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 |
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51,801 | Fallacy in p-value definition | This is a helpful link.
More formally, if you observed a p-value that was less than 5%, you could say: "The probability of the available (or of even less likely) data, given that the null hypothesis is true, is less than 5%. | Fallacy in p-value definition | This is a helpful link.
More formally, if you observed a p-value that was less than 5%, you could say: "The probability of the available (or of even less likely) data, given that the null hypothesis i | Fallacy in p-value definition
This is a helpful link.
More formally, if you observed a p-value that was less than 5%, you could say: "The probability of the available (or of even less likely) data, given that the null hypothesis is true, is less than 5%. | Fallacy in p-value definition
This is a helpful link.
More formally, if you observed a p-value that was less than 5%, you could say: "The probability of the available (or of even less likely) data, given that the null hypothesis i |
51,802 | Data visualization of average and standard deviation over a small time series | Why not a line plot? A line plot seems pretty fitting if you'd like to show general trends in mean and SD provided individual specie is not the focal point.
Anyway, here is an alternative, which strictly speaking is still a line plot but time is not one of the axes. It is also good for discussing individual species. x... | Data visualization of average and standard deviation over a small time series | Why not a line plot? A line plot seems pretty fitting if you'd like to show general trends in mean and SD provided individual specie is not the focal point.
Anyway, here is an alternative, which stri | Data visualization of average and standard deviation over a small time series
Why not a line plot? A line plot seems pretty fitting if you'd like to show general trends in mean and SD provided individual specie is not the focal point.
Anyway, here is an alternative, which strictly speaking is still a line plot but tim... | Data visualization of average and standard deviation over a small time series
Why not a line plot? A line plot seems pretty fitting if you'd like to show general trends in mean and SD provided individual specie is not the focal point.
Anyway, here is an alternative, which stri |
51,803 | Data visualization of average and standard deviation over a small time series | You mean you don't want a line plot like this? :)
Time is a natural for the X axis and line plots. Here's a better view using a small multiples approach.
Sometimes it helps to order the panels by something analytical. Here's an example ordered by average std:
With so many category levels (20), another technique is ... | Data visualization of average and standard deviation over a small time series | You mean you don't want a line plot like this? :)
Time is a natural for the X axis and line plots. Here's a better view using a small multiples approach.
Sometimes it helps to order the panels by s | Data visualization of average and standard deviation over a small time series
You mean you don't want a line plot like this? :)
Time is a natural for the X axis and line plots. Here's a better view using a small multiples approach.
Sometimes it helps to order the panels by something analytical. Here's an example ord... | Data visualization of average and standard deviation over a small time series
You mean you don't want a line plot like this? :)
Time is a natural for the X axis and line plots. Here's a better view using a small multiples approach.
Sometimes it helps to order the panels by s |
51,804 | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? Weak? | If you were to blindly apply Cohen's criteria for describing the strength of a correlation, an r = .59 would be described as a "large" effect to have been observed.
However, you should note that this "large" effect might not actually be statistically significant or even that meaningful. For the former argument, if y... | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? | If you were to blindly apply Cohen's criteria for describing the strength of a correlation, an r = .59 would be described as a "large" effect to have been observed.
However, you should note that thi | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? Weak?
If you were to blindly apply Cohen's criteria for describing the strength of a correlation, an r = .59 would be described as a "large" effect to have been observed.
However, you should note that this "large" effe... | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong?
If you were to blindly apply Cohen's criteria for describing the strength of a correlation, an r = .59 would be described as a "large" effect to have been observed.
However, you should note that thi |
51,805 | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? Weak? | What is considered strong and weak tends to differ considerably between disciplines, and for good reasons. It helps to have a correlation in mind from your field that is considered very strong. In my case that would be the correlation of the years of education of spouses (about .60). This gives a bit more substance to ... | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? | What is considered strong and weak tends to differ considerably between disciplines, and for good reasons. It helps to have a correlation in mind from your field that is considered very strong. In my | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? Weak?
What is considered strong and weak tends to differ considerably between disciplines, and for good reasons. It helps to have a correlation in mind from your field that is considered very strong. In my case that woul... | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong?
What is considered strong and weak tends to differ considerably between disciplines, and for good reasons. It helps to have a correlation in mind from your field that is considered very strong. In my |
51,806 | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? Weak? | Without actually seeing the plot, a 'pro' statistician wouldn't bother interpreting it as a 'strong' or 'weak' correlation because, as you word it, it seems you are implying causality. Remember that dependence sometimes implies (linear, in the case you are referring to the $r^2$ given by a linear fit) correlation, but ... | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? | Without actually seeing the plot, a 'pro' statistician wouldn't bother interpreting it as a 'strong' or 'weak' correlation because, as you word it, it seems you are implying causality. Remember that d | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong? Weak?
Without actually seeing the plot, a 'pro' statistician wouldn't bother interpreting it as a 'strong' or 'weak' correlation because, as you word it, it seems you are implying causality. Remember that dependence some... | $r^2 = 35\%$, $r = 0.59$ How does a (pro) statistician formally interpret this correlation? Strong?
Without actually seeing the plot, a 'pro' statistician wouldn't bother interpreting it as a 'strong' or 'weak' correlation because, as you word it, it seems you are implying causality. Remember that d |
51,807 | Can the coefficient of determination (R-squared) for a linear regression ever be zero? | Yes, when ever there is no linear relationship between variables. For example, when either X or Y are constant, or where each high-low data points are balanced by high-high, or low-low data points. For example, $X=(1,1,2,2)$, $Y=(1,2,1,2)$, or $X=(-2,1,0,1,2)$, $Y=X^2$
Here are some examples: all of these have correlat... | Can the coefficient of determination (R-squared) for a linear regression ever be zero? | Yes, when ever there is no linear relationship between variables. For example, when either X or Y are constant, or where each high-low data points are balanced by high-high, or low-low data points. Fo | Can the coefficient of determination (R-squared) for a linear regression ever be zero?
Yes, when ever there is no linear relationship between variables. For example, when either X or Y are constant, or where each high-low data points are balanced by high-high, or low-low data points. For example, $X=(1,1,2,2)$, $Y=(1,2... | Can the coefficient of determination (R-squared) for a linear regression ever be zero?
Yes, when ever there is no linear relationship between variables. For example, when either X or Y are constant, or where each high-low data points are balanced by high-high, or low-low data points. Fo |
51,808 | Can the coefficient of determination (R-squared) for a linear regression ever be zero? | The null hypothesis is always false, basically. That's why people shouldn't just report p values (to make up a stupid example, in the UK highly significant correlation between house number and income: sample size of 20 million, r=0.004, p<.0001). | Can the coefficient of determination (R-squared) for a linear regression ever be zero? | The null hypothesis is always false, basically. That's why people shouldn't just report p values (to make up a stupid example, in the UK highly significant correlation between house number and income: | Can the coefficient of determination (R-squared) for a linear regression ever be zero?
The null hypothesis is always false, basically. That's why people shouldn't just report p values (to make up a stupid example, in the UK highly significant correlation between house number and income: sample size of 20 million, r=0.0... | Can the coefficient of determination (R-squared) for a linear regression ever be zero?
The null hypothesis is always false, basically. That's why people shouldn't just report p values (to make up a stupid example, in the UK highly significant correlation between house number and income: |
51,809 | Residuals correlated positively with response variable strongly in linear regression | 1) Residuals do correlate positively with observed values in many, many cases. Think of it this way - a very large positive error ("error" is the "true residual", to misuse the language) means that the corresponding observation is, all other things equal, likely to be very large in a positive direction. A very large ... | Residuals correlated positively with response variable strongly in linear regression | 1) Residuals do correlate positively with observed values in many, many cases. Think of it this way - a very large positive error ("error" is the "true residual", to misuse the language) means that t | Residuals correlated positively with response variable strongly in linear regression
1) Residuals do correlate positively with observed values in many, many cases. Think of it this way - a very large positive error ("error" is the "true residual", to misuse the language) means that the corresponding observation is, al... | Residuals correlated positively with response variable strongly in linear regression
1) Residuals do correlate positively with observed values in many, many cases. Think of it this way - a very large positive error ("error" is the "true residual", to misuse the language) means that t |
51,810 | Residuals correlated positively with response variable strongly in linear regression | residuals almost always correlate with your observations as long es your regressors do not fully explain the true underlying data model. So the presence of high correlation between $y$ and residuals is evidence for the presence of noise/variation that is not captured by your explanatory variables.
This could have sever... | Residuals correlated positively with response variable strongly in linear regression | residuals almost always correlate with your observations as long es your regressors do not fully explain the true underlying data model. So the presence of high correlation between $y$ and residuals i | Residuals correlated positively with response variable strongly in linear regression
residuals almost always correlate with your observations as long es your regressors do not fully explain the true underlying data model. So the presence of high correlation between $y$ and residuals is evidence for the presence of nois... | Residuals correlated positively with response variable strongly in linear regression
residuals almost always correlate with your observations as long es your regressors do not fully explain the true underlying data model. So the presence of high correlation between $y$ and residuals i |
51,811 | Is there a limit to the SPSS random number generator? | I think SPSS, like most modern software, uses the Mersenne Twister. Its period is $2^{19937} − 1$ so you’re pretty safe from this point of view.
Up to 623 successive outcomes are uncorrelated, so you can safely consider a few consecutive outcomes as independent (this would not be the case with a classical Linear congru... | Is there a limit to the SPSS random number generator? | I think SPSS, like most modern software, uses the Mersenne Twister. Its period is $2^{19937} − 1$ so you’re pretty safe from this point of view.
Up to 623 successive outcomes are uncorrelated, so you | Is there a limit to the SPSS random number generator?
I think SPSS, like most modern software, uses the Mersenne Twister. Its period is $2^{19937} − 1$ so you’re pretty safe from this point of view.
Up to 623 successive outcomes are uncorrelated, so you can safely consider a few consecutive outcomes as independent (thi... | Is there a limit to the SPSS random number generator?
I think SPSS, like most modern software, uses the Mersenne Twister. Its period is $2^{19937} − 1$ so you’re pretty safe from this point of view.
Up to 623 successive outcomes are uncorrelated, so you |
51,812 | Is there a limit to the SPSS random number generator? | SPSS Statistics provides both the Mersenne Twister and, for compatibility, an older shift-congruential generator. By default, the older generator is used. Use SET RNG=MT or the Transform>Random Number Generators menu item to change this. The MT should give you all the numbers you need.
There is also a user-contribut... | Is there a limit to the SPSS random number generator? | SPSS Statistics provides both the Mersenne Twister and, for compatibility, an older shift-congruential generator. By default, the older generator is used. Use SET RNG=MT or the Transform>Random Numb | Is there a limit to the SPSS random number generator?
SPSS Statistics provides both the Mersenne Twister and, for compatibility, an older shift-congruential generator. By default, the older generator is used. Use SET RNG=MT or the Transform>Random Number Generators menu item to change this. The MT should give you al... | Is there a limit to the SPSS random number generator?
SPSS Statistics provides both the Mersenne Twister and, for compatibility, an older shift-congruential generator. By default, the older generator is used. Use SET RNG=MT or the Transform>Random Numb |
51,813 | Is there a limit to the SPSS random number generator? | I used the SPSS uniform function to create a random sample weekly for two years. Do not do this. They DO NOT generate random samples. The same dataset will generate the same random sample upon re-opening SPSS. Not all cases have the same probability to be selected (depends on sorting of your file).
My recommendation wo... | Is there a limit to the SPSS random number generator? | I used the SPSS uniform function to create a random sample weekly for two years. Do not do this. They DO NOT generate random samples. The same dataset will generate the same random sample upon re-open | Is there a limit to the SPSS random number generator?
I used the SPSS uniform function to create a random sample weekly for two years. Do not do this. They DO NOT generate random samples. The same dataset will generate the same random sample upon re-opening SPSS. Not all cases have the same probability to be selected (... | Is there a limit to the SPSS random number generator?
I used the SPSS uniform function to create a random sample weekly for two years. Do not do this. They DO NOT generate random samples. The same dataset will generate the same random sample upon re-open |
51,814 | How can I test the quality of a RNG? | J.M. already mentioned the original Diehard battery of tests by George Marsaglia. As far as I know, this test set is no longer being maintained.
Robert Brown has been working for years on DieHarder which is
a GPL'ed reimplementation of the DieHard suite
plus additional tests from the NIST suite
plus development of ne... | How can I test the quality of a RNG? | J.M. already mentioned the original Diehard battery of tests by George Marsaglia. As far as I know, this test set is no longer being maintained.
