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Deviations above the mean, above the mean. You could view this as a z-score. It's a z-score of 2.1. We are 2.1 above the mean in this situation. Now let's think about how he did on the MCAT. On the MCAT, he scored a 37. He scored a 37. | Comparing with z-scores Modeling data distributions AP Statistics Khan Academy.mp3 |
We are 2.1 above the mean in this situation. Now let's think about how he did on the MCAT. On the MCAT, he scored a 37. He scored a 37. The mean is a 25.1. And there is a standard deviation of 6.4. So let's see, 37.1 minus 25 would be 12, but now it's gonna be 11.9. | Comparing with z-scores Modeling data distributions AP Statistics Khan Academy.mp3 |
He scored a 37. The mean is a 25.1. And there is a standard deviation of 6.4. So let's see, 37.1 minus 25 would be 12, but now it's gonna be 11.9. 11.9 divided by 6.4. So without even looking at this, this is going to be approximately, well, this is gonna be a little bit less than two. This is going to be less than two... | Comparing with z-scores Modeling data distributions AP Statistics Khan Academy.mp3 |
So let's see, 37.1 minus 25 would be 12, but now it's gonna be 11.9. 11.9 divided by 6.4. So without even looking at this, this is going to be approximately, well, this is gonna be a little bit less than two. This is going to be less than two. So based on this information, and we could figure out the exact number here.... | Comparing with z-scores Modeling data distributions AP Statistics Khan Academy.mp3 |
This is going to be less than two. So based on this information, and we could figure out the exact number here. In fact, let me get my calculator out. So you get the calculator. So if we do 11.9 divided by 6.4, that's gonna get us to 1 point, I'll just say approximately 1.86. So approximately 1.86. So relatively speaki... | Comparing with z-scores Modeling data distributions AP Statistics Khan Academy.mp3 |
So you get the calculator. So if we do 11.9 divided by 6.4, that's gonna get us to 1 point, I'll just say approximately 1.86. So approximately 1.86. So relatively speaking, he did slightly better on the LSAT. He did more standard deviations, although this is close. I would say they're comparable. He did roughly two sta... | Comparing with z-scores Modeling data distributions AP Statistics Khan Academy.mp3 |
So relatively speaking, he did slightly better on the LSAT. He did more standard deviations, although this is close. I would say they're comparable. He did roughly two standard deviations if we were around to the nearest standard deviation, but if you wanted to get precise, he did a little bit better, relatively speaki... | Comparing with z-scores Modeling data distributions AP Statistics Khan Academy.mp3 |
So here it tells us Cheryl Dixon is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake in milligrams and the number of hours spent studying. A scatterplot of the data showed a linear relationship. This is a... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
This is a computer output from a least squares regression analysis on the data. So we have these things called the predictors, coefficient, and then we have these other things, standard error of coefficient, T and P, and then all of these things down here. How do we make sense of this in order to come up with an equati... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
So let's just get straight on our variables. Let's just say that we say that Y is the thing that we're trying to predict. So this is the hours spent studying, hours studying, and then let's say X is what we think explains the hours studying or is one of the things that explains the hours studying, and this is the amoun... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
So this is caffeine consumed in milligrams. And so our regression line would have the form Y hat. This tells us that this is a linear regression. It's trying to estimate the actual Y values for given Xs. It's going to be equal to MX plus B. Now how do we figure out what M and B are based on this computer output? So whe... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
It's trying to estimate the actual Y values for given Xs. It's going to be equal to MX plus B. Now how do we figure out what M and B are based on this computer output? So when you look at this table here, this first column says predictor, and it says constant, and it has caffeine. And so all this is saying is when you'... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
So when you look at this table here, this first column says predictor, and it says constant, and it has caffeine. And so all this is saying is when you're trying to predict the number of hours studying, when you're trying to predict Y, there's essentially two inputs there. There is the constant value, and there is your... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
And so this tells you the coefficients on each. The coefficient on a constant is the constant. You could view this as the coefficient on the X to the zeroth term. And so the coefficient on the constant, that is the constant, 2.544. And then the coefficient on the caffeine, well, we just said that X is the caffeine cons... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
And so the coefficient on the constant, that is the constant, 2.544. And then the coefficient on the caffeine, well, we just said that X is the caffeine consumed, so this is that coefficient, 0.164. So just like that, we actually have the equation for the regression line. That is why these computer things are useful. S... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
That is why these computer things are useful. So we can just write it out. Y hat is equal to 0.164X plus 2.544, 2.544. So that's the regression line. What is this other information they give us? Well, I won't give you a very satisfying answer because all of this is actually useful for inferential statistics. To think a... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
