 | Alternatives to the Baron-Kenny approach to modeling mediation | Baron and Kenny is distinctly old fashioned these days. They see mediation as a "yes-no" "present-absent" quality; more recent approaches (lots of work by MacKinnon and others) treats it as a continuum. This makes more sense to me. | Alternatives to the Baron-Kenny approach to modeling mediation | Baron and Kenny is distinctly old fashioned these days. They see mediation as a "yes-no" "present-absent" quality; more recent approaches (lots of work by MacKinnon and others) treats it as a continuu | Alternatives to the Baron-Kenny approach to modeling mediation
Baron and Kenny is distinctly old fashioned these days. They see mediation as a "yes-no" "present-absent" quality; more recent approaches (lots of work by MacKinnon and others) treats it as a continuum. This makes more sense to me. | Alternatives to the Baron-Kenny approach to modeling mediation
Baron and Kenny is distinctly old fashioned these days. They see mediation as a "yes-no" "present-absent" quality; more recent approaches (lots of work by MacKinnon and others) treats it as a continuu |
51,475 | Alternatives to the Baron-Kenny approach to modeling mediation | I agree with the above answer, and I would like to add more information in a form of a succinct summary.
Baron and Kenny's (1986) method of testing mediation has been extensively applied, but there are many papers discussing severe limitations of this approach, which broadly include:
1) Not directly testing the signifi... | Alternatives to the Baron-Kenny approach to modeling mediation | I agree with the above answer, and I would like to add more information in a form of a succinct summary.
Baron and Kenny's (1986) method of testing mediation has been extensively applied, but there ar | Alternatives to the Baron-Kenny approach to modeling mediation
I agree with the above answer, and I would like to add more information in a form of a succinct summary.
Baron and Kenny's (1986) method of testing mediation has been extensively applied, but there are many papers discussing severe limitations of this appro... | Alternatives to the Baron-Kenny approach to modeling mediation
I agree with the above answer, and I would like to add more information in a form of a succinct summary.
Baron and Kenny's (1986) method of testing mediation has been extensively applied, but there ar |
51,476 | Same SE for all coefficients of a linear model | Mathematically, if writing the linear model as $y = X\beta + \epsilon$, where $X = \begin{bmatrix}e & x_1 & x_2 & \cdots & x_p\end{bmatrix}$, $\beta = \begin{bmatrix}\beta_0 & \beta_1 & \beta_2 & \cdots & \beta_p\end{bmatrix}$. The standard error of $\hat{\beta}_j, 1 \leq j \leq p$, denoted by $\hat{\sigma}_{\hat{\beta... | Same SE for all coefficients of a linear model | Mathematically, if writing the linear model as $y = X\beta + \epsilon$, where $X = \begin{bmatrix}e & x_1 & x_2 & \cdots & x_p\end{bmatrix}$, $\beta = \begin{bmatrix}\beta_0 & \beta_1 & \beta_2 & \cdo | Same SE for all coefficients of a linear model
Mathematically, if writing the linear model as $y = X\beta + \epsilon$, where $X = \begin{bmatrix}e & x_1 & x_2 & \cdots & x_p\end{bmatrix}$, $\beta = \begin{bmatrix}\beta_0 & \beta_1 & \beta_2 & \cdots & \beta_p\end{bmatrix}$. The standard error of $\hat{\beta}_j, 1 \leq ... | Same SE for all coefficients of a linear model
Mathematically, if writing the linear model as $y = X\beta + \epsilon$, where $X = \begin{bmatrix}e & x_1 & x_2 & \cdots & x_p\end{bmatrix}$, $\beta = \begin{bmatrix}\beta_0 & \beta_1 & \beta_2 & \cdo |
51,477 | Same SE for all coefficients of a linear model | It doesn't look like there's an issue.
Your standard errors are equal because you presumably have a balanced data set, i.e. two observations for each of the 18 possible combinations of reef and site. | Same SE for all coefficients of a linear model | It doesn't look like there's an issue.
Your standard errors are equal because you presumably have a balanced data set, i.e. two observations for each of the 18 possible combinations of reef and site. | Same SE for all coefficients of a linear model
It doesn't look like there's an issue.