Robert Brown has been working for years on DieHarder w | How can I test the quality of a RNG?
J.M. already mentioned the original Diehard battery of tests by George Marsaglia. As far as I know, this test set is no longer being maintained.
Robert Brown has been working for years on DieHarder which is
a GPL'ed reimplementation of the DieHard suite
plus additional tests from ... | How can I test the quality of a RNG?
J.M. already mentioned the original Diehard battery of tests by George Marsaglia. As far as I know, this test set is no longer being maintained.
Robert Brown has been working for years on DieHarder w |
51,815 | How can I test the quality of a RNG? | You're right: testing is empirical. It's all done in a standard hypothesis testing framework. Different tests are applied to assess different alternative behaviors of RNGs. As always, the user is free to choose the level of confidence with which each test is conducted. This level determines the critical region of e... | How can I test the quality of a RNG? | You're right: testing is empirical. It's all done in a standard hypothesis testing framework. Different tests are applied to assess different alternative behaviors of RNGs. As always, the user is f | How can I test the quality of a RNG?
You're right: testing is empirical. It's all done in a standard hypothesis testing framework. Different tests are applied to assess different alternative behaviors of RNGs. As always, the user is free to choose the level of confidence with which each test is conducted. This leve... | How can I test the quality of a RNG?
You're right: testing is empirical. It's all done in a standard hypothesis testing framework. Different tests are applied to assess different alternative behaviors of RNGs. As always, the user is f |
51,816 | Cross tabulation of two categorical variables: recommended techniques | I think you need to rework this question. It all depends on the problem/data which has generated the cross-tab. | Cross tabulation of two categorical variables: recommended techniques | I think you need to rework this question. It all depends on the problem/data which has generated the cross-tab. | Cross tabulation of two categorical variables: recommended techniques
I think you need to rework this question. It all depends on the problem/data which has generated the cross-tab. | Cross tabulation of two categorical variables: recommended techniques
I think you need to rework this question. It all depends on the problem/data which has generated the cross-tab. |
51,817 | Cross tabulation of two categorical variables: recommended techniques | Arguably, the question is not very precise. Rather than enumerating all measures of association for $2\times 2$ tables, I shall concentrate on the way such measures may be constructed and how to select the one that is most appropriate with respect to hypothesis or constraints relevant to a cross-classification.
The ver... | Cross tabulation of two categorical variables: recommended techniques | Arguably, the question is not very precise. Rather than enumerating all measures of association for $2\times 2$ tables, I shall concentrate on the way such measures may be constructed and how to selec | Cross tabulation of two categorical variables: recommended techniques
Arguably, the question is not very precise. Rather than enumerating all measures of association for $2\times 2$ tables, I shall concentrate on the way such measures may be constructed and how to select the one that is most appropriate with respect to... | Cross tabulation of two categorical variables: recommended techniques
Arguably, the question is not very precise. Rather than enumerating all measures of association for $2\times 2$ tables, I shall concentrate on the way such measures may be constructed and how to selec |
51,818 | Cross tabulation of two categorical variables: recommended techniques | I would use Fisher's Exact Test, even for large N. I wouldn't know why not. Any performance argument predates today's fast computers. | Cross tabulation of two categorical variables: recommended techniques | I would use Fisher's Exact Test, even for large N. I wouldn't know why not. Any performance argument predates today's fast computers. | Cross tabulation of two categorical variables: recommended techniques
I would use Fisher's Exact Test, even for large N. I wouldn't know why not. Any performance argument predates today's fast computers. | Cross tabulation of two categorical variables: recommended techniques
I would use Fisher's Exact Test, even for large N. I wouldn't know why not. Any performance argument predates today's fast computers. |
51,819 | Cross tabulation of two categorical variables: recommended techniques | I must agree.. there is no single best analysis!
not just in cross tabulations or analysis of categorical data but in any data analysis... and thank god for that!
if there was just a single best way to address these analyses well many of us would not have a job to start with... not to mention the loss of the thrill of ... | Cross tabulation of two categorical variables: recommended techniques | I must agree.. there is no single best analysis!
not just in cross tabulations or analysis of categorical data but in any data analysis... and thank god for that!
if there was just a single best way t | Cross tabulation of two categorical variables: recommended techniques
I must agree.. there is no single best analysis!
not just in cross tabulations or analysis of categorical data but in any data analysis... and thank god for that!
if there was just a single best way to address these analyses well many of us would not... | Cross tabulation of two categorical variables: recommended techniques
I must agree.. there is no single best analysis!
not just in cross tabulations or analysis of categorical data but in any data analysis... and thank god for that!
if there was just a single best way t |
51,820 | Where can I find useful R tutorials with various implementations? [duplicate] | Quick R site is basic, but quite nice for start http://www.statmethods.net/index.html . | Where can I find useful R tutorials with various implementations? [duplicate] | Quick R site is basic, but quite nice for start http://www.statmethods.net/index.html . | Where can I find useful R tutorials with various implementations? [duplicate]
Quick R site is basic, but quite nice for start http://www.statmethods.net/index.html . | Where can I find useful R tutorials with various implementations? [duplicate]
Quick R site is basic, but quite nice for start http://www.statmethods.net/index.html . |
51,821 | Where can I find useful R tutorials with various implementations? [duplicate] | R bloggers has been steadily supplying me with a lot of good pragmatic content.
From the author:
R-Bloggers.com is a central hub (e.g: A blog aggregator) of content
collected from bloggers who write about R (in English).
The site will help R bloggers and users to connect and follow
the “R blogosphere”. | Where can I find useful R tutorials with various implementations? [duplicate] | R bloggers has been steadily supplying me with a lot of good pragmatic content.
From the author:
R-Bloggers.com is a central hub (e.g: A blog aggregator) of content
collected from bloggers who write | Where can I find useful R tutorials with various implementations? [duplicate]
R bloggers has been steadily supplying me with a lot of good pragmatic content.
From the author:
R-Bloggers.com is a central hub (e.g: A blog aggregator) of content
collected from bloggers who write about R (in English).
The site will help ... | Where can I find useful R tutorials with various implementations? [duplicate]
R bloggers has been steadily supplying me with a lot of good pragmatic content.
From the author:
R-Bloggers.com is a central hub (e.g: A blog aggregator) of content
collected from bloggers who write |
51,822 | Where can I find useful R tutorials with various implementations? [duplicate] | Another great resource is the LearnR blog, which went through an extensive study of visualizations with lattice and ggplot2. | Where can I find useful R tutorials with various implementations? [duplicate] | Another great resource is the LearnR blog, which went through an extensive study of visualizations with lattice and ggplot2. | Where can I find useful R tutorials with various implementations? [duplicate]
Another great resource is the LearnR blog, which went through an extensive study of visualizations with lattice and ggplot2. | Where can I find useful R tutorials with various implementations? [duplicate]
Another great resource is the LearnR blog, which went through an extensive study of visualizations with lattice and ggplot2. |
51,823 | Where can I find useful R tutorials with various implementations? [duplicate] | R is designed around ideas such as "reproducible research" and "trustworthy software", as John Chambers says in his excellent book "Software for Data Analysis: Programming with R".
One of the best ways to learn R is to look at the wealth of source code that available on CRAN (with 2461 packages and counting). Simple... | Where can I find useful R tutorials with various implementations? [duplicate] | R is designed around ideas such as "reproducible research" and "trustworthy software", as John Chambers says in his excellent book "Software for Data Analysis: Programming with R".
One of the best w | Where can I find useful R tutorials with various implementations? [duplicate]
R is designed around ideas such as "reproducible research" and "trustworthy software", as John Chambers says in his excellent book "Software for Data Analysis: Programming with R".
One of the best ways to learn R is to look at the wealth of... | Where can I find useful R tutorials with various implementations? [duplicate]
R is designed around ideas such as "reproducible research" and "trustworthy software", as John Chambers says in his excellent book "Software for Data Analysis: Programming with R".
One of the best w |
51,824 | Where can I find useful R tutorials with various implementations? [duplicate] | I found this rather helpful: http://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf | Where can I find useful R tutorials with various implementations? [duplicate] | I found this rather helpful: http://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf | Where can I find useful R tutorials with various implementations? [duplicate]
I found this rather helpful: http://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf | Where can I find useful R tutorials with various implementations? [duplicate]
I found this rather helpful: http://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf |
51,825 | What test does summary() perform on a glm() model using a Gamma distribution in r? | But a Wald test is a parametric test which assumes a normal distribution. Is R perhaps performing a Wald Log-Linear Chi-Square Test instead of a normal Wald test in these cases?
The coefficients are maximum likelihood estimates, which are asymptotically normal. The resulting test is indeed a Wald test a t-test as not... | What test does summary() perform on a glm() model using a Gamma distribution in r? | But a Wald test is a parametric test which assumes a normal distribution. Is R perhaps performing a Wald Log-Linear Chi-Square Test instead of a normal Wald test in these cases?
The coefficients are | What test does summary() perform on a glm() model using a Gamma distribution in r?
But a Wald test is a parametric test which assumes a normal distribution. Is R perhaps performing a Wald Log-Linear Chi-Square Test instead of a normal Wald test in these cases?
The coefficients are maximum likelihood estimates, which a... | What test does summary() perform on a glm() model using a Gamma distribution in r?
But a Wald test is a parametric test which assumes a normal distribution. Is R perhaps performing a Wald Log-Linear Chi-Square Test instead of a normal Wald test in these cases?
The coefficients are |
51,826 | What test does summary() perform on a glm() model using a Gamma distribution in r? | Demetri Pananos makes the critical point about regression models (+1): the coefficient estimates are taken to have underlying multivariate normal distributions, at least in the asymptotic limit of large numbers of observations. That does not necessarily require a normal distribution of data, as the reviewer evidently t... | What test does summary() perform on a glm() model using a Gamma distribution in r? | Demetri Pananos makes the critical point about regression models (+1): the coefficient estimates are taken to have underlying multivariate normal distributions, at least in the asymptotic limit of lar | What test does summary() perform on a glm() model using a Gamma distribution in r?
Demetri Pananos makes the critical point about regression models (+1): the coefficient estimates are taken to have underlying multivariate normal distributions, at least in the asymptotic limit of large numbers of observations. That does... | What test does summary() perform on a glm() model using a Gamma distribution in r?
Demetri Pananos makes the critical point about regression models (+1): the coefficient estimates are taken to have underlying multivariate normal distributions, at least in the asymptotic limit of lar |
51,827 | Can I use Pearson correlation for discrete variables? [closed] | Sure!
set.seed(2022)
N <- 100
x1 <- rpois(N, 5) # Poisson(5)
x2 <- rpois(N, 7) # Poisson(7)
cor(x1, x2)
At no point does the Pearson correlation make distribution assumptions beyond the covariance and variances existing. | Can I use Pearson correlation for discrete variables? [closed] | Sure!
set.seed(2022)
N <- 100
x1 <- rpois(N, 5) # Poisson(5)
x2 <- rpois(N, 7) # Poisson(7)
cor(x1, x2)
At no point does the Pearson correlation make distribution assumptions beyond the covariance an | Can I use Pearson correlation for discrete variables? [closed]
Sure!
set.seed(2022)
N <- 100
x1 <- rpois(N, 5) # Poisson(5)
x2 <- rpois(N, 7) # Poisson(7)
cor(x1, x2)
At no point does the Pearson correlation make distribution assumptions beyond the covariance and variances existing. | Can I use Pearson correlation for discrete variables? [closed]
Sure!
set.seed(2022)
N <- 100
x1 <- rpois(N, 5) # Poisson(5)
x2 <- rpois(N, 7) # Poisson(7)
cor(x1, x2)
At no point does the Pearson correlation make distribution assumptions beyond the covariance an |
51,828 | Can I use Pearson correlation for discrete variables? [closed] | The correlation coefficient, sure, if you're interested in measuring linear correlation.
If you want to test it, maybe -- you might sometimes need to consider using something else in place of the usual test, though.
The usual test is typically pretty level-robust but for example with count data (and often with other fo... | Can I use Pearson correlation for discrete variables? [closed] | The correlation coefficient, sure, if you're interested in measuring linear correlation.
If you want to test it, maybe -- you might sometimes need to consider using something else in place of the usua | Can I use Pearson correlation for discrete variables? [closed]
The correlation coefficient, sure, if you're interested in measuring linear correlation.
If you want to test it, maybe -- you might sometimes need to consider using something else in place of the usual test, though.
The usual test is typically pretty level-... | Can I use Pearson correlation for discrete variables? [closed]
The correlation coefficient, sure, if you're interested in measuring linear correlation.