So that's the regression line. What is this other information they give us? Well, I won't give you a very satisfying answer because all of this is actually useful for inferential statistics. To think about things like, well, what is the probability that this is chance that we got something to fit this well? So this rig... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
To think about things like, well, what is the probability that this is chance that we got something to fit this well? So this right over here is the R squared. And if you wanted to figure out the R from this, you would just take the square root here. We could say that R is going to be equal to the square root of 0.6003... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
We could say that R is going to be equal to the square root of 0.60032, depending on how much precision you have. But you might say, well, how do we know if R is a positive square root or the negative square root of that? R can take on values between negative one and positive one. And the answer is, you would look at t... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
And the answer is, you would look at the slope here. We have a positive slope, which tells us that R is going to be positive. If we had a negative slope, then we would take the negative square root. Now, this right here is the adjusted R squared. And we really don't have to worry about it too much when we're thinking a... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
Now, this right here is the adjusted R squared. And we really don't have to worry about it too much when we're thinking about just bivariate data. We're talking about caffeine and hour studying in this case. If we started to have more variables that tried to explain the hour studying, then we would care about adjusted ... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
If we started to have more variables that tried to explain the hour studying, then we would care about adjusted R squared, but we're not gonna do that just yet. Last but not least, this S variable, this is the standard deviation of the residuals, which we study in other videos. And why is that useful? Well, that's a me... | Interpreting computer regression data AP Statistics Khan Academy.mp3 |
So let's say you were to go to a restaurant, and just out of curiosity, you want to see what the makeup of the ages at the restaurant are. So you go around the restaurant, and you write down everyone's age. And so these are the ages of everyone in the restaurant at that moment. And so you're interested in somehow prese... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
And so you're interested in somehow presenting this, somehow visualizing the distribution of the ages, because you want to just say, well, are there more young people, are there more teenagers, are there more middle-aged people, are there more seniors here? And so when you just look at these numbers, it really doesn't ... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
And so how could you do that? Well, one way to think about it is is to put these ages into different buckets, and then to think about how many people are there in each of those buckets, or sometimes someone might say, how many in each of those bins? So let's do that. So let's do buckets or categories. So I like, someti... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
So let's do buckets or categories. So I like, sometimes it's called a bin. So the bucket, I like to think of it more as a bucket. The bucket, and then the number in the bucket. The number in the bucket. Number, I'll just write the number, whoops. It's the, whoops. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
The bucket, and then the number in the bucket. The number in the bucket. Number, I'll just write the number, whoops. It's the, whoops. It's the number. It's the number in the bucket. All right, so let's just make buckets, let's make them 10-year ranges. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
It's the, whoops. It's the number. It's the number in the bucket. All right, so let's just make buckets, let's make them 10-year ranges. So let's say the first one is ages zero to nine. So how many people, and we just define all of the buckets here. So the next one is ages 10 to 19, then 20 to 29, then 30 to 39, and 40... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
All right, so let's just make buckets, let's make them 10-year ranges. So let's say the first one is ages zero to nine. So how many people, and we just define all of the buckets here. So the next one is ages 10 to 19, then 20 to 29, then 30 to 39, and 40 to 49, 50 to 59. Make sure you can read that properly. Then you h... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
So the next one is ages 10 to 19, then 20 to 29, then 30 to 39, and 40 to 49, 50 to 59. Make sure you can read that properly. Then you have 60 to 69. I think that covers everyone. I don't see anyone 70 years old or older here. So then how many people fall into the zero to nine-year-old bucket? Well, it's gonna be one, ... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
I think that covers everyone. I don't see anyone 70 years old or older here. So then how many people fall into the zero to nine-year-old bucket? Well, it's gonna be one, two, three, four, five, six people fall into that bucket. How many people fall into the, how many people fall into the 10 to 19-year-old bucket? Well,... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
Well, it's gonna be one, two, three, four, five, six people fall into that bucket. How many people fall into the, how many people fall into the 10 to 19-year-old bucket? Well, let's see. One, two, three. Three people. And I think you see where this is going. What about 20 to 29? | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