Your standard errors are equal because you presumably have a balanced data set, i.e. two observations for each of the 18 possible combinations of reef and site. | Same SE for all coefficients of a linear model
It doesn't look like there's an issue.
Your standard errors are equal because you presumably have a balanced data set, i.e. two observations for each of the 18 possible combinations of reef and site. |
51,478 | Same SE for all coefficients of a linear model | To accompany Doctor Milt's answer (+1) [and Zhanxiong's answer, also +1, which was written while I was posting mine], here is a simulation showing the same thing happening with random data of the same size and structure as yours. You can play around and see whether the std errors are equal as you change the sample size... | Same SE for all coefficients of a linear model | To accompany Doctor Milt's answer (+1) [and Zhanxiong's answer, also +1, which was written while I was posting mine], here is a simulation showing the same thing happening with random data of the same | Same SE for all coefficients of a linear model
To accompany Doctor Milt's answer (+1) [and Zhanxiong's answer, also +1, which was written while I was posting mine], here is a simulation showing the same thing happening with random data of the same size and structure as yours. You can play around and see whether the std... | Same SE for all coefficients of a linear model
To accompany Doctor Milt's answer (+1) [and Zhanxiong's answer, also +1, which was written while I was posting mine], here is a simulation showing the same thing happening with random data of the same |
51,479 | Same SE for all coefficients of a linear model | The (usual) equation for the variance of a regression parameter (not the intercept) $\hat\beta_j$ is as follows.
$$
\widehat{\text{var}}\left(
\hat\beta_j
\right)
=
\dfrac{
s^2
}{
(n-1)s^2_{X_j}
}\times\dfrac{1}{
1-R^2_j
}
$$
$s^2$ is the residual variance.
$n$ is the sample size
$s^2_{X_j}$ is the variance of the feat... | Same SE for all coefficients of a linear model | The (usual) equation for the variance of a regression parameter (not the intercept) $\hat\beta_j$ is as follows.
$$
\widehat{\text{var}}\left(
\hat\beta_j
\right)
=
\dfrac{
s^2
}{
(n-1)s^2_{X_j}
}\tim | Same SE for all coefficients of a linear model
The (usual) equation for the variance of a regression parameter (not the intercept) $\hat\beta_j$ is as follows.
$$
\widehat{\text{var}}\left(
\hat\beta_j
\right)
=
\dfrac{
s^2
}{
(n-1)s^2_{X_j}
}\times\dfrac{1}{
1-R^2_j
}
$$
$s^2$ is the residual variance.
$n$ is the samp... | Same SE for all coefficients of a linear model
The (usual) equation for the variance of a regression parameter (not the intercept) $\hat\beta_j$ is as follows.
$$
\widehat{\text{var}}\left(
\hat\beta_j
\right)
=
\dfrac{
s^2
}{
(n-1)s^2_{X_j}
}\tim |
51,480 | Why Logistic Regression is not a generative model? | The fundamental difference between Generative Model and Discriminative Model is, one is learning about $ P(X,y) $ while discriminative model is learning $ P(y|X) $
According to this definition, Logistic Regression is not a generative model.
For your example "create a vector x that maximizes $ P(y=i|X=x)$ ", it was not ... | Why Logistic Regression is not a generative model? | The fundamental difference between Generative Model and Discriminative Model is, one is learning about $ P(X,y) $ while discriminative model is learning $ P(y|X) $
According to this definition, Logist | Why Logistic Regression is not a generative model?
The fundamental difference between Generative Model and Discriminative Model is, one is learning about $ P(X,y) $ while discriminative model is learning $ P(y|X) $
According to this definition, Logistic Regression is not a generative model.
For your example "create a v... | Why Logistic Regression is not a generative model?
The fundamental difference between Generative Model and Discriminative Model is, one is learning about $ P(X,y) $ while discriminative model is learning $ P(y|X) $
According to this definition, Logist |
51,481 | Why Logistic Regression is not a generative model? | To elaborate on @Bayesian's (correct) answer, consider a logistic regression model where cases of diabetes ($y$) are predicted by sugar intake ($x$).