If you want to test it, maybe -- you might sometimes need to consider using something else in place of the usua |
51,829 | Can I use Pearson correlation for discrete variables? [closed] | Yes, of course. Discrete variables belong to numerical data with ratio scale, and not categorical data. So you can use Pearson correlation coefficient to measure the relationship between those two variables. | Can I use Pearson correlation for discrete variables? [closed] | Yes, of course. Discrete variables belong to numerical data with ratio scale, and not categorical data. So you can use Pearson correlation coefficient to measure the relationship between those two var | Can I use Pearson correlation for discrete variables? [closed]
Yes, of course. Discrete variables belong to numerical data with ratio scale, and not categorical data. So you can use Pearson correlation coefficient to measure the relationship between those two variables. | Can I use Pearson correlation for discrete variables? [closed]
Yes, of course. Discrete variables belong to numerical data with ratio scale, and not categorical data. So you can use Pearson correlation coefficient to measure the relationship between those two var |
51,830 | Can I use Pearson correlation for discrete variables? [closed] | In the case of binary variables, this is even given a special name, either Matthew's Correlation Coefficient (MCC) or the "Phi coefficient". MCC is simply the Pearson correlation of two binary variables. | Can I use Pearson correlation for discrete variables? [closed] | In the case of binary variables, this is even given a special name, either Matthew's Correlation Coefficient (MCC) or the "Phi coefficient". MCC is simply the Pearson correlation of two binary variabl | Can I use Pearson correlation for discrete variables? [closed]
In the case of binary variables, this is even given a special name, either Matthew's Correlation Coefficient (MCC) or the "Phi coefficient". MCC is simply the Pearson correlation of two binary variables. | Can I use Pearson correlation for discrete variables? [closed]
In the case of binary variables, this is even given a special name, either Matthew's Correlation Coefficient (MCC) or the "Phi coefficient". MCC is simply the Pearson correlation of two binary variabl |
51,831 | Can I use Pearson correlation for discrete variables? [closed] | It depends on what you mean in "discrete". You can use Pearson's R for discrete numeric variable. If the data are in ordinal scale, you should use Spearman's correlation. If the data are in nominal scale, then Pearson's and Spearman's coefficients are not valid, even if you code the categories by numbers. | Can I use Pearson correlation for discrete variables? [closed] | It depends on what you mean in "discrete". You can use Pearson's R for discrete numeric variable. If the data are in ordinal scale, you should use Spearman's correlation. If the data are in nominal sc | Can I use Pearson correlation for discrete variables? [closed]
It depends on what you mean in "discrete". You can use Pearson's R for discrete numeric variable. If the data are in ordinal scale, you should use Spearman's correlation. If the data are in nominal scale, then Pearson's and Spearman's coefficients are not v... | Can I use Pearson correlation for discrete variables? [closed]
It depends on what you mean in "discrete". You can use Pearson's R for discrete numeric variable. If the data are in ordinal scale, you should use Spearman's correlation. If the data are in nominal sc |
51,832 | Introduction to Statistical Learning Eq. 4.32 | It is an issue of expanding and tidying up. You have for example
$(x-\mu_k)^T\Sigma^{-1}(x-\mu_k) = x^T\Sigma^{-1}x - \mu_k^T\Sigma^{-1}x-x^T\Sigma^{-1}\mu_k+\mu_k^T\Sigma^{-1}\mu_k$ and
$\mu_k^T\Sigma^{-1}x=x^T\Sigma^{-1}\mu_k$ and $\mu_k^T\Sigma^{-1}\mu_K=\mu_K^T\Sigma^{-1}\mu_k$ and
$(\mu_k+\mu_K)^T\Sigma^{-1}(\mu... | Introduction to Statistical Learning Eq. 4.32 | It is an issue of expanding and tidying up. You have for example
$(x-\mu_k)^T\Sigma^{-1}(x-\mu_k) = x^T\Sigma^{-1}x - \mu_k^T\Sigma^{-1}x-x^T\Sigma^{-1}\mu_k+\mu_k^T\Sigma^{-1}\mu_k$ and
$\mu_k^T\Si | Introduction to Statistical Learning Eq. 4.32
It is an issue of expanding and tidying up. You have for example
$(x-\mu_k)^T\Sigma^{-1}(x-\mu_k) = x^T\Sigma^{-1}x - \mu_k^T\Sigma^{-1}x-x^T\Sigma^{-1}\mu_k+\mu_k^T\Sigma^{-1}\mu_k$ and
$\mu_k^T\Sigma^{-1}x=x^T\Sigma^{-1}\mu_k$ and $\mu_k^T\Sigma^{-1}\mu_K=\mu_K^T\Sigma^... | Introduction to Statistical Learning Eq. 4.32
It is an issue of expanding and tidying up. You have for example
$(x-\mu_k)^T\Sigma^{-1}(x-\mu_k) = x^T\Sigma^{-1}x - \mu_k^T\Sigma^{-1}x-x^T\Sigma^{-1}\mu_k+\mu_k^T\Sigma^{-1}\mu_k$ and
$\mu_k^T\Si |
51,833 | Introduction to Statistical Learning Eq. 4.32 | Another way would be adding some terms to make the first multiplicands the same, and group (subtract the added terms outside of the parantheses as well):
$$\begin{align}A&=-\frac{1}{2}(x-\mu_k-\overbrace{\mu_K}^{new})^T\Sigma^{-1}(x-\mu_k)+\frac{1}{2}(x-\mu_K-\overbrace{\mu_k}^{new})^T\Sigma^{-1}(x-\mu_K)\\&- \frac{1}{... | Introduction to Statistical Learning Eq. 4.32 | Another way would be adding some terms to make the first multiplicands the same, and group (subtract the added terms outside of the parantheses as well):
$$\begin{align}A&=-\frac{1}{2}(x-\mu_k-\overbr | Introduction to Statistical Learning Eq. 4.32
Another way would be adding some terms to make the first multiplicands the same, and group (subtract the added terms outside of the parantheses as well):
$$\begin{align}A&=-\frac{1}{2}(x-\mu_k-\overbrace{\mu_K}^{new})^T\Sigma^{-1}(x-\mu_k)+\frac{1}{2}(x-\mu_K-\overbrace{\mu... | Introduction to Statistical Learning Eq. 4.32
Another way would be adding some terms to make the first multiplicands the same, and group (subtract the added terms outside of the parantheses as well):
$$\begin{align}A&=-\frac{1}{2}(x-\mu_k-\overbr |
51,834 | Calculate E[X/Y] from E[XY] for two random variables with zero mean | You will have to know the full joint distribution of $X$ and $Y$ in order to calculate $$E[X/Y] = \int (x/y) p(x,y) ~dx dy. $$
Note that $E[X/Y]$ might not even be defined - this is the case for example when $X$ and $Y$ are normally distributed, and the ratio has a Cauchy distribution which has no mean.
See also Ratio ... | Calculate E[X/Y] from E[XY] for two random variables with zero mean | You will have to know the full joint distribution of $X$ and $Y$ in order to calculate $$E[X/Y] = \int (x/y) p(x,y) ~dx dy. $$
Note that $E[X/Y]$ might not even be defined - this is the case for examp | Calculate E[X/Y] from E[XY] for two random variables with zero mean
You will have to know the full joint distribution of $X$ and $Y$ in order to calculate $$E[X/Y] = \int (x/y) p(x,y) ~dx dy. $$
Note that $E[X/Y]$ might not even be defined - this is the case for example when $X$ and $Y$ are normally distributed, and th... | Calculate E[X/Y] from E[XY] for two random variables with zero mean
You will have to know the full joint distribution of $X$ and $Y$ in order to calculate $$E[X/Y] = \int (x/y) p(x,y) ~dx dy. $$
Note that $E[X/Y]$ might not even be defined - this is the case for examp |
51,835 | Calculate E[X/Y] from E[XY] for two random variables with zero mean | Intuitively, take the singular density in $\mathbb{R}^2$ that is only nonzero along some line $X = a Y$, $var(Y) = b$, $Y$ always nonzero, and that has $E[X] = E[Y] = 0$, as you required. Then:
$$
E\left[\frac{X}{Y}\right] = E[a] = a
$$
and
$$
E[XY] = a\,E[Y^2] = a \; var(Y) = ab.
$$
So you cannot compute $E\left[\frac... | Calculate E[X/Y] from E[XY] for two random variables with zero mean | Intuitively, take the singular density in $\mathbb{R}^2$ that is only nonzero along some line $X = a Y$, $var(Y) = b$, $Y$ always nonzero, and that has $E[X] = E[Y] = 0$, as you required. Then:
$$
E\l | Calculate E[X/Y] from E[XY] for two random variables with zero mean
Intuitively, take the singular density in $\mathbb{R}^2$ that is only nonzero along some line $X = a Y$, $var(Y) = b$, $Y$ always nonzero, and that has $E[X] = E[Y] = 0$, as you required. Then:
$$
E\left[\frac{X}{Y}\right] = E[a] = a
$$
and
$$
E[XY] = ... | Calculate E[X/Y] from E[XY] for two random variables with zero mean
Intuitively, take the singular density in $\mathbb{R}^2$ that is only nonzero along some line $X = a Y$, $var(Y) = b$, $Y$ always nonzero, and that has $E[X] = E[Y] = 0$, as you required. Then:
$$
E\l |
51,836 | Mean is not a sufficient statistic for the normal distribution when variance is not known? | $\bar X$ is not a sufficient statistic because it does not contain all the information about $(\mu,\sigma^2)$, which is what it would mean for it to be sufficient.
However, $\bar X$ does contain all the information about $\mu$ in the sample, whether or not $\sigma^2$ is known. For example, $\bar X$ attains the Cramèr-R... | Mean is not a sufficient statistic for the normal distribution when variance is not known? | $\bar X$ is not a sufficient statistic because it does not contain all the information about $(\mu,\sigma^2)$, which is what it would mean for it to be sufficient.
However, $\bar X$ does contain all t | Mean is not a sufficient statistic for the normal distribution when variance is not known?
$\bar X$ is not a sufficient statistic because it does not contain all the information about $(\mu,\sigma^2)$, which is what it would mean for it to be sufficient.
However, $\bar X$ does contain all the information about $\mu$ in... | Mean is not a sufficient statistic for the normal distribution when variance is not known?
$\bar X$ is not a sufficient statistic because it does not contain all the information about $(\mu,\sigma^2)$, which is what it would mean for it to be sufficient.
However, $\bar X$ does contain all t |
51,837 | Mean is not a sufficient statistic for the normal distribution when variance is not known? | There is a relationship between the sample range and the sample standard deviation. It is not as good as using the sufficient statistic, but not useless.
[The somewhat bogus 'rule' of thumb, mentioned in some elementary tests, that $S$ is well-estimated by the range divided by 5 or 6, is not what I have in mind; for no... | Mean is not a sufficient statistic for the normal distribution when variance is not known? | There is a relationship between the sample range and the sample standard deviation. It is not as good as using the sufficient statistic, but not useless.
[The somewhat bogus 'rule' of thumb, mentioned | Mean is not a sufficient statistic for the normal distribution when variance is not known?
There is a relationship between the sample range and the sample standard deviation. It is not as good as using the sufficient statistic, but not useless.
[The somewhat bogus 'rule' of thumb, mentioned in some elementary tests, th... | Mean is not a sufficient statistic for the normal distribution when variance is not known?
There is a relationship between the sample range and the sample standard deviation. It is not as good as using the sufficient statistic, but not useless.
[The somewhat bogus 'rule' of thumb, mentioned |
51,838 | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable? | Using the formula for covariance that you gave, you can reexpress the covariance as follows:
$$\begin{aligned}
\text{Cov}\left(X, \frac{1}{X}\right) &= E \left[ X\frac{1}{X}\right]-E[X]E\left[\frac{1}{X}\right] \\ &= 1 - E[X]E\left[\frac{1}{X}\right] \end{aligned}$$
Let $\varphi(Y) = \frac{1}{Y}$, which is a convex f... | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable? | Using the formula for covariance that you gave, you can reexpress the covariance as follows:
$$\begin{aligned}
\text{Cov}\left(X, \frac{1}{X}\right) &= E \left[ X\frac{1}{X}\right]-E[X]E\left[\frac{1 | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable?
Using the formula for covariance that you gave, you can reexpress the covariance as follows:
$$\begin{aligned}
\text{Cov}\left(X, \frac{1}{X}\right) &= E \left[ X\frac{1}{X}\right]-E[X]E\left[\frac{1}{X}\right] \\ &= 1 - E[X]E\left[\frac{1}{X}\rig... | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable?