One, two, three. Three people. And I think you see where this is going. What about 20 to 29? So it's one, two, three, four, five people. Five people fall into that bucket. All right, what about 30 to 39? | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
What about 20 to 29? So it's one, two, three, four, five people. Five people fall into that bucket. All right, what about 30 to 39? We have one, and that's it. Only one person in that 30 to 39 bin or bucket or category. All right, what about 40 to 49? | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
All right, what about 30 to 39? We have one, and that's it. Only one person in that 30 to 39 bin or bucket or category. All right, what about 40 to 49? We have one, two people. Two people are in that bucket. And then 50 to 59. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
All right, what about 40 to 49? We have one, two people. Two people are in that bucket. And then 50 to 59. So you have one, two people. Two people. And then finally, finally, ages 60 to 69, let me do it in a different color, 60 to 69, there is one person right over there. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
And then 50 to 59. So you have one, two people. Two people. And then finally, finally, ages 60 to 69, let me do it in a different color, 60 to 69, there is one person right over there. So this is one way of thinking about how the ages are distributed, but let's actually make a visualization of this. And the visualizati... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
And then finally, finally, ages 60 to 69, let me do it in a different color, 60 to 69, there is one person right over there. So this is one way of thinking about how the ages are distributed, but let's actually make a visualization of this. And the visualization that we're gonna create, this is called a histogram. Hist... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
Histogram. Histogram. We're taking data that can take on a whole bunch of different values. We're putting them into categories, and we're gonna plot how many folks are in each category. How big are each of those categories? And actually, I wrote histogram. I wrote histograph, I should have written histogram. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
We're putting them into categories, and we're gonna plot how many folks are in each category. How big are each of those categories? And actually, I wrote histogram. I wrote histograph, I should have written histogram. So a histogram. So let's do this. All right, so on this axis, let's see, the largest category has six. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
I wrote histograph, I should have written histogram. So a histogram. So let's do this. All right, so on this axis, let's see, the largest category has six. So this is the number. Number of folks, and it's gonna go one, two, three, four, five, six. One, two, three, four, five, six. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
All right, so on this axis, let's see, the largest category has six. So this is the number. Number of folks, and it's gonna go one, two, three, four, five, six. One, two, three, four, five, six. This is the number, and on this axis, I'm gonna make the buckets. The buckets, and let me scroll up a little bit now that I h... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
One, two, three, four, five, six. This is the number, and on this axis, I'm gonna make the buckets. The buckets, and let me scroll up a little bit now that I have my data here, I don't have to look at my data set again. So I have one bucket. This is going to be the zero to nine bucket, right over here. Zero to nine. Th... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
So I have one bucket. This is going to be the zero to nine bucket, right over here. Zero to nine. Then I'm going to have the three, actually, let me just plot them, since I have my pen that color. So zero to nine, there are six people. Zero to nine, there are six people. So I'll just plot it like that. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
Then I'm going to have the three, actually, let me just plot them, since I have my pen that color. So zero to nine, there are six people. Zero to nine, there are six people. So I'll just plot it like that. And then we have the 10 to 19. There are three people. So 10 to 19, there are three people. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
So I'll just plot it like that. And then we have the 10 to 19. There are three people. So 10 to 19, there are three people. So I'll do a bar like this. Then 20 to 29, I have five people. 20 to 29, which is gonna be this one, which is getting, I'm writing too big. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
So 10 to 19, there are three people. So I'll do a bar like this. Then 20 to 29, I have five people. 20 to 29, which is gonna be this one, which is getting, I'm writing too big. So 20 to 29, this is gonna be this bar. There's five people. Five people there. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
20 to 29, which is gonna be this one, which is getting, I'm writing too big. So 20 to 29, this is gonna be this bar. There's five people. Five people there. So it'll look like this. I should have made the bars wide enough so I could write below them, but I've already, that train has already left. All right, then 30 to ... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
Five people there. So it'll look like this. I should have made the bars wide enough so I could write below them, but I've already, that train has already left. All right, then 30 to 39. I'll try to write smaller. 30 to 39, that's gonna be this bar right over here. We have one person. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
All right, then 30 to 39. I'll try to write smaller. 30 to 39, that's gonna be this bar right over here. We have one person. One person. And then we have 40 to 49. We have two people. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