The model learns $P(y = 1 | x) = \text{logit}^{-1}(\alpha + \beta x)$ - that is, $P(\text{Diabetes}|\text{Sugar intake})$, but since it doesn't learn the distribution of ... | Why Logistic Regression is not a generative model? | To elaborate on @Bayesian's (correct) answer, consider a logistic regression model where cases of diabetes ($y$) are predicted by sugar intake ($x$).
The model learns $P(y = 1 | x) = \text{logit}^{-1} | Why Logistic Regression is not a generative model?
To elaborate on @Bayesian's (correct) answer, consider a logistic regression model where cases of diabetes ($y$) are predicted by sugar intake ($x$).
The model learns $P(y = 1 | x) = \text{logit}^{-1}(\alpha + \beta x)$ - that is, $P(\text{Diabetes}|\text{Sugar intake}... | Why Logistic Regression is not a generative model?
To elaborate on @Bayesian's (correct) answer, consider a logistic regression model where cases of diabetes ($y$) are predicted by sugar intake ($x$).
The model learns $P(y = 1 | x) = \text{logit}^{-1} |
51,482 | Why is random sampling good? | You seem to be conflating the idea of random sampling with the separate question of whether objects are sampled with or without replacement. The first method you describe is a simple-random-sample with replacement and the second is a simple-random-sample without replacement. In the second case the sample is the whole... | Why is random sampling good? | You seem to be conflating the idea of random sampling with the separate question of whether objects are sampled with or without replacement. The first method you describe is a simple-random-sample wi | Why is random sampling good?
You seem to be conflating the idea of random sampling with the separate question of whether objects are sampled with or without replacement. The first method you describe is a simple-random-sample with replacement and the second is a simple-random-sample without replacement. In the second... | Why is random sampling good?
You seem to be conflating the idea of random sampling with the separate question of whether objects are sampled with or without replacement. The first method you describe is a simple-random-sample wi |
51,483 | Why is random sampling good? | The Central Limit Theorem may be the theory you're looking for. It shows that random sample means follow a Normal distribution (even if the population isn't Normally distributed) and that allows us to use a lot of popular statistics like standard deviations, p-values, etc.
Of course, if your entire population of inter... | Why is random sampling good? | The Central Limit Theorem may be the theory you're looking for. It shows that random sample means follow a Normal distribution (even if the population isn't Normally distributed) and that allows us t | Why is random sampling good?
The Central Limit Theorem may be the theory you're looking for. It shows that random sample means follow a Normal distribution (even if the population isn't Normally distributed) and that allows us to use a lot of popular statistics like standard deviations, p-values, etc.
Of course, if yo... | Why is random sampling good?
The Central Limit Theorem may be the theory you're looking for. It shows that random sample means follow a Normal distribution (even if the population isn't Normally distributed) and that allows us t |
51,484 | Why is random sampling good? | A non-random sample may be good for a particular purpose, or it may be bad. A random sample can be shown with high probability to be "good" for many purposes.
In particular, in statistics, our purpose is to learn general properties of a population. There are some non-random samples we can draw that help us do that very... | Why is random sampling good? | A non-random sample may be good for a particular purpose, or it may be bad. A random sample can be shown with high probability to be "good" for many purposes.
In particular, in statistics, our purpose | Why is random sampling good?
A non-random sample may be good for a particular purpose, or it may be bad. A random sample can be shown with high probability to be "good" for many purposes.
In particular, in statistics, our purpose is to learn general properties of a population. There are some non-random samples we can d... | Why is random sampling good?
A non-random sample may be good for a particular purpose, or it may be bad. A random sample can be shown with high probability to be "good" for many purposes.
In particular, in statistics, our purpose |
51,485 | Using PCA vs Linear Regression | PCA does not involve a dependent variable: All the variables are treated the same. It is primarily dimension reduction method.
Factor analysis also doesn't involve a dependent variable, but its goal is somewhat different: It is to uncover latent factors.
Some people use either the components or the factors (or a subse... | Using PCA vs Linear Regression | PCA does not involve a dependent variable: All the variables are treated the same. It is primarily dimension reduction method.