Using the formula for covariance that you gave, you can reexpress the covariance as follows:
$$\begin{aligned}
\text{Cov}\left(X, \frac{1}{X}\right) &= E \left[ X\frac{1}{X}\right]-E[X]E\left[\frac{1 |
51,839 | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable? | Via, Jensen's inequality, you'll have $$\frac{1}{E[X]}\leq E\left[\frac{1}{X}\right]$$
because $f(x)=1/x$ is a convex function for positive $x$. If you substitute this into the covariance definition, you'll reach the desired result. | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable? | Via, Jensen's inequality, you'll have $$\frac{1}{E[X]}\leq E\left[\frac{1}{X}\right]$$
because $f(x)=1/x$ is a convex function for positive $x$. If you substitute this into the covariance definition, | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable?
Via, Jensen's inequality, you'll have $$\frac{1}{E[X]}\leq E\left[\frac{1}{X}\right]$$
because $f(x)=1/x$ is a convex function for positive $x$. If you substitute this into the covariance definition, you'll reach the desired result. | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable?
Via, Jensen's inequality, you'll have $$\frac{1}{E[X]}\leq E\left[\frac{1}{X}\right]$$
because $f(x)=1/x$ is a convex function for positive $x$. If you substitute this into the covariance definition, |
51,840 | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable? | One proof is to note that
\begin{align}
\mathbf{Cov} (X, X^{-1}) &= \frac{1}{2}\mathbf{E} \left[ \left( X_1 - X_2 \right) \cdot \left( X_1^{-1} - X_2^{-1} \right) \right] \\
&= -\frac{1}{2}\mathbf{E} \left[ \frac{\left( X_1 - X_2 \right)^2}{X_1\cdot X_2} \right] \leq 0.
\end{align} | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable? | One proof is to note that
\begin{align}
\mathbf{Cov} (X, X^{-1}) &= \frac{1}{2}\mathbf{E} \left[ \left( X_1 - X_2 \right) \cdot \left( X_1^{-1} - X_2^{-1} \right) \right] \\
&= -\frac{1}{2}\mathbf{E} | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable?
One proof is to note that
\begin{align}
\mathbf{Cov} (X, X^{-1}) &= \frac{1}{2}\mathbf{E} \left[ \left( X_1 - X_2 \right) \cdot \left( X_1^{-1} - X_2^{-1} \right) \right] \\
&= -\frac{1}{2}\mathbf{E} \left[ \frac{\left( X_1 - X_2 \right)^2}{X_1\cdot... | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable?
One proof is to note that
\begin{align}
\mathbf{Cov} (X, X^{-1}) &= \frac{1}{2}\mathbf{E} \left[ \left( X_1 - X_2 \right) \cdot \left( X_1^{-1} - X_2^{-1} \right) \right] \\
&= -\frac{1}{2}\mathbf{E} |
51,841 | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable? | This result is not due to the positivity of $X,$ nor to the convexity of the function $x\to 1/x,$ nor to any particular property of this function apart from that it decreases. It would be less than satisfactory, then, to rely on the standard convexity inequalities such as Jensen's Inequality.
Consider this characteriz... | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable? | This result is not due to the positivity of $X,$ nor to the convexity of the function $x\to 1/x,$ nor to any particular property of this function apart from that it decreases. It would be less than s | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable?
This result is not due to the positivity of $X,$ nor to the convexity of the function $x\to 1/x,$ nor to any particular property of this function apart from that it decreases. It would be less than satisfactory, then, to rely on the standard convex... | Show That $Cov(X,\frac{1}{X})\le0$ if $X$ Is Positive Random Variable?
This result is not due to the positivity of $X,$ nor to the convexity of the function $x\to 1/x,$ nor to any particular property of this function apart from that it decreases. It would be less than s |
51,842 | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$? | I would like to add a thing to the answer by @Thomas Lumley
One can come up with the following:
$$\begin{align}
E[\max(X,a)]&=P(X\geq a)\cdot E[\max(X,a)|X\geq a]+P(X<a)\cdot E[\max(X,a)|X<a]\\
&=P(X\geq a)\cdot E[X|X\geq a]+P(X<a)\cdot a\\
&=P(X\geq a)\cdot E[X|X\geq a]+(1-P(X\geq a))\cdot a\\
&=P(X\geq a)\cdot (E[X|X... | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$? | I would like to add a thing to the answer by @Thomas Lumley
One can come up with the following:
$$\begin{align}
E[\max(X,a)]&=P(X\geq a)\cdot E[\max(X,a)|X\geq a]+P(X<a)\cdot E[\max(X,a)|X<a]\\
&=P(X\ | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$?
I would like to add a thing to the answer by @Thomas Lumley
One can come up with the following:
$$\begin{align}
E[\max(X,a)]&=P(X\geq a)\cdot E[\max(X,a)|X\geq a]+P(X<a)\cdot E[\max(X,a)|X<a]\\
&=P(X\geq a)\cdot E[X|X\geq a]+P(X<a)\c... | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$?
I would like to add a thing to the answer by @Thomas Lumley
One can come up with the following:
$$\begin{align}
E[\max(X,a)]&=P(X\geq a)\cdot E[\max(X,a)|X\geq a]+P(X<a)\cdot E[\max(X,a)|X<a]\\
&=P(X\ |
51,843 | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$? | There's a connection to the conditional expectation. I'll write $S_X(x)=1=F_X(x)$ for the survival function. The conditional survival function conditional on $X\geq a$ is
$$S_{a}(x)= \frac{P(X>a \cap X>x)}{P(X>a)}$$
which is 1 for $x<a$ and $S_X(x)/S_x(a)$ for $x\geq a$. So the conditional expectation is
$$E[X|X\geq ... | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$? | There's a connection to the conditional expectation. I'll write $S_X(x)=1=F_X(x)$ for the survival function. The conditional survival function conditional on $X\geq a$ is
$$S_{a}(x)= \frac{P(X>a \ca | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$?
There's a connection to the conditional expectation. I'll write $S_X(x)=1=F_X(x)$ for the survival function. The conditional survival function conditional on $X\geq a$ is
$$S_{a}(x)= \frac{P(X>a \cap X>x)}{P(X>a)}$$
which is 1 for ... | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$?
There's a connection to the conditional expectation. I'll write $S_X(x)=1=F_X(x)$ for the survival function. The conditional survival function conditional on $X\geq a$ is
$$S_{a}(x)= \frac{P(X>a \ca |
51,844 | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$? | For simplicity, consider the case where $X$ is continuous with density function $f_X$. The standard expectation rule for non-negative random variables is derived by using integration by parts to alter the standard moment integral. We will use the same technique here. Using integration by parts and L'Hôpital's rule w... | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$? | For simplicity, consider the case where $X$ is continuous with density function $f_X$. The standard expectation rule for non-negative random variables is derived by using integration by parts to alte | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$?
For simplicity, consider the case where $X$ is continuous with density function $f_X$. The standard expectation rule for non-negative random variables is derived by using integration by parts to alter the standard moment integral. ... | Expected value of a random variable by integrating $1-CDF$ when lower limit $a\neq 0$?
For simplicity, consider the case where $X$ is continuous with density function $f_X$. The standard expectation rule for non-negative random variables is derived by using integration by parts to alte |
51,845 | Why are the ends of the prediction interval wider in the regression? [duplicate] | When performing a linear regression, there are 2 types of uncertainty in the prediction.
First is the prediction of the overall mean of the estimate (ie the center of the fit). The second is the uncertainly in the estimate calculating the slope.
Thus when you combine both uncertainties of the prediction there is a sp... | Why are the ends of the prediction interval wider in the regression? [duplicate] | When performing a linear regression, there are 2 types of uncertainty in the prediction.
First is the prediction of the overall mean of the estimate (ie the center of the fit). The second is the unce | Why are the ends of the prediction interval wider in the regression? [duplicate]
When performing a linear regression, there are 2 types of uncertainty in the prediction.
First is the prediction of the overall mean of the estimate (ie the center of the fit). The second is the uncertainly in the estimate calculating the... | Why are the ends of the prediction interval wider in the regression? [duplicate]
When performing a linear regression, there are 2 types of uncertainty in the prediction.
First is the prediction of the overall mean of the estimate (ie the center of the fit). The second is the unce |
51,846 | Why are the ends of the prediction interval wider in the regression? [duplicate] | Its very easy to determine the prediction interval for the data.
$$\operatorname{Var}(y) = \operatorname{Var}(\beta_0 + \beta_1 x) + \operatorname{Var}(\varepsilon) = \sigma^2_{\beta_0} + \sigma^2_{\beta_1}x^2 + 2x \operatorname{Cov}(\beta_0, \beta_1)+ \sigma^2_{\epsilon}$$
As you can see, this is a quadratic function ... | Why are the ends of the prediction interval wider in the regression? [duplicate] | Its very easy to determine the prediction interval for the data.
$$\operatorname{Var}(y) = \operatorname{Var}(\beta_0 + \beta_1 x) + \operatorname{Var}(\varepsilon) = \sigma^2_{\beta_0} + \sigma^2_{\b | Why are the ends of the prediction interval wider in the regression? [duplicate]
Its very easy to determine the prediction interval for the data.
$$\operatorname{Var}(y) = \operatorname{Var}(\beta_0 + \beta_1 x) + \operatorname{Var}(\varepsilon) = \sigma^2_{\beta_0} + \sigma^2_{\beta_1}x^2 + 2x \operatorname{Cov}(\beta... | Why are the ends of the prediction interval wider in the regression? [duplicate]
Its very easy to determine the prediction interval for the data.
$$\operatorname{Var}(y) = \operatorname{Var}(\beta_0 + \beta_1 x) + \operatorname{Var}(\varepsilon) = \sigma^2_{\beta_0} + \sigma^2_{\b |
51,847 | Why are the ends of the prediction interval wider in the regression? [duplicate] | This reference, for example, clearly gives the formula of a prediction interval for a simple linear regression model, which contains the expression:
$\sqrt{({1/n + (x_p - x_m)^2}/{(n-1){s_x}^2}}$
So, as the prediction for the explanatory variable $x_p$ becomes more removed from its mean $x_m$, the interval widens.
In p... | Why are the ends of the prediction interval wider in the regression? [duplicate] | This reference, for example, clearly gives the formula of a prediction interval for a simple linear regression model, which contains the expression:
$\sqrt{({1/n + (x_p - x_m)^2}/{(n-1){s_x}^2}}$
So, | Why are the ends of the prediction interval wider in the regression? [duplicate]
This reference, for example, clearly gives the formula of a prediction interval for a simple linear regression model, which contains the expression:
$\sqrt{({1/n + (x_p - x_m)^2}/{(n-1){s_x}^2}}$
So, as the prediction for the explanatory v... | Why are the ends of the prediction interval wider in the regression? [duplicate]
This reference, for example, clearly gives the formula of a prediction interval for a simple linear regression model, which contains the expression:
$\sqrt{({1/n + (x_p - x_m)^2}/{(n-1){s_x}^2}}$
So, |
51,848 | What is sigma function in the YOLO object detector? | It is the logistic sigmoid function:
$$
\sigma(x) = \frac 1 {1+e^{-x}}
$$
It is bounded between 0 and 1, which is a desired property in their case (image from Wikipedia):
Regarding the exponential, see this answer. | What is sigma function in the YOLO object detector? | It is the logistic sigmoid function:
$$
\sigma(x) = \frac 1 {1+e^{-x}}
$$
It is bounded between 0 and 1, which is a desired property in their case (image from Wikipedia):
Regarding the exponential, s | What is sigma function in the YOLO object detector?
It is the logistic sigmoid function:
$$
\sigma(x) = \frac 1 {1+e^{-x}}
$$
It is bounded between 0 and 1, which is a desired property in their case (image from Wikipedia):
Regarding the exponential, see this answer. | What is sigma function in the YOLO object detector?
It is the logistic sigmoid function:
$$
\sigma(x) = \frac 1 {1+e^{-x}}
$$
It is bounded between 0 and 1, which is a desired property in their case (image from Wikipedia):
Regarding the exponential, s |
51,849 | What is sigma function in the YOLO object detector? | In addition to the notation using the symbol $\sigma$, the caption to one image names this function the "sigmoid" function. From the paper,
Figure 3: Bounding boxes with dimension priors and location
prediction. We predict the width and height of the box as offsets
from cluster centroids. We predict the center coo... | What is sigma function in the YOLO object detector? | In addition to the notation using the symbol $\sigma$, the caption to one image names this function the "sigmoid" function. From the paper,
Figure 3: Bounding boxes with dimension priors and location | What is sigma function in the YOLO object detector?