We have one person. One person. And then we have 40 to 49. We have two people. 40 to 49, two people. So it looks like this. 40 to 49, two people. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
We have two people. 40 to 49, two people. So it looks like this. 40 to 49, two people. Almost there, 50 to 59. We have two people. 50 to 59, we also have two people. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
40 to 49, two people. Almost there, 50 to 59. We have two people. 50 to 59, we also have two people. So that's that right over there. That's this category. And then finally, 60 to 69, we have one person. | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
50 to 59, we also have two people. So that's that right over there. That's this category. And then finally, 60 to 69, we have one person. 60 to 69, we have one person. We have one person. And what I have just constructed, I took our data, I put it into buckets that are kind of representative of the categories I care ab... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
And then finally, 60 to 69, we have one person. 60 to 69, we have one person. We have one person. And what I have just constructed, I took our data, I put it into buckets that are kind of representative of the categories I care about, zero to nine is kind of young kids, 10 to 19, I guess you could call them adolescents... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
And what I have just constructed, I took our data, I put it into buckets that are kind of representative of the categories I care about, zero to nine is kind of young kids, 10 to 19, I guess you could call them adolescents or roughly teenagers, although obviously if you're 10 you're not quite a teenager yet. And then a... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
This must be some type of a restaurant that gives away toys or something because there's a lot of younger people. Maybe it's very family friendly. So every adult that comes in, maybe there's a lot of young adults with kids or maybe grandparents up here, and they just bring a lot of kids to this restaurant. So it gives ... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
So it gives you a view of what's going on here. Just a lot of kids here, a lot fewer senior citizens. So once again, this is just a way of visualizing things. We took a lot of data that can take multiple data points. Instead of plotting each data point like we might do in a dot plot, instead of saying how many one year... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
We took a lot of data that can take multiple data points. Instead of plotting each data point like we might do in a dot plot, instead of saying how many one year olds are there, well there's only one one year old, how many three year olds are there? There's only one three year old. That wouldn't give us much informatio... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
That wouldn't give us much information. We would just have like these single dots if we were doing a dot plot. But as a histogram, we're able to put them into buckets. And we're just like, hey, generally between the ages zero and nine, we have six people. And so you see that plotted out just like that. And obviously th... | How to create a histogram Data and statistics 6th grade Khan Academy.mp3 |
Accident frequency, and I'm just making this up. And I could just show these data points, maybe for some kind of statistical survey, that when the age is this, whatever number this is, maybe this is 20 years old, this is the accident frequency, and it could be a number of accidents per hundred. And that when the age is... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And so these data scientists or statisticians went and plotted all of these in this scatter plot. This is often known as bivariate data, which is a very fancy way of saying, hey, you're plotting things that take two variables into consideration, and you're trying to see whether there's a pattern with how they relate. A... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
Does it look like there's a linear or nonlinear relationship between the variables on the different axes? How strong is that variable? Is it a positive, is it a negative relationship? And then we'll think about this idea of outliers. So let's just first think about whether there's a linear or nonlinear relationship. An... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And then we'll think about this idea of outliers. So let's just first think about whether there's a linear or nonlinear relationship. And I'll get my little ruler tool out here. So this data right over here, it looks like I could put a line through it that gets pretty close through the data. You're not gonna, it's very... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
So this data right over here, it looks like I could put a line through it that gets pretty close through the data. You're not gonna, it's very unlikely you're gonna be able to go through all of the data points, but you can try to get a line, and I'm just doing this. There's more numerical, more precise ways of doing th... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And it looks like I could plot a line that looks something like that that goes roughly through the data. So this looks pretty linear. So I would call this a linear relationship. And since as we increase one variable, it looks like the other variable decreases. This is a downward-sloping line. I would say this is a nega... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And since as we increase one variable, it looks like the other variable decreases. This is a downward-sloping line. I would say this is a negative, this is a negative linear relationship. But this one looks pretty strong. So because the dots aren't that far from my line, this one gets a little bit further, but it's not... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