Factor analysis also doesn't involve a dependent variable, but its goal | Using PCA vs Linear Regression
PCA does not involve a dependent variable: All the variables are treated the same. It is primarily dimension reduction method.
Factor analysis also doesn't involve a dependent variable, but its goal is somewhat different: It is to uncover latent factors.
Some people use either the compon... | Using PCA vs Linear Regression
PCA does not involve a dependent variable: All the variables are treated the same. It is primarily dimension reduction method.
Factor analysis also doesn't involve a dependent variable, but its goal |
51,486 | Using PCA vs Linear Regression | These techniques are not exclusive, and they can be complimentary.
PCA is a dimension reduction technique. The number of dimensions in your dataset corresponds to the number of observations you have per case. For example, imagine your data is survey data, and you administered a 100 item questionnaire. Each individual... | Using PCA vs Linear Regression | These techniques are not exclusive, and they can be complimentary.
PCA is a dimension reduction technique. The number of dimensions in your dataset corresponds to the number of observations you have | Using PCA vs Linear Regression
These techniques are not exclusive, and they can be complimentary.
PCA is a dimension reduction technique. The number of dimensions in your dataset corresponds to the number of observations you have per case. For example, imagine your data is survey data, and you administered a 100 item... | Using PCA vs Linear Regression
These techniques are not exclusive, and they can be complimentary.
PCA is a dimension reduction technique. The number of dimensions in your dataset corresponds to the number of observations you have |
51,487 | Using PCA vs Linear Regression | As other answers have said, PCA and Linear Regression (in general) are different tools.
PCA is an unsupervised method (only takes in data, no dependent variables) and Linear regression (in general) is a supervised learning method. If you have a dependent variable, a supervised method would be suited to your goals.
If ... | Using PCA vs Linear Regression | As other answers have said, PCA and Linear Regression (in general) are different tools.
PCA is an unsupervised method (only takes in data, no dependent variables) and Linear regression (in general) i | Using PCA vs Linear Regression
As other answers have said, PCA and Linear Regression (in general) are different tools.
PCA is an unsupervised method (only takes in data, no dependent variables) and Linear regression (in general) is a supervised learning method. If you have a dependent variable, a supervised method wou... | Using PCA vs Linear Regression
As other answers have said, PCA and Linear Regression (in general) are different tools.
PCA is an unsupervised method (only takes in data, no dependent variables) and Linear regression (in general) i |
51,488 | Using PCA vs Linear Regression | If you are just looking for correlation between variables, you can estimate this simply with the correlation coefficient. It will tell you the strength of the correlation between two variables. | Using PCA vs Linear Regression | If you are just looking for correlation between variables, you can estimate this simply with the correlation coefficient. It will tell you the strength of the correlation between two variables. | Using PCA vs Linear Regression
If you are just looking for correlation between variables, you can estimate this simply with the correlation coefficient. It will tell you the strength of the correlation between two variables. | Using PCA vs Linear Regression
If you are just looking for correlation between variables, you can estimate this simply with the correlation coefficient. It will tell you the strength of the correlation between two variables. |
51,489 | Interquartile range exceeds the median | Note that the IQR can never be negative, but medians certainly can be negative; it's not clear that it usually makes sense to compare the two, since one is a location measure and the other is a measure of spread.
If you had data that was restricted to be always positive (no such restriction is mentioned, though), you c... | Interquartile range exceeds the median | Note that the IQR can never be negative, but medians certainly can be negative; it's not clear that it usually makes sense to compare the two, since one is a location measure and the other is a measur | Interquartile range exceeds the median
Note that the IQR can never be negative, but medians certainly can be negative; it's not clear that it usually makes sense to compare the two, since one is a location measure and the other is a measure of spread.