In addition to the notation using the symbol $\sigma$, the caption to one image names this function the "sigmoid" function. From the paper,
Figure 3: Bounding boxes with dimension priors and location
prediction. We predict the width and height of the box as offsets... | What is sigma function in the YOLO object detector?
In addition to the notation using the symbol $\sigma$, the caption to one image names this function the "sigmoid" function. From the paper,
Figure 3: Bounding boxes with dimension priors and location |
51,850 | Is there any truth to the phrase "statistics mean nothing to the individual"? | I think "nothing" is too strong, but I imagine the statement is a pedagogical challenge meant to address one or more issues:
I. It may be addressing the reification of statistical models.
II. As you say, it may be addressing point summaries, which do not necessarily represent any individual. (In fact, the summary value... | Is there any truth to the phrase "statistics mean nothing to the individual"? | I think "nothing" is too strong, but I imagine the statement is a pedagogical challenge meant to address one or more issues:
I. It may be addressing the reification of statistical models.
II. As you s | Is there any truth to the phrase "statistics mean nothing to the individual"?
I think "nothing" is too strong, but I imagine the statement is a pedagogical challenge meant to address one or more issues:
I. It may be addressing the reification of statistical models.
II. As you say, it may be addressing point summaries, ... | Is there any truth to the phrase "statistics mean nothing to the individual"?
I think "nothing" is too strong, but I imagine the statement is a pedagogical challenge meant to address one or more issues:
I. It may be addressing the reification of statistical models.
II. As you s |
51,851 | Is there any truth to the phrase "statistics mean nothing to the individual"? | I agree with the other answers, but I would like to add that in the New Causal Revolution, particularly with the highest level of reasoning - the counterfactual - it is possible to reason about individuals. That only works if you have an accurate model. The three-step process of abduction, action or intervention, and p... | Is there any truth to the phrase "statistics mean nothing to the individual"? | I agree with the other answers, but I would like to add that in the New Causal Revolution, particularly with the highest level of reasoning - the counterfactual - it is possible to reason about indivi | Is there any truth to the phrase "statistics mean nothing to the individual"?
I agree with the other answers, but I would like to add that in the New Causal Revolution, particularly with the highest level of reasoning - the counterfactual - it is possible to reason about individuals. That only works if you have an accu... | Is there any truth to the phrase "statistics mean nothing to the individual"?
I agree with the other answers, but I would like to add that in the New Causal Revolution, particularly with the highest level of reasoning - the counterfactual - it is possible to reason about indivi |
51,852 | Is there any truth to the phrase "statistics mean nothing to the individual"? | No, it's a statement made by people who don't understand probability.
If you contract a disease with a 95% mortality rate, you can't say you will certainly die.
But you absolutely can say "I will probably die." You can go further and say "The probability of my dying is 0.9." That's an awfully specific and highly inform... | Is there any truth to the phrase "statistics mean nothing to the individual"? | No, it's a statement made by people who don't understand probability.
If you contract a disease with a 95% mortality rate, you can't say you will certainly die.
But you absolutely can say "I will prob | Is there any truth to the phrase "statistics mean nothing to the individual"?
No, it's a statement made by people who don't understand probability.
If you contract a disease with a 95% mortality rate, you can't say you will certainly die.
But you absolutely can say "I will probably die." You can go further and say "The... | Is there any truth to the phrase "statistics mean nothing to the individual"?
No, it's a statement made by people who don't understand probability.
If you contract a disease with a 95% mortality rate, you can't say you will certainly die.
But you absolutely can say "I will prob |
51,853 | Is there any truth to the phrase "statistics mean nothing to the individual"? | It is true in general that statistical quantities pertaining to a single individual have more variance than those that average over a larger group subsuming that individual. This holds for any set of quantities that are not perfectly positively correlated. In this sense, it is reasonable to say that statistics predic... | Is there any truth to the phrase "statistics mean nothing to the individual"? | It is true in general that statistical quantities pertaining to a single individual have more variance than those that average over a larger group subsuming that individual. This holds for any set of | Is there any truth to the phrase "statistics mean nothing to the individual"?
It is true in general that statistical quantities pertaining to a single individual have more variance than those that average over a larger group subsuming that individual. This holds for any set of quantities that are not perfectly positiv... | Is there any truth to the phrase "statistics mean nothing to the individual"?
It is true in general that statistical quantities pertaining to a single individual have more variance than those that average over a larger group subsuming that individual. This holds for any set of |
51,854 | Is there any truth to the phrase "statistics mean nothing to the individual"? | Summary: we can derive statistics about individuals.
However, depending on the problem at hand, they may only tell us that we do not have sufficient information (e.g., because the correlation between our independent and dependent variable is too low) to draw meaningful conclusions.
Some sources claim that IQ is corre... | Is there any truth to the phrase "statistics mean nothing to the individual"? | Summary: we can derive statistics about individuals.
However, depending on the problem at hand, they may only tell us that we do not have sufficient information (e.g., because the correlation between | Is there any truth to the phrase "statistics mean nothing to the individual"?
Summary: we can derive statistics about individuals.
However, depending on the problem at hand, they may only tell us that we do not have sufficient information (e.g., because the correlation between our independent and dependent variable is ... | Is there any truth to the phrase "statistics mean nothing to the individual"?
Summary: we can derive statistics about individuals.
However, depending on the problem at hand, they may only tell us that we do not have sufficient information (e.g., because the correlation between |
51,855 | Is there any truth to the phrase "statistics mean nothing to the individual"? | There is SOME truth to that phrase.
The problem occurs when people misapply statistics to an individual in a way that restricts the possibility of that individual not being in the described group...most often in racial profiling.
If you have a disease that consistently kills 95% of those who catch it and 100 people cat... | Is there any truth to the phrase "statistics mean nothing to the individual"? | There is SOME truth to that phrase.
The problem occurs when people misapply statistics to an individual in a way that restricts the possibility of that individual not being in the described group...mo | Is there any truth to the phrase "statistics mean nothing to the individual"?
There is SOME truth to that phrase.
The problem occurs when people misapply statistics to an individual in a way that restricts the possibility of that individual not being in the described group...most often in racial profiling.
If you have ... | Is there any truth to the phrase "statistics mean nothing to the individual"?
There is SOME truth to that phrase.
The problem occurs when people misapply statistics to an individual in a way that restricts the possibility of that individual not being in the described group...mo |
51,856 | Is there any truth to the phrase "statistics mean nothing to the individual"? | Ironically, this statement is sort of meta and illustrates its own shortcomings.
A few people have mentioned the Ecological Fallacy and this statement arguably a way to summarize or describe an aspect of the fallacy. In ecology (or any field that uses statistics which is all sciences and many of the humanities), you ar... | Is there any truth to the phrase "statistics mean nothing to the individual"? | Ironically, this statement is sort of meta and illustrates its own shortcomings.
A few people have mentioned the Ecological Fallacy and this statement arguably a way to summarize or describe an aspect | Is there any truth to the phrase "statistics mean nothing to the individual"?
Ironically, this statement is sort of meta and illustrates its own shortcomings.
A few people have mentioned the Ecological Fallacy and this statement arguably a way to summarize or describe an aspect of the fallacy. In ecology (or any field ... | Is there any truth to the phrase "statistics mean nothing to the individual"?
Ironically, this statement is sort of meta and illustrates its own shortcomings.
A few people have mentioned the Ecological Fallacy and this statement arguably a way to summarize or describe an aspect |
51,857 | When is it valid to use race/ethnicity in causal inference? | Race and ethnicity are variables that cannot be "controlled" in experiments, since it is not possible for the researcher to assign or change this characteristic of the study participant.$^\dagger$ For this reason, causal inference relating to race and ethnicity cannot generally rely on randomised controlled trials, an... | When is it valid to use race/ethnicity in causal inference? | Race and ethnicity are variables that cannot be "controlled" in experiments, since it is not possible for the researcher to assign or change this characteristic of the study participant.$^\dagger$ Fo | When is it valid to use race/ethnicity in causal inference?
Race and ethnicity are variables that cannot be "controlled" in experiments, since it is not possible for the researcher to assign or change this characteristic of the study participant.$^\dagger$ For this reason, causal inference relating to race and ethnici... | When is it valid to use race/ethnicity in causal inference?
Race and ethnicity are variables that cannot be "controlled" in experiments, since it is not possible for the researcher to assign or change this characteristic of the study participant.$^\dagger$ Fo |
51,858 | When is it valid to use race/ethnicity in causal inference? | There is nothing special about race when it comes to causal inference. You can look for its effects just as you might look for the effect of the season.
The difficulty with a lot of causal models in the social sciences is mediation analysis: you want to know when A causes B directly, but not through C (What Ben means ... | When is it valid to use race/ethnicity in causal inference? | There is nothing special about race when it comes to causal inference. You can look for its effects just as you might look for the effect of the season.
The difficulty with a lot of causal models in | When is it valid to use race/ethnicity in causal inference?
There is nothing special about race when it comes to causal inference. You can look for its effects just as you might look for the effect of the season.
The difficulty with a lot of causal models in the social sciences is mediation analysis: you want to know ... | When is it valid to use race/ethnicity in causal inference?
There is nothing special about race when it comes to causal inference. You can look for its effects just as you might look for the effect of the season.
The difficulty with a lot of causal models in |
51,859 | When is it valid to use race/ethnicity in causal inference? | The idea that race can be a cause is not without dispute.
In a 1986 JASA article, Paul Holland discussed how he and Don Rubin coined the expression, “no causation without manipulation”.
The idea here is that causal inference requires a strict definition of a cause that identifies an intervention that hypothetically cou... | When is it valid to use race/ethnicity in causal inference? | The idea that race can be a cause is not without dispute.
In a 1986 JASA article, Paul Holland discussed how he and Don Rubin coined the expression, “no causation without manipulation”.
The idea here | When is it valid to use race/ethnicity in causal inference?
The idea that race can be a cause is not without dispute.
In a 1986 JASA article, Paul Holland discussed how he and Don Rubin coined the expression, “no causation without manipulation”.
The idea here is that causal inference requires a strict definition of a c... | When is it valid to use race/ethnicity in causal inference?
The idea that race can be a cause is not without dispute.
In a 1986 JASA article, Paul Holland discussed how he and Don Rubin coined the expression, “no causation without manipulation”.
The idea here |
51,860 | Are dimensionality reduction techniques useful in deep learning? | $t$-SNE
Two obvious reasons that tsne is not commonly used as a dimension reduction method is that it is non-deterministic and it can't be applied in a consistent fashion to test-set data. See: Are there cases where PCA is more suitable than t-SNE?
PCA
First, pca is not inherently a dimensionality reduction method. It'... | Are dimensionality reduction techniques useful in deep learning? | $t$-SNE
Two obvious reasons that tsne is not commonly used as a dimension reduction method is that it is non-deterministic and it can't be applied in a consistent fashion to test-set data. See: Are th | Are dimensionality reduction techniques useful in deep learning?
$t$-SNE
Two obvious reasons that tsne is not commonly used as a dimension reduction method is that it is non-deterministic and it can't be applied in a consistent fashion to test-set data. See: Are there cases where PCA is more suitable than t-SNE?
PCA
Fi... | Are dimensionality reduction techniques useful in deep learning?
$t$-SNE
Two obvious reasons that tsne is not commonly used as a dimension reduction method is that it is non-deterministic and it can't be applied in a consistent fashion to test-set data. See: Are th |
51,861 | Are dimensionality reduction techniques useful in deep learning? | Complementary to @Sycorax's nice answer (+1):
Remember that one of the "deep-learning" strengths is the ability of deep neural network to perform automatic feature extraction and encapsulate non-linear relations (e.g. through convolutions (ConvNNets), recurrences (RNNs), etc.). Making a highly condensed version of the... | Are dimensionality reduction techniques useful in deep learning? | Complementary to @Sycorax's nice answer (+1):
Remember that one of the "deep-learning" strengths is the ability of deep neural network to perform automatic feature extraction and encapsulate non-line | Are dimensionality reduction techniques useful in deep learning?
Complementary to @Sycorax's nice answer (+1):
Remember that one of the "deep-learning" strengths is the ability of deep neural network to perform automatic feature extraction and encapsulate non-linear relations (e.g. through convolutions (ConvNNets), re... | Are dimensionality reduction techniques useful in deep learning?
Complementary to @Sycorax's nice answer (+1):
Remember that one of the "deep-learning" strengths is the ability of deep neural network to perform automatic feature extraction and encapsulate non-line |
51,862 | Are dimensionality reduction techniques useful in deep learning? | But, i rarely noticed anyone doing it for deep learning projects. Is there a specific reason for not using Dimensionality reduction techniques in deep learning?