But this one looks pretty strong. So because the dots aren't that far from my line, this one gets a little bit further, but it's not, you know, there's not some dots way out there. So most of them are pretty close to the line. So I'll call this a negative, reasonably strong linear relationship. Negative, strong. I call... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
So I'll call this a negative, reasonably strong linear relationship. Negative, strong. I call reasonably, I ought to say strong, but reasonably strong linear, linear relationship between these two variables. Now let's look at this one, and pause this video and think about what this one would be for you. Well, let's see... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
Now let's look at this one, and pause this video and think about what this one would be for you. Well, let's see. I'll get my ruler tool out again. It looks like I can try to put a line. It looks like generally speaking, as one variable increases, the other variable increases as well. So something like this goes throug... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
It looks like I can try to put a line. It looks like generally speaking, as one variable increases, the other variable increases as well. So something like this goes through the data and approximates the direction. And this looks positive. As one variable increases, the other variable increases, roughly. So this is a p... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And this looks positive. As one variable increases, the other variable increases, roughly. So this is a positive relationship. But this is weak. A lot of the data is off, well off of the line. So positive, weak. But I'd say this is still linear. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
But this is weak. A lot of the data is off, well off of the line. So positive, weak. But I'd say this is still linear. It seems that as we increase one, the other one increases at roughly the same rate, although these data points are all over the place. So I would still call this linear. Now there's also this notion of... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
But I'd say this is still linear. It seems that as we increase one, the other one increases at roughly the same rate, although these data points are all over the place. So I would still call this linear. Now there's also this notion of outliers. If I said, hey, this line is trying to describe the data, well, we have so... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
Now there's also this notion of outliers. If I said, hey, this line is trying to describe the data, well, we have some data that is fairly off the line. So for example, even though we're saying it's a positive, weak, linear relationship, this one over here is reasonably high on the vertical variable, but it's low on th... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And so this one right over here is an outlier. It's quite far away from the line. You could view that as an outlier. And this is a little bit subjective. Outliers, well, what looks pretty far from the rest of the data? This could also be an outlier. Let me label these. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And this is a little bit subjective. Outliers, well, what looks pretty far from the rest of the data? This could also be an outlier. Let me label these. Outlier. Now pause the video and see if you can think about this one. Is this positive or negative? | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
Let me label these. Outlier. Now pause the video and see if you can think about this one. Is this positive or negative? Is it linear, non-linear? Is it strong or weak? I'll get my ruler tool out here. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
Is this positive or negative? Is it linear, non-linear? Is it strong or weak? I'll get my ruler tool out here. So this goes here. It seems like I can fit a line pretty well to this. So I could fit, maybe I'll do the line in purple. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
I'll get my ruler tool out here. So this goes here. It seems like I can fit a line pretty well to this. So I could fit, maybe I'll do the line in purple. I could fit a line that looks like that. And so this one looks like it's positive. As one variable increases, the other one does for these data points. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
So I could fit, maybe I'll do the line in purple. I could fit a line that looks like that. And so this one looks like it's positive. As one variable increases, the other one does for these data points. So it's a positive. I'd say this is pretty strong. The dots are pretty close to the line. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
As one variable increases, the other one does for these data points. So it's a positive. I'd say this is pretty strong. The dots are pretty close to the line. It really does look like a little bit of a fat line if you just look at the dots. So positive, strong, linear, linear relationship. And none of these data points... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
The dots are pretty close to the line. It really does look like a little bit of a fat line if you just look at the dots. So positive, strong, linear, linear relationship. And none of these data points are really strong outliers. This one's a little bit further out. But they're all pretty close to the line and seem to d... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And none of these data points are really strong outliers. This one's a little bit further out. But they're all pretty close to the line and seem to describe that trend roughly. All right, now let's look at this data right over here. So let me get my line tool out again. So it looks like I can fit a line. So it looks li... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