If you had data that was restricted to be always positive (no such r... | Interquartile range exceeds the median
Note that the IQR can never be negative, but medians certainly can be negative; it's not clear that it usually makes sense to compare the two, since one is a location measure and the other is a measur |
51,490 | Interquartile range exceeds the median | In general, comparing the IQR to the median won't give you any extra insight about the dispersion. For example, consider these distributions:
They have the same IQR; in fact they're identical copies, just shifted along the x axis. But the IQR is greater than the median for distribution 1, and less for distribution 2. ... | Interquartile range exceeds the median | In general, comparing the IQR to the median won't give you any extra insight about the dispersion. For example, consider these distributions:
They have the same IQR; in fact they're identical copies, | Interquartile range exceeds the median
In general, comparing the IQR to the median won't give you any extra insight about the dispersion. For example, consider these distributions:
They have the same IQR; in fact they're identical copies, just shifted along the x axis. But the IQR is greater than the median for distri... | Interquartile range exceeds the median
In general, comparing the IQR to the median won't give you any extra insight about the dispersion. For example, consider these distributions:
They have the same IQR; in fact they're identical copies, |
51,491 | Why does the correlation function in R, cor() return a matrix with fewer rows that you started with? | Correlation is calculated between columns and not between rows.
The output should be read as, correlation between column-i and column j.
Since you have 6 columns, you get a 6x6 correlation matrix. All 8 rows have been considered while calculating these correlations. | Why does the correlation function in R, cor() return a matrix with fewer rows that you started with? | Correlation is calculated between columns and not between rows.
The output should be read as, correlation between column-i and column j.
Since you have 6 columns, you get a 6x6 correlation matrix. All | Why does the correlation function in R, cor() return a matrix with fewer rows that you started with?
Correlation is calculated between columns and not between rows.
The output should be read as, correlation between column-i and column j.
Since you have 6 columns, you get a 6x6 correlation matrix. All 8 rows have been c... | Why does the correlation function in R, cor() return a matrix with fewer rows that you started with?
Correlation is calculated between columns and not between rows.
The output should be read as, correlation between column-i and column j.
Since you have 6 columns, you get a 6x6 correlation matrix. All |
51,492 | Why does the correlation function in R, cor() return a matrix with fewer rows that you started with? | In the $G^TG$ operation, $G^T$ is an $6 \times 8$ matrix, and $G$ an $8 \times 6$. Hence, the matrix multiplication will yield a $6 \times 6$ matrix.
Addressing the comments and the underlying issue, let's pretend that we have a matrix corresponding to returns of different stocks (in the columns) versus 5 consecutive y... | Why does the correlation function in R, cor() return a matrix with fewer rows that you started with? | In the $G^TG$ operation, $G^T$ is an $6 \times 8$ matrix, and $G$ an $8 \times 6$. Hence, the matrix multiplication will yield a $6 \times 6$ matrix.
Addressing the comments and the underlying issue, | Why does the correlation function in R, cor() return a matrix with fewer rows that you started with?
In the $G^TG$ operation, $G^T$ is an $6 \times 8$ matrix, and $G$ an $8 \times 6$. Hence, the matrix multiplication will yield a $6 \times 6$ matrix.
Addressing the comments and the underlying issue, let's pretend that ... | Why does the correlation function in R, cor() return a matrix with fewer rows that you started with?
In the $G^TG$ operation, $G^T$ is an $6 \times 8$ matrix, and $G$ an $8 \times 6$. Hence, the matrix multiplication will yield a $6 \times 6$ matrix.
Addressing the comments and the underlying issue, |
51,493 | Probability that the minimum of a normal random sample will exceed the maximum of another? | Since the datapoints are drawn independently from a continuous distribution, probability of obtaining equal values is $0$ and thus the question is equivalent to "What is the probability that $g_2$ largest values are assigned to group $G_2$".
Assuming $g_1$ and $g_2$ are constants and the random partition into groups is... | Probability that the minimum of a normal random sample will exceed the maximum of another? | Since the datapoints are drawn independently from a continuous distribution, probability of obtaining equal values is $0$ and thus the question is equivalent to "What is the probability that $g_2$ lar | Probability that the minimum of a normal random sample will exceed the maximum of another?
Since the datapoints are drawn independently from a continuous distribution, probability of obtaining equal values is $0$ and thus the question is equivalent to "What is the probability that $g_2$ largest values are assigned to g... | Probability that the minimum of a normal random sample will exceed the maximum of another?