That depends on the aims of these projects.
For example for projects/papers dealing with representation learning it's pretty common:
Reducing the Dimensional... | Are dimensionality reduction techniques useful in deep learning? | But, i rarely noticed anyone doing it for deep learning projects. Is there a specific reason for not using Dimensionality reduction techniques in deep learning?
That depends on the aims of these proj | Are dimensionality reduction techniques useful in deep learning?
But, i rarely noticed anyone doing it for deep learning projects. Is there a specific reason for not using Dimensionality reduction techniques in deep learning?
That depends on the aims of these projects.
For example for projects/papers dealing with repr... | Are dimensionality reduction techniques useful in deep learning?
But, i rarely noticed anyone doing it for deep learning projects. Is there a specific reason for not using Dimensionality reduction techniques in deep learning?
That depends on the aims of these proj |
51,863 | Tensorflow - Why do we need tensors? [duplicate] | Tensors, as defined by the deep learning software are multidimensional arrays, so if you need only to conduct simple (small-scale) mathematical operations and transformations on the data, then TensorFlow is an overkill. But TensorFlow is much more then this,
it implements most of the common building bricks for buildin... | Tensorflow - Why do we need tensors? [duplicate] | Tensors, as defined by the deep learning software are multidimensional arrays, so if you need only to conduct simple (small-scale) mathematical operations and transformations on the data, then TensorF | Tensorflow - Why do we need tensors? [duplicate]
Tensors, as defined by the deep learning software are multidimensional arrays, so if you need only to conduct simple (small-scale) mathematical operations and transformations on the data, then TensorFlow is an overkill. But TensorFlow is much more then this,
it implemen... | Tensorflow - Why do we need tensors? [duplicate]
Tensors, as defined by the deep learning software are multidimensional arrays, so if you need only to conduct simple (small-scale) mathematical operations and transformations on the data, then TensorF |
51,864 | Tensorflow - Why do we need tensors? [duplicate] | I am assuming that a) you do not question why do we have TensorFlow itself, and understand its value; and b) you only question why wouldn't TF use np.array class instead of creating a new class tf.Tensor.
When you write any kind of extensive framework such as TensorFlow, you end up creating many types and even type hie... | Tensorflow - Why do we need tensors? [duplicate] | I am assuming that a) you do not question why do we have TensorFlow itself, and understand its value; and b) you only question why wouldn't TF use np.array class instead of creating a new class tf.Ten | Tensorflow - Why do we need tensors? [duplicate]
I am assuming that a) you do not question why do we have TensorFlow itself, and understand its value; and b) you only question why wouldn't TF use np.array class instead of creating a new class tf.Tensor.
When you write any kind of extensive framework such as TensorFlow,... | Tensorflow - Why do we need tensors? [duplicate]
I am assuming that a) you do not question why do we have TensorFlow itself, and understand its value; and b) you only question why wouldn't TF use np.array class instead of creating a new class tf.Ten |
51,865 | Tensorflow - Why do we need tensors? [duplicate] | In addition to the other answer, I think a Tensor can also be an operation. In short a Tensor is an abstraction of a data or operation and it represents a node in the computational graph. The graph is the set of calculations to be done by TF in order to train, predict, etc. | Tensorflow - Why do we need tensors? [duplicate] | In addition to the other answer, I think a Tensor can also be an operation. In short a Tensor is an abstraction of a data or operation and it represents a node in the computational graph. The graph is | Tensorflow - Why do we need tensors? [duplicate]
In addition to the other answer, I think a Tensor can also be an operation. In short a Tensor is an abstraction of a data or operation and it represents a node in the computational graph. The graph is the set of calculations to be done by TF in order to train, predict, e... | Tensorflow - Why do we need tensors? [duplicate]
In addition to the other answer, I think a Tensor can also be an operation. In short a Tensor is an abstraction of a data or operation and it represents a node in the computational graph. The graph is |
51,866 | Rolling a $6$ Sided Die | This is very much not about the order in which you roll dice or whether you roll them at the same time or one after the other. It is about whether you examine the conditional probability or the overall probability.
Given die one shows a 6, die two has a 6-probability of $1/6$.
Not given that any one of them has a 6, th... | Rolling a $6$ Sided Die | This is very much not about the order in which you roll dice or whether you roll them at the same time or one after the other. It is about whether you examine the conditional probability or the overal | Rolling a $6$ Sided Die
This is very much not about the order in which you roll dice or whether you roll them at the same time or one after the other. It is about whether you examine the conditional probability or the overall probability.
Given die one shows a 6, die two has a 6-probability of $1/6$.
Not given that any... | Rolling a $6$ Sided Die
This is very much not about the order in which you roll dice or whether you roll them at the same time or one after the other. It is about whether you examine the conditional probability or the overal |
51,867 | Rolling a $6$ Sided Die | Dice rolls are independent. The die doesn't "remember" if you just rolled a six (or any other number).
What this means is that the probability of a 6 on a single roll is always $\frac{1}{6}$.
The apparent contradiction in your question arises from conditional probability.
Conditional probability expresses the event "g... | Rolling a $6$ Sided Die | Dice rolls are independent. The die doesn't "remember" if you just rolled a six (or any other number).
What this means is that the probability of a 6 on a single roll is always $\frac{1}{6}$.
The app | Rolling a $6$ Sided Die
Dice rolls are independent. The die doesn't "remember" if you just rolled a six (or any other number).
What this means is that the probability of a 6 on a single roll is always $\frac{1}{6}$.
The apparent contradiction in your question arises from conditional probability.
Conditional probabilit... | Rolling a $6$ Sided Die
Dice rolls are independent. The die doesn't "remember" if you just rolled a six (or any other number).
What this means is that the probability of a 6 on a single roll is always $\frac{1}{6}$.
The app |
51,868 | Rolling a $6$ Sided Die | Here's a way to think about it that clearly shows that the results of rolling two simultaneously have the same probability as one after the other:
Since you asked specifically about the chance of failure, lets make that explicit: You correctly noted that the chance of success when rolling simultaneously is 1/36, so the... | Rolling a $6$ Sided Die | Here's a way to think about it that clearly shows that the results of rolling two simultaneously have the same probability as one after the other:
Since you asked specifically about the chance of fail | Rolling a $6$ Sided Die
Here's a way to think about it that clearly shows that the results of rolling two simultaneously have the same probability as one after the other:
Since you asked specifically about the chance of failure, lets make that explicit: You correctly noted that the chance of success when rolling simult... | Rolling a $6$ Sided Die
Here's a way to think about it that clearly shows that the results of rolling two simultaneously have the same probability as one after the other:
Since you asked specifically about the chance of fail |
51,869 | Difference between Pearson's r ~= 0 and p > 0.05 | The p-values and Pearson's correlation coefficient $r$ measure different things.
$r$ measures the strength of the correlation. The p-value, on the other hand, measures how likely you would be to observe a correlation of this strength under the null hypothesis - e.g., under the assumption that your random variables are ... | Difference between Pearson's r ~= 0 and p > 0.05 | The p-values and Pearson's correlation coefficient $r$ measure different things.
$r$ measures the strength of the correlation. The p-value, on the other hand, measures how likely you would be to obser | Difference between Pearson's r ~= 0 and p > 0.05
The p-values and Pearson's correlation coefficient $r$ measure different things.
$r$ measures the strength of the correlation. The p-value, on the other hand, measures how likely you would be to observe a correlation of this strength under the null hypothesis - e.g., und... | Difference between Pearson's r ~= 0 and p > 0.05
The p-values and Pearson's correlation coefficient $r$ measure different things.
$r$ measures the strength of the correlation. The p-value, on the other hand, measures how likely you would be to obser |
51,870 | Difference between Pearson's r ~= 0 and p > 0.05 | I upvoted the answer by rinspy. Here, I’ll try to add a few things.
~ ~ ~
r and p-value measure different things.
The p-value indicates the probability of getting data as extreme† as the observed data assuming that the null hypothesis is true. By our decision rule, if p < alpha, we have sufficient evidence to rejec... | Difference between Pearson's r ~= 0 and p > 0.05 | I upvoted the answer by rinspy. Here, I’ll try to add a few things.
~ ~ ~
r and p-value measure different things.
The p-value indicates the probability of getting data as extreme† as the observed d | Difference between Pearson's r ~= 0 and p > 0.05
I upvoted the answer by rinspy. Here, I’ll try to add a few things.
~ ~ ~
r and p-value measure different things.
The p-value indicates the probability of getting data as extreme† as the observed data assuming that the null hypothesis is true. By our decision rule, i... | Difference between Pearson's r ~= 0 and p > 0.05
I upvoted the answer by rinspy. Here, I’ll try to add a few things.
~ ~ ~
r and p-value measure different things.
The p-value indicates the probability of getting data as extreme† as the observed d |
51,871 | If X can predict Y in regression, why isn't Y guaranteed to predict X? | The answer depends on what you mean by “predict”. If you imply any kind of causation then obviously it is one way road. Suppose sunrise causes you to wake up. If I wake you up in the middle of the night sun will not rise suddenly.
On the other hand, if you mean by predicting an explanatory power of X in a multiple regr... | If X can predict Y in regression, why isn't Y guaranteed to predict X? | The answer depends on what you mean by “predict”. If you imply any kind of causation then obviously it is one way road. Suppose sunrise causes you to wake up. If I wake you up in the middle of the nig | If X can predict Y in regression, why isn't Y guaranteed to predict X?
The answer depends on what you mean by “predict”. If you imply any kind of causation then obviously it is one way road. Suppose sunrise causes you to wake up. If I wake you up in the middle of the night sun will not rise suddenly.
On the other hand,... | If X can predict Y in regression, why isn't Y guaranteed to predict X?
The answer depends on what you mean by “predict”. If you imply any kind of causation then obviously it is one way road. Suppose sunrise causes you to wake up. If I wake you up in the middle of the nig |
51,872 | If X can predict Y in regression, why isn't Y guaranteed to predict X? | When you use the regression equation to make a prediction by plugging in a value of $x$, you are not predicting the value of $y$ for that value of $x$. You are predicting the mean of the $y$-values for that value of $x$. In detail:
The regression equation
$$y = \beta_0 + \beta_1 x + \epsilon$$
says that $y$ is equal to... | If X can predict Y in regression, why isn't Y guaranteed to predict X? | When you use the regression equation to make a prediction by plugging in a value of $x$, you are not predicting the value of $y$ for that value of $x$. You are predicting the mean of the $y$-values fo | If X can predict Y in regression, why isn't Y guaranteed to predict X?
When you use the regression equation to make a prediction by plugging in a value of $x$, you are not predicting the value of $y$ for that value of $x$. You are predicting the mean of the $y$-values for that value of $x$. In detail:
The regression eq... | If X can predict Y in regression, why isn't Y guaranteed to predict X?
When you use the regression equation to make a prediction by plugging in a value of $x$, you are not predicting the value of $y$ for that value of $x$. You are predicting the mean of the $y$-values fo |
51,873 | If X can predict Y in regression, why isn't Y guaranteed to predict X? | This is an interesting question. In the case of single variable linear regression, there is a (assumption) symmetric relationship but the same is not true for multiple linear regression.
A symmetric relationship can exist for some problems, a contrived example is training a linear regression model to behave like an AND... | If X can predict Y in regression, why isn't Y guaranteed to predict X? | This is an interesting question. In the case of single variable linear regression, there is a (assumption) symmetric relationship but the same is not true for multiple linear regression.
A symmetric r | If X can predict Y in regression, why isn't Y guaranteed to predict X?
This is an interesting question. In the case of single variable linear regression, there is a (assumption) symmetric relationship but the same is not true for multiple linear regression.
A symmetric relationship can exist for some problems, a contri... | If X can predict Y in regression, why isn't Y guaranteed to predict X?
This is an interesting question. In the case of single variable linear regression, there is a (assumption) symmetric relationship but the same is not true for multiple linear regression.
A symmetric r |
51,874 | SVM - why quadratic programming problem? | Because the optimal separating hyperplane between classes of data
\begin{equation}
D(\mathbf{x})=\mathbf{w}^T\mathbf{x} + b = c \quad \quad -1 < c < 1,
\end{equation}
is found by minimizing the objective function
\begin{equation}
\begin{split}
Q(\mathbf{w})&=\frac{1}{2} ||\mathbf{w}||^2\\
\mathrm{w.r.t } & \quad y_i(... | SVM - why quadratic programming problem? | Because the optimal separating hyperplane between classes of data
\begin{equation}
D(\mathbf{x})=\mathbf{w}^T\mathbf{x} + b = c \quad \quad -1 < c < 1,
\end{equation}
is found by minimizing the obje | SVM - why quadratic programming problem?
