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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

Liz's math test included a survey question asking how many hours students spent studying for the test the scatterplot 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 scatterplot this shows that some students who spent some time between half an hour and hour studying got a little bit less than a 45 on the test the students here who got a little bit higher than a 60 spent a little under two hours studying the student over here who looks like they got like a 94 or 95 spent over four hour setting 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 the slope well if you think this line is indicative of the trend but it does look like that from the scatterplot 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 the vertical direction are 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 students 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 now we didn't we didn't see that students if you 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 like a 37 or 38 so 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 the 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 and first of all ours is the thing that we've used 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