Since the datapoints are drawn independently from a continuous distribution, probability of obtaining equal values is $0$ and thus the question is equivalent to "What is the probability that $g_2$ lar |
51,494 | Probability that the minimum of a normal random sample will exceed the maximum of another? | I would rather comment, but lack the reputation to do so. As such, this is not a complete answer.
It is equivalent to say "What is the probability that the minimum member of $G_2$ is larger than the maximum member of $G_1$?". This sounds like a job for order statistics! In case you are unfamiliar, order statistics are ... | Probability that the minimum of a normal random sample will exceed the maximum of another? | I would rather comment, but lack the reputation to do so. As such, this is not a complete answer.
It is equivalent to say "What is the probability that the minimum member of $G_2$ is larger than the m | Probability that the minimum of a normal random sample will exceed the maximum of another?
I would rather comment, but lack the reputation to do so. As such, this is not a complete answer.
It is equivalent to say "What is the probability that the minimum member of $G_2$ is larger than the maximum member of $G_1$?". Thi... | Probability that the minimum of a normal random sample will exceed the maximum of another?
I would rather comment, but lack the reputation to do so. As such, this is not a complete answer.
It is equivalent to say "What is the probability that the minimum member of $G_2$ is larger than the m |
51,495 | Probability that the minimum of a normal random sample will exceed the maximum of another? | You have two samples $G_1$ and $G_2$ taken from the same population (assuming that you divide your initial sample randomly), this means that as your sample grows you expect each of those two sample to be more and more similar to the initial population. This means that as your sample grows, probability of all value from... | Probability that the minimum of a normal random sample will exceed the maximum of another? | You have two samples $G_1$ and $G_2$ taken from the same population (assuming that you divide your initial sample randomly), this means that as your sample grows you expect each of those two sample to | Probability that the minimum of a normal random sample will exceed the maximum of another?
You have two samples $G_1$ and $G_2$ taken from the same population (assuming that you divide your initial sample randomly), this means that as your sample grows you expect each of those two sample to be more and more similar to ... | Probability that the minimum of a normal random sample will exceed the maximum of another?
You have two samples $G_1$ and $G_2$ taken from the same population (assuming that you divide your initial sample randomly), this means that as your sample grows you expect each of those two sample to |
51,496 | Why does multiple linear regression fail when the number of variables are larger than the number of samples? | I will provide a visual in a very simple case because it is the easiest case to visualize. Imagine you are trying to fit the following linear model: $Y\sim \alpha + X\beta + \epsilon$. In this situation you have two parameters, $\alpha$ and $\beta$, and imagine you only have a sample size of $n=1$.
Your single piece of... | Why does multiple linear regression fail when the number of variables are larger than the number of | I will provide a visual in a very simple case because it is the easiest case to visualize. Imagine you are trying to fit the following linear model: $Y\sim \alpha + X\beta + \epsilon$. In this situati | Why does multiple linear regression fail when the number of variables are larger than the number of samples?
I will provide a visual in a very simple case because it is the easiest case to visualize. Imagine you are trying to fit the following linear model: $Y\sim \alpha + X\beta + \epsilon$. In this situation you have... | Why does multiple linear regression fail when the number of variables are larger than the number of
I will provide a visual in a very simple case because it is the easiest case to visualize. Imagine you are trying to fit the following linear model: $Y\sim \alpha + X\beta + \epsilon$. In this situati |
51,497 | Why does multiple linear regression fail when the number of variables are larger than the number of samples? | I believe what Nick was saying in his comment is: your MLR with N variables is trying to fix N values (coefficients) in N-dimensional space, but you are trying to do it with M (M < N) pieces of data. How will you do this?
Since you only have M data points, the other M-N dimensions of your answer are free-floating, as h... | Why does multiple linear regression fail when the number of variables are larger than the number of | I believe what Nick was saying in his comment is: your MLR with N variables is trying to fix N values (coefficients) in N-dimensional space, but you are trying to do it with M (M < N) pieces of data. | Why does multiple linear regression fail when the number of variables are larger than the number of samples?