Because the optimal separating hyperplane between classes of data
\begin{equation}
D(\mathbf{x})=\mathbf{w}^T\mathbf{x} + b = c \quad \quad -1 < c < 1,
\end{equation}
is found by minimizing the objective function
\begin{equation}
\begin{split}
Q(\mathbf{w})&=\frac{1}{2} ||\mat... | SVM - why quadratic programming problem?
Because the optimal separating hyperplane between classes of data
\begin{equation}
D(\mathbf{x})=\mathbf{w}^T\mathbf{x} + b = c \quad \quad -1 < c < 1,
\end{equation}
is found by minimizing the obje |
51,875 | SVM - why quadratic programming problem? | In order to find an optimal separating hyperplane, the norm of the weight vector $||\overline{w}||$ should be minimized, subject to constraints $y_i(\overline{w} \cdot \varphi(x_i) + b) ≥ 1 − \xi_i$, $\xi_i \geqslant 0, i=1,\dots, l$ (see here).
While it's technically possible to minimize $\mathcal{l}^1$-norm $||\overl... | SVM - why quadratic programming problem? | In order to find an optimal separating hyperplane, the norm of the weight vector $||\overline{w}||$ should be minimized, subject to constraints $y_i(\overline{w} \cdot \varphi(x_i) + b) ≥ 1 − \xi_i$, | SVM - why quadratic programming problem?
In order to find an optimal separating hyperplane, the norm of the weight vector $||\overline{w}||$ should be minimized, subject to constraints $y_i(\overline{w} \cdot \varphi(x_i) + b) ≥ 1 − \xi_i$, $\xi_i \geqslant 0, i=1,\dots, l$ (see here).
While it's technically possible t... | SVM - why quadratic programming problem?
In order to find an optimal separating hyperplane, the norm of the weight vector $||\overline{w}||$ should be minimized, subject to constraints $y_i(\overline{w} \cdot \varphi(x_i) + b) ≥ 1 − \xi_i$, |
51,876 | SVM - why quadratic programming problem? | This has nothing to do with the L1 norm. Both are the Euclidean norm. Conversion to QP is due to practical reasons so that the gradient is continuous at the origin.
See https://math.stackexchange.com/a/439168/532462 | SVM - why quadratic programming problem? | This has nothing to do with the L1 norm. Both are the Euclidean norm. Conversion to QP is due to practical reasons so that the gradient is continuous at the origin.
See https://math.stackexchange.com/ | SVM - why quadratic programming problem?
This has nothing to do with the L1 norm. Both are the Euclidean norm. Conversion to QP is due to practical reasons so that the gradient is continuous at the origin.
See https://math.stackexchange.com/a/439168/532462 | SVM - why quadratic programming problem?
This has nothing to do with the L1 norm. Both are the Euclidean norm. Conversion to QP is due to practical reasons so that the gradient is continuous at the origin.
See https://math.stackexchange.com/ |
51,877 | Is it logical to use correlation between percentages | One reason that someone might assert that "you cannot run correlation on percentages" is that percentages are bounded by [0, 1], and the underlying assumption of the Pearson r test is that values are normally distributed; these are manifestly incompatible.
If your percentages are concentrated in a not-too-wide band not... | Is it logical to use correlation between percentages | One reason that someone might assert that "you cannot run correlation on percentages" is that percentages are bounded by [0, 1], and the underlying assumption of the Pearson r test is that values are | Is it logical to use correlation between percentages
One reason that someone might assert that "you cannot run correlation on percentages" is that percentages are bounded by [0, 1], and the underlying assumption of the Pearson r test is that values are normally distributed; these are manifestly incompatible.
If your pe... | Is it logical to use correlation between percentages
One reason that someone might assert that "you cannot run correlation on percentages" is that percentages are bounded by [0, 1], and the underlying assumption of the Pearson r test is that values are |
51,878 | Is it logical to use correlation between percentages | The video you linked here in one of your comments makes reference to compositional data. This would be an issue if you tried to compare percentages adding up to $100\%$, but this is not the case in your question. Regardless of whether you express the variable independent contractors as counts or a percentage, it wouldn... | Is it logical to use correlation between percentages | The video you linked here in one of your comments makes reference to compositional data. This would be an issue if you tried to compare percentages adding up to $100\%$, but this is not the case in yo | Is it logical to use correlation between percentages
The video you linked here in one of your comments makes reference to compositional data. This would be an issue if you tried to compare percentages adding up to $100\%$, but this is not the case in your question. Regardless of whether you express the variable indepen... | Is it logical to use correlation between percentages
The video you linked here in one of your comments makes reference to compositional data. This would be an issue if you tried to compare percentages adding up to $100\%$, but this is not the case in yo |
51,879 | Is it logical to use correlation between percentages | Where did you read that you cannot use correlation between percentages? I think that the meaning of the correlation coefficient will be preserved (e.g "If X increases, Y is likely to increase." or "High values of X are associated with high values of Y."), so correlation is fair game.
One thing to watch out for may be ... | Is it logical to use correlation between percentages | Where did you read that you cannot use correlation between percentages? I think that the meaning of the correlation coefficient will be preserved (e.g "If X increases, Y is likely to increase." or "H | Is it logical to use correlation between percentages
Where did you read that you cannot use correlation between percentages? I think that the meaning of the correlation coefficient will be preserved (e.g "If X increases, Y is likely to increase." or "High values of X are associated with high values of Y."), so correla... | Is it logical to use correlation between percentages
Where did you read that you cannot use correlation between percentages? I think that the meaning of the correlation coefficient will be preserved (e.g "If X increases, Y is likely to increase." or "H |
51,880 | Quadratic effect in OLS regression | You don't have to use a linear term to use a quadratic, but it's usually a good idea. The only situation I wouldn't use it is when your theory tells you that you have a quadratic process. For instance, if you somehow are measuring kinetic energy as a function of speed, then there's no linear term in theory:
$$e=m\frac{... | Quadratic effect in OLS regression | You don't have to use a linear term to use a quadratic, but it's usually a good idea. The only situation I wouldn't use it is when your theory tells you that you have a quadratic process. For instance | Quadratic effect in OLS regression
You don't have to use a linear term to use a quadratic, but it's usually a good idea. The only situation I wouldn't use it is when your theory tells you that you have a quadratic process. For instance, if you somehow are measuring kinetic energy as a function of speed, then there's no... | Quadratic effect in OLS regression
You don't have to use a linear term to use a quadratic, but it's usually a good idea. The only situation I wouldn't use it is when your theory tells you that you have a quadratic process. For instance |
51,881 | Quadratic effect in OLS regression | In my experience, I would say yes you would always adjust for lower level terms when fitting polynomial trends. This is the approach that is advocated in most of the biostatistics textbooks I've encountered. The reason for this is that the terms are guaranteed to have the correct interpretation. For instance, if you om... | Quadratic effect in OLS regression | In my experience, I would say yes you would always adjust for lower level terms when fitting polynomial trends. This is the approach that is advocated in most of the biostatistics textbooks I've encou | Quadratic effect in OLS regression
In my experience, I would say yes you would always adjust for lower level terms when fitting polynomial trends. This is the approach that is advocated in most of the biostatistics textbooks I've encountered. The reason for this is that the terms are guaranteed to have the correct inte... | Quadratic effect in OLS regression
In my experience, I would say yes you would always adjust for lower level terms when fitting polynomial trends. This is the approach that is advocated in most of the biostatistics textbooks I've encou |
51,882 | In residual sum of squares, why do we need to square? [duplicate] | Squaring the residuals changes the shape of the regularization function. In particular, large errors are penalized more with the square of the error. Imagine two cases, one where you have one point with an error of 0 and another with an error of 10, versus another case where you have two points with an error of 5. The ... | In residual sum of squares, why do we need to square? [duplicate] | Squaring the residuals changes the shape of the regularization function. In particular, large errors are penalized more with the square of the error. Imagine two cases, one where you have one point wi | In residual sum of squares, why do we need to square? [duplicate]
Squaring the residuals changes the shape of the regularization function. In particular, large errors are penalized more with the square of the error. Imagine two cases, one where you have one point with an error of 0 and another with an error of 10, vers... | In residual sum of squares, why do we need to square? [duplicate]
Squaring the residuals changes the shape of the regularization function. In particular, large errors are penalized more with the square of the error. Imagine two cases, one where you have one point wi |
51,883 | In residual sum of squares, why do we need to square? [duplicate] | @ocram's answer is good, but one point I'd add is the connection between least squares and maximum likelihood estimation. If we have a regression model of the form $y_i = \beta_0 + \sum_{j=1}^{p} \beta_j x_{ij} + \epsilon_i$ where the $\epsilon_i$ are independent normal$(0, \sigma^2)$ random variables then the likelih... | In residual sum of squares, why do we need to square? [duplicate] | @ocram's answer is good, but one point I'd add is the connection between least squares and maximum likelihood estimation. If we have a regression model of the form $y_i = \beta_0 + \sum_{j=1}^{p} \be | In residual sum of squares, why do we need to square? [duplicate]
@ocram's answer is good, but one point I'd add is the connection between least squares and maximum likelihood estimation. If we have a regression model of the form $y_i = \beta_0 + \sum_{j=1}^{p} \beta_j x_{ij} + \epsilon_i$ where the $\epsilon_i$ are i... | In residual sum of squares, why do we need to square? [duplicate]
@ocram's answer is good, but one point I'd add is the connection between least squares and maximum likelihood estimation. If we have a regression model of the form $y_i = \beta_0 + \sum_{j=1}^{p} \be |
51,884 | In residual sum of squares, why do we need to square? [duplicate] | If you do not square, a negative residual (below the line) can offset the impact of a positive residual (above the line). Squaring is a remedy. Taking the absolute values of the residuals provides an alternative. But squaring is much easier to handle from a mathematical point of view (cf. derivatives). | In residual sum of squares, why do we need to square? [duplicate] | If you do not square, a negative residual (below the line) can offset the impact of a positive residual (above the line). Squaring is a remedy. Taking the absolute values of the residuals provides an | In residual sum of squares, why do we need to square? [duplicate]
If you do not square, a negative residual (below the line) can offset the impact of a positive residual (above the line). Squaring is a remedy. Taking the absolute values of the residuals provides an alternative. But squaring is much easier to handle fro... | In residual sum of squares, why do we need to square? [duplicate]
If you do not square, a negative residual (below the line) can offset the impact of a positive residual (above the line). Squaring is a remedy. Taking the absolute values of the residuals provides an |
51,885 | Why does this neural network in keras fail so badly? | Here are a few observations:
Your first layer of a single sigmoid neuron is a big bottleneck. Unless you are very lucky and the neuron is initialised to map your input onto the near-linear central part of the sigmoid, you end up with unnecessary information loss and vanishing gradient in the first layer right from the... | Why does this neural network in keras fail so badly? | Here are a few observations:
Your first layer of a single sigmoid neuron is a big bottleneck. Unless you are very lucky and the neuron is initialised to map your input onto the near-linear central pa | Why does this neural network in keras fail so badly?
Here are a few observations:
Your first layer of a single sigmoid neuron is a big bottleneck. Unless you are very lucky and the neuron is initialised to map your input onto the near-linear central part of the sigmoid, you end up with unnecessary information loss and... | Why does this neural network in keras fail so badly?
Here are a few observations:
Your first layer of a single sigmoid neuron is a big bottleneck. Unless you are very lucky and the neuron is initialised to map your input onto the near-linear central pa |
51,886 | Normalizing logistic regression coefficients? | The short answer is that normalizing the coefficients will not affect the predictions, but it will mess up the estimated class probabilities. Don't do it.
The coefficients don't represent the odds ratios but rather the feature weights. They can be negative. If a coefficient is strongly positive, it means that the corre... | Normalizing logistic regression coefficients? | The short answer is that normalizing the coefficients will not affect the predictions, but it will mess up the estimated class probabilities. Don't do it.
The coefficients don't represent the odds rat | Normalizing logistic regression coefficients?
The short answer is that normalizing the coefficients will not affect the predictions, but it will mess up the estimated class probabilities. Don't do it.
The coefficients don't represent the odds ratios but rather the feature weights. They can be negative. If a coefficient... | Normalizing logistic regression coefficients?
The short answer is that normalizing the coefficients will not affect the predictions, but it will mess up the estimated class probabilities. Don't do it.
