Example of direction in scatterplots (video) | Khan Academy
Sal answers a question about scatter plots that show the relationship between study Both. This Concept introdices scatterplots and linear correlation for bivariate data. Correlation Patterns in Scatterplot Graphs. Examining a. Scatter Plot Showing Strong Positive Linear Correlation, scatter plot showing strong positive linear correlation. Discussion, Note in the plot above of the LEW3.
So this is study time on this axis and this is the test grade on this axis. And the second graph shows the relationship between test grades and shoes size. So shoe size on this axis and then test grade. Choose the best description of the relationship between the graphs. So first, before looking at the explanations, let's look at the actual graphs.
So this one on the left right over here, it looks like there is a positive linear relationship right over here. I could almost fit a line that would go just like that. And it makes sense that there would be, that the more time that you spend studying, the better score that you would get. Now for a certain amount of time studying, some people might do better than others, but it does seem like there's this relationship.
Here it doesn't seem like there's really much of a relationship. You see the shoe sizes, for a given shoe size, some people do not so well and some people do very well. Someone else, looks like they got A minus or a B plus on the exam.
And it really would be hard to somehow fit a line here.
No matter how you draw a line, these dots don't seem to form a trend. So let's see which of these choices apply. There's a negative linear relationship between study time and score.
No, that's not true. So this is a positive relationship. But this is weak. A lot of the data is off, well off of the line.
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 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 the horizontal variable.
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. 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. 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.
So it's a positive. I'd say this was pretty strong. The dots are pretty close to the line there. 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 describe that trend roughly.
Bivariate relationship linearity, strength and direction (video) | Khan Academy
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, and it looks like it's a positive relationship. The line would be upward sloping.Scatter Plots : Introduction to Positive and Negative Correlation
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 positive, but I would say, this one is a weak linear relationship, 'cause we 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. This one over here is pretty far, pretty far out. Pause this video and think about, is it positive or negative, is strong or weak? Is this linear or non-linear? Well, the first thing we wanna do is let's think about it with linear or non-linear. 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, you'll 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.
Example of direction in scatterplots
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 non-linear.