I believe what Nick was saying in his comment is: your MLR with N variables is trying to fix N values (coefficients) in N-dimensional space, but you are trying to do it with M (M < N) pieces of data. How will yo... | Why does multiple linear regression fail when the number of variables are larger than the number of
I believe what Nick was saying in his comment is: your MLR with N variables is trying to fix N values (coefficients) in N-dimensional space, but you are trying to do it with M (M < N) pieces of data. |
51,498 | Why does multiple linear regression fail when the number of variables are larger than the number of samples? | Analyst's answer is in fact correct. If p>n you end up with an underdetermined system and can use pseudo-inverse to solve it.
When you have more parameters than equations as in this case, using
pseudo-inverse
finds the minimum euclidian norm solution.
This is the best assumption you can do since this solution has the ... | Why does multiple linear regression fail when the number of variables are larger than the number of | Analyst's answer is in fact correct. If p>n you end up with an underdetermined system and can use pseudo-inverse to solve it.
When you have more parameters than equations as in this case, using
pseud | Why does multiple linear regression fail when the number of variables are larger than the number of samples?
Analyst's answer is in fact correct. If p>n you end up with an underdetermined system and can use pseudo-inverse to solve it.
When you have more parameters than equations as in this case, using
pseudo-inverse
f... | Why does multiple linear regression fail when the number of variables are larger than the number of
Analyst's answer is in fact correct. If p>n you end up with an underdetermined system and can use pseudo-inverse to solve it.
When you have more parameters than equations as in this case, using
pseud |
51,499 | Why does multiple linear regression fail when the number of variables are larger than the number of samples? | If P, number of variables, is larger than N number of observations then you have underdetermined system of equations.
There exist pseudo-inverse which can solve this:
http://people.csail.mit.edu/bkph/articles/Pseudo_Inverse.pdf | Why does multiple linear regression fail when the number of variables are larger than the number of | If P, number of variables, is larger than N number of observations then you have underdetermined system of equations.
There exist pseudo-inverse which can solve this:
http://people.csail.mit.edu/bkp | Why does multiple linear regression fail when the number of variables are larger than the number of samples?
If P, number of variables, is larger than N number of observations then you have underdetermined system of equations.
There exist pseudo-inverse which can solve this:
http://people.csail.mit.edu/bkph/articles/... | Why does multiple linear regression fail when the number of variables are larger than the number of
If P, number of variables, is larger than N number of observations then you have underdetermined system of equations.
There exist pseudo-inverse which can solve this:
http://people.csail.mit.edu/bkp |
51,500 | Why does multiple linear regression fail when the number of variables are larger than the number of samples? | Let's take an example:
Case A (n = 1, p = 1):
RSS = $(y-α-Xβ)^2$
Since RSS is a squared number, the minimum possible value it can have is zero.
$(y-α-Xβ)^2$ = 0
$(y-α-Xβ)$ = 0
$y=α+Xβ$
Say x=1, y=4 then:
$4=α+β$
Now as n=1 only, for this RSS equation we can have infinite solutions.
Case B (n = 2, p = 1):
RSS = $(y-α-Xβ... | Why does multiple linear regression fail when the number of variables are larger than the number of | Let's take an example:
Case A (n = 1, p = 1):
RSS = $(y-α-Xβ)^2$
Since RSS is a squared number, the minimum possible value it can have is zero.
$(y-α-Xβ)^2$ = 0
$(y-α-Xβ)$ = 0
$y=α+Xβ$
Say x=1, y=4 th | Why does multiple linear regression fail when the number of variables are larger than the number of samples?
Let's take an example:
Case A (n = 1, p = 1):
RSS = $(y-α-Xβ)^2$
Since RSS is a squared number, the minimum possible value it can have is zero.
$(y-α-Xβ)^2$ = 0
$(y-α-Xβ)$ = 0
$y=α+Xβ$
Say x=1, y=4 then:
$4=α+β$... | Why does multiple linear regression fail when the number of variables are larger than the number of
Let's take an example:
Case A (n = 1, p = 1):
RSS = $(y-α-Xβ)^2$
Since RSS is a squared number, the minimum possible value it can have is zero.
$(y-α-Xβ)^2$ = 0
$(y-α-Xβ)$ = 0
$y=α+Xβ$
Say x=1, y=4 th |
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