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## Least-squares regression equations

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# Interpreting slope of regression line

AP Stats: DAT‑1 (EU), DAT‑1.H (LO), DAT‑1.H.2 (EK)

## Video transcript

- [Instructor] Liz's math test
included a survey question asking, how many hours
students that 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, the line fitted to model the data has a slope of 15. So, the line they're talking about is right here. So this is the scatter
plot, this shows that some student who spent
some time in 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 a 95 spent over four hours studying. And so then they fit a line to it and this line has a slope of 15. And before I even read these choices what's the best
interpretation of this 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. So, if we start over here and we were to increase by one hour our score should improve by 15. And it does, indeed, look like that. We're going from, we're going in the horizontal direction,
we're going one hour. And then in the vertical
direction we're going from 45 to 60. So that's how I would interpret it. Every hour, based on this regression, you could, it's not unreasonable to expect 15 points improvement. Or at least that's what we're seeing 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, we didn't see that. Students, 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 a 38. So, don't like that choice. The model predicts 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 the score by 15 points. The model predicts that the study time will increase 15 hours for each additional point scored. Well, no. And first of all, the hours is the thing that we use the independent variable and the points being
the dependent variable, and this is phrasing it the other way. And you definitely wouldn't
expect to do an extra 15 hours for each point.

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