All right, now let's look at this data right over here. So let me get my line tool out again. So it looks like I can fit a line. So it looks like it's a positive relationship. The line would be upward sloping. It would look something like this. And once again, I'm eyeballing it. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
So it looks like it's a positive relationship. The line would be upward sloping. It would look something like this. And once again, I'm eyeballing it. You can use computers and other methods to actually find a more precise line that minimizes the collective distance to all of the points. But it looks like there is a po... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And once again, I'm eyeballing it. You can use computers and other methods to actually find a more precise line that minimizes the collective distance to all of the points. But it looks like there is a positive. But I would say this one is a weak linear relationship because you have a lot of points that are far off the... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
But I would say this one is a weak linear relationship because you have a lot of points that are far off the line. So not so strong. So I would call this a positive, weak, linear relationship. And there's a lot of outliers here. You know, this one over here is pretty far out. Now let's look at this one. Pause this vide... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And there's a lot of outliers here. You know, this one over here is pretty far out. Now let's look at this one. Pause this video and think about is it positive, negative? Is it strong or weak? Is this linear, nonlinear? Well, the first thing we wanna do is just think about it in linear, nonlinear. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
Pause this video and think about is it positive, negative? Is it strong or weak? Is this linear, nonlinear? Well, the first thing we wanna do is just think about it in linear, nonlinear. I could try to put a line on it. But if I try to put a line on it, it's actually quite difficult. If I try to do a line like this, no... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
Well, the first thing we wanna do is just think about it in linear, nonlinear. I could try to put a line on it. But if I try to put a line on it, it's actually quite difficult. If I try to do a line like this, notice everything is kind of bending away from the line. It looks like generally as one variable increases, th... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
If I try to do a line like this, notice everything is kind of bending away from the line. It looks like generally as one variable increases, the other variable decreases. But they're not doing it in a linear fashion. It looks like there's some other type of curve at play. So I could try to do a fancier curve that looks... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
It looks like there's some other type of curve at play. So I could try to do a fancier curve that looks something like this. And this seems to fit the data a lot better. So this one I would describe as nonlinear. And it is a negative relationship. As one variable increases, the other variable decreases. So this is a ne... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
So this one I would describe as nonlinear. And it is a negative relationship. As one variable increases, the other variable decreases. So this is a negative, I would say reasonably strong nonlinear relationship. Pretty strong. Pretty strong. Once again, this is subjective. | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
So this is a negative, I would say reasonably strong nonlinear relationship. Pretty strong. Pretty strong. Once again, this is subjective. So I'll say negative, reasonably strong, nonlinear relationship. And maybe you could call this one an outlier, but it's not that far. And I might even be able to fit a curve that ge... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
Once again, this is subjective. So I'll say negative, reasonably strong, nonlinear relationship. And maybe you could call this one an outlier, but it's not that far. And I might even be able to fit a curve that gets a little bit closer to that. Once again, I'm eyeballing this. Now let's do this last one. So this one lo... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
And I might even be able to fit a curve that gets a little bit closer to that. Once again, I'm eyeballing this. Now let's do this last one. So this one looks like a negative linear relationship to me. A fairly strong negative linear relationship, although there's some outliers. So let me draw this line. So that seems t... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
So this one looks like a negative linear relationship to me. A fairly strong negative linear relationship, although there's some outliers. So let me draw this line. So that seems to fit the data pretty good. So this is a negative, reasonably strong, reasonably strong linear relationship. But these are very clear outlie... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
So that seems to fit the data pretty good. So this is a negative, reasonably strong, reasonably strong linear relationship. But these are very clear outliers. These are well away from the data or from the cluster of where most of the points are. So with some significant, with at least these two significant outliers her... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
These are well away from the data or from the cluster of where most of the points are. So with some significant, with at least these two significant outliers here. So hopefully this makes you a little bit familiar with some of this terminology. And it's important to keep in mind, this is a little bit subjective. There'... | Bivariate relationship linearity, strength and direction AP Statistics Khan Academy.mp3 |
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