The coefficients don't represent the odds rat |
51,887 | Normalizing logistic regression coefficients? | The correct way to compare coefficients on the same scale is to rescale the predictors themselves. A common transformation is to turn continuous predictors into Z-scores by subtracting the sample mean and dividing by the sample standard deviation. (Gelman[1] recommends two standard deviations)
This will change the valu... | Normalizing logistic regression coefficients? | The correct way to compare coefficients on the same scale is to rescale the predictors themselves. A common transformation is to turn continuous predictors into Z-scores by subtracting the sample mean | Normalizing logistic regression coefficients?
The correct way to compare coefficients on the same scale is to rescale the predictors themselves. A common transformation is to turn continuous predictors into Z-scores by subtracting the sample mean and dividing by the sample standard deviation. (Gelman[1] recommends two ... | Normalizing logistic regression coefficients?
The correct way to compare coefficients on the same scale is to rescale the predictors themselves. A common transformation is to turn continuous predictors into Z-scores by subtracting the sample mean |
51,888 | Normalizing logistic regression coefficients? | To show the relative contribution of each predictor, and to be able to handle the common case where the predictor is represented by multiple variables (indicator variables or nonlinear terms), I prefer to make a dot chart of the chunk test partial $\chi^2$ statistic for each predictor. You can also get a meaningful ch... | Normalizing logistic regression coefficients? | To show the relative contribution of each predictor, and to be able to handle the common case where the predictor is represented by multiple variables (indicator variables or nonlinear terms), I prefe | Normalizing logistic regression coefficients?
To show the relative contribution of each predictor, and to be able to handle the common case where the predictor is represented by multiple variables (indicator variables or nonlinear terms), I prefer to make a dot chart of the chunk test partial $\chi^2$ statistic for eac... | Normalizing logistic regression coefficients?
To show the relative contribution of each predictor, and to be able to handle the common case where the predictor is represented by multiple variables (indicator variables or nonlinear terms), I prefe |
51,889 | Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to one that does not integrate to a finite value? | Strictly speaking, an everywhere non-negative prior that integrated to some finite positive value other than 1 would not be a proper density and so arguably could in that sense be referred to as "improper", but since
(a) if it integrates to $k$, say, it's easy enough to scale if you need that
(b) frequently in Bayesian... | Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to on | Strictly speaking, an everywhere non-negative prior that integrated to some finite positive value other than 1 would not be a proper density and so arguably could in that sense be referred to as "impr | Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to one that does not integrate to a finite value?
Strictly speaking, an everywhere non-negative prior that integrated to some finite positive value other than 1 would not be a proper density and so arguably could in that sens... | Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to on
Strictly speaking, an everywhere non-negative prior that integrated to some finite positive value other than 1 would not be a proper density and so arguably could in that sense be referred to as "impr |
51,890 | Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to one that does not integrate to a finite value? | A density function integrates to infinity, then the density function is termed as being "improper". A pdf is termed as being "proper" if it integrates to a finite quantity.
Ideally, a proper function will integrate to 1. However, sometimes density functions are known only up to a normalizing constant. That is $p(x) = c... | Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to on | A density function integrates to infinity, then the density function is termed as being "improper". A pdf is termed as being "proper" if it integrates to a finite quantity.
Ideally, a proper function | Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to one that does not integrate to a finite value?
A density function integrates to infinity, then the density function is termed as being "improper". A pdf is termed as being "proper" if it integrates to a finite quantity.
Id... | Does "improper" posterior or prior refer to a density function that does not integrate to 1 or to on
A density function integrates to infinity, then the density function is termed as being "improper". A pdf is termed as being "proper" if it integrates to a finite quantity.
Ideally, a proper function |
51,891 | Making up for a low sample size by increasing the number of observations | Another way to look at this is to consider that all the measures you take reflect a systematic source of variance (which you are interested in) compounded by various sources of errors (i.e. variance you are not interested in).
Depending on your objectives and the relative magnitude of these sources of errors, different... | Making up for a low sample size by increasing the number of observations | Another way to look at this is to consider that all the measures you take reflect a systematic source of variance (which you are interested in) compounded by various sources of errors (i.e. variance y | Making up for a low sample size by increasing the number of observations
Another way to look at this is to consider that all the measures you take reflect a systematic source of variance (which you are interested in) compounded by various sources of errors (i.e. variance you are not interested in).
Depending on your ob... | Making up for a low sample size by increasing the number of observations
Another way to look at this is to consider that all the measures you take reflect a systematic source of variance (which you are interested in) compounded by various sources of errors (i.e. variance y |
51,892 | Making up for a low sample size by increasing the number of observations | Simple counter-example would be probably enough for you to figure the answer yourself. Say, that you have to make a study on human height, however you do not have enough time to conduct a full-scale survey. In this case you decide to ask your roommate 1000 times about his height. | Making up for a low sample size by increasing the number of observations | Simple counter-example would be probably enough for you to figure the answer yourself. Say, that you have to make a study on human height, however you do not have enough time to conduct a full-scale s | Making up for a low sample size by increasing the number of observations
Simple counter-example would be probably enough for you to figure the answer yourself. Say, that you have to make a study on human height, however you do not have enough time to conduct a full-scale survey. In this case you decide to ask your room... | Making up for a low sample size by increasing the number of observations
Simple counter-example would be probably enough for you to figure the answer yourself. Say, that you have to make a study on human height, however you do not have enough time to conduct a full-scale s |
51,893 | Making up for a low sample size by increasing the number of observations | Asking the same person to perform the same trial will increase your information about within-person variance but not between-person variance. If within-person variance is what you're interested in, then the logic makes sense. If it's not what you're interested in, then it doesn't. | Making up for a low sample size by increasing the number of observations | Asking the same person to perform the same trial will increase your information about within-person variance but not between-person variance. If within-person variance is what you're interested in, th | Making up for a low sample size by increasing the number of observations
Asking the same person to perform the same trial will increase your information about within-person variance but not between-person variance. If within-person variance is what you're interested in, then the logic makes sense. If it's not what you'... | Making up for a low sample size by increasing the number of observations
Asking the same person to perform the same trial will increase your information about within-person variance but not between-person variance. If within-person variance is what you're interested in, th |
51,894 | How to calculate SE of an odds ratio | @FrankHarrell is right that the standard error for an odds ratio is a problematic number in the sense that you can do better by testing on the corresponding log(odds ratio) scale, as the sampling distribution of the log(odds ratio) is more likely to be normally distributed.
Nonetheless, the standard error of the odds r... | How to calculate SE of an odds ratio | @FrankHarrell is right that the standard error for an odds ratio is a problematic number in the sense that you can do better by testing on the corresponding log(odds ratio) scale, as the sampling dist | How to calculate SE of an odds ratio
@FrankHarrell is right that the standard error for an odds ratio is a problematic number in the sense that you can do better by testing on the corresponding log(odds ratio) scale, as the sampling distribution of the log(odds ratio) is more likely to be normally distributed.
Nonethel... | How to calculate SE of an odds ratio
@FrankHarrell is right that the standard error for an odds ratio is a problematic number in the sense that you can do better by testing on the corresponding log(odds ratio) scale, as the sampling dist |
51,895 | How to calculate SE of an odds ratio | OR is not a valid quantity to compute a SE of in the sense that it cannot have a symmetric distribution. Applying +/- SE to it may lead to negative ORs. | How to calculate SE of an odds ratio | OR is not a valid quantity to compute a SE of in the sense that it cannot have a symmetric distribution. Applying +/- SE to it may lead to negative ORs. | How to calculate SE of an odds ratio
OR is not a valid quantity to compute a SE of in the sense that it cannot have a symmetric distribution. Applying +/- SE to it may lead to negative ORs. | How to calculate SE of an odds ratio
OR is not a valid quantity to compute a SE of in the sense that it cannot have a symmetric distribution. Applying +/- SE to it may lead to negative ORs. |
51,896 | How to calculate SE of an odds ratio | Instead of a standard error why not compute the standard deviation of the posterior distribution of the OR? You can solve for it numerically very easily using an MCMC sampler.
Here is some R and JAGS code to do so.
################################################################
### ... | How to calculate SE of an odds ratio | Instead of a standard error why not compute the standard deviation of the posterior distribution of the OR? You can solve for it numerically very easily using an MCMC sampler.
Here is some R and JAGS | How to calculate SE of an odds ratio
Instead of a standard error why not compute the standard deviation of the posterior distribution of the OR? You can solve for it numerically very easily using an MCMC sampler.
Here is some R and JAGS code to do so.
################################################################
##... | How to calculate SE of an odds ratio
Instead of a standard error why not compute the standard deviation of the posterior distribution of the OR? You can solve for it numerically very easily using an MCMC sampler.
Here is some R and JAGS |
51,897 | What does "Virgin Data" mean? | When the virgin flag is set to FALSE, it indicates that all data in the training and testing sets have corresponding labels.
When the virgin flag is set to TRUE, it indicates that the testing set is unclassified data with no known true values. | What does "Virgin Data" mean? | When the virgin flag is set to FALSE, it indicates that all data in the training and testing sets have corresponding labels.
When the virgin flag is set to TRUE, it indicates that the testing set is u | What does "Virgin Data" mean?
When the virgin flag is set to FALSE, it indicates that all data in the training and testing sets have corresponding labels.
When the virgin flag is set to TRUE, it indicates that the testing set is unclassified data with no known true values. | What does "Virgin Data" mean?
When the virgin flag is set to FALSE, it indicates that all data in the training and testing sets have corresponding labels.
When the virgin flag is set to TRUE, it indicates that the testing set is u |
51,898 | What does "Virgin Data" mean? | The answer by @pratik_m is correct.
As a historical note, this terminology comes from Laver et al. 2003. Although it's not stated explicitly, Laver et al. use 'virgin' to refer to a document that a) has no target value because b) it is out of sample. What makes things confusing is that in the paper (though not in RTe... | What does "Virgin Data" mean? | The answer by @pratik_m is correct.
As a historical note, this terminology comes from Laver et al. 2003. Although it's not stated explicitly, Laver et al. use 'virgin' to refer to a document that a) | What does "Virgin Data" mean?
The answer by @pratik_m is correct.
As a historical note, this terminology comes from Laver et al. 2003. Although it's not stated explicitly, Laver et al. use 'virgin' to refer to a document that a) has no target value because b) it is out of sample. What makes things confusing is that i... | What does "Virgin Data" mean?
The answer by @pratik_m is correct.
As a historical note, this terminology comes from Laver et al. 2003. Although it's not stated explicitly, Laver et al. use 'virgin' to refer to a document that a) |
51,899 | Weird fitted values/residuals plot | You can answer the question for yourself with simple mathematics. If observed $y \ge 0$ and $\hat y$ denotes fitted $y$, then residual $e = y - \hat y$ must be $\ge -\hat y$. The line $e = - \hat y$ is thus a lower limit on your residuals. Despite your unconventional axis choice, it is clear that your data follow s... | Weird fitted values/residuals plot | You can answer the question for yourself with simple mathematics. If observed $y \ge 0$ and $\hat y$ denotes fitted $y$, then residual $e = y - \hat y$ must be $\ge -\hat y$. The line $e = - \hat | Weird fitted values/residuals plot
You can answer the question for yourself with simple mathematics. If observed $y \ge 0$ and $\hat y$ denotes fitted $y$, then residual $e = y - \hat y$ must be $\ge -\hat y$. The line $e = - \hat y$ is thus a lower limit on your residuals. Despite your unconventional axis choice, ... | Weird fitted values/residuals plot
You can answer the question for yourself with simple mathematics. If observed $y \ge 0$ and $\hat y$ denotes fitted $y$, then residual $e = y - \hat y$ must be $\ge -\hat y$. The line $e = - \hat |
51,900 | Weird fitted values/residuals plot | There are two major aspects I see in the plot that I expect you might wonder about.
(I took the liberty of flipping your plot about to the way I'm more used to looking at them, with the random quantity on the y-axis.)
The first aspect is what looks like hard lower bound on the y-values (which is presumably 0), as you ... | Weird fitted values/residuals plot | There are two major aspects I see in the plot that I expect you might wonder about.
(I took the liberty of flipping your plot about to the way I'm more used to looking at them, with the random quanti | Weird fitted values/residuals plot
There are two major aspects I see in the plot that I expect you might wonder about.
(I took the liberty of flipping your plot about to the way I'm more used to looking at them, with the random quantity on the y-axis.)
The first aspect is what looks like hard lower bound on the y-valu... | Weird fitted values/residuals plot
There are two major aspects I see in the plot that I expect you might wonder about.
(I took the liberty of flipping your plot about to the way I'm more used to looking at them, with the random quanti |
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