Interpreting slope of regression line | AP Statistics | Khan Academy

Lizz's math test included a survey question asking how many hours students spent studying for the test. The scatter plot and trend line below show the relationship between how many hours students spent studying and their score on the test. The line fitted to the model has a slope of 15.

So, the line that they're talking about is right here. This is the scatter plot. This shows that some student who spent some time between half an hour and an hour studying got a little bit less than a 45 on the test. This student here, who got a little bit higher than a 60, spent a little under two hours studying. This student over here, who looks like they got like a 94 or 95, spent over 4 hours studying.

And so then they fit a line to it, and this line has a slope of 15. Before I even read these choices, what's the best interpretation of the slope? Well, if you think this line is indicative of the trend—and it does look like that from this scatter plot—that implies that roughly every extra hour that you study is going to improve your score by 15.

You could say on average, according to this regression, if we start over here and we were to increase by 1 hour, our score should improve by 15. It does indeed look like that, as we're going from— we're going in the horizontal direction, we're going 1 hour, and then the vertical direction we're going from 45 to 60.

So that's how I would interpret it. Every hour, based on this regression, it's not unreasonable to expect a 15 points improvement, or at least that's what we're seeing from the regression of the data.

So let's look at which of these choices actually describe something like that. The model predicts that the student who scored zero studied for an average of 15 hours? No, it definitely doesn't say that.

The model predicts that students who didn't study at all will have an average score of 15 points? No, we didn't see that. If you take this, if you believe this model, someone who doesn't study at all would get close to— would get between 35 and 40 points, so like a 37 or 38. So, I don't like that choice.

The model predicts that the score will increase 15 points for each additional hour of study time? Yes, that is exactly what we were thinking about when we were looking at the model. That's what a slope of 15 tells you; you increase studying time by an hour, it increases score by 15 points.

The model predicts that the study time will increase 15 hours for each additional point scored? Well, no. First of all, hours is the thing that we've viewed as the independent variable and the points being the dependent variable, and this is phrasing it the other way. You definitely wouldn't expect to do an extra 15 hours for each point.