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# Interpreting a trend line

Video transcript

Sira's math test included a survey question asking how many hours students had spent studying for the test . the graph below shows the relationship between how many hours students spent studying and their score on the test。 Sira draw the line below to show the trend in the data. Assuming the line is correct, what does the line slope of 15 mean? So let's see, the horizontal axis is time study in hours, vertical axis is the score on the test. each of these blue dots represents the time and score for a given student. so this student right over here spent I don't know times about 0.6 hours studying, and he didn't do too well on the exam,， it looks like he got below 45 ,44 or 43 on the exam; this student over here spent almost 4 and half hours studying, and got ,looks like 94 close to 95 on the exam. what sira did is trying to draw a line that tries to fit the trend,It seems like he did a pretty good job of at least showing the trend in the data. now the slope of 15 means that if I am on the line, , let's say if I am here, if I increase horizontal direction by 1, I should be increasing in vertical direction by 15 on the test , now what it means is the trend shows in general along this trend, , if someone studies an extra hour , that if we are going with this trend it seems reasonable that they might expect to see a 15% gain on their test. now let's see which of these are consistent. in general the student who didn't study at all got scores about 15 on the test, this is neither true, these are the people who didn't study at all they didn't get 15 on the test, that's definitely not what this 15 implies. this doesn't say what people didn't study at all get, so this is not true. let's try this one: if one student studied for 1 hour more than another student, the student who studied more got exactly 15 points more on the test. this is getting closer to the spirit what the slope means, but this word "exactly" is ，what at least in my mind messes this choice up. because this isn't saying that guarantees if you studied a hour extra that you can get 15 % more on the test. this is just saying this is a general trend that this line seems , it's not guaranteed. for example we could find a student here who studied for exactly 2hours, and if we look at the student who studied for 3 hours,well there is no one exactly at 3 hours, but some of them, so let's see the student who was at 2 hours, you go to 3 hours, there is no one exactly there but there is going to be students who got better than what would be expected and students who might get a little bit worse, notice there are points above the trend line, there are points below the trend line, so this " exactly" you can't say it's guanranteed an hour more turns into 15%. let's try this choice, in general ,studying for one extra hour was associated with a 15-point improvement in test score that feels about right. in general studying for 15 extra hours was associated with a 1-point improvement in test score. well, no, that would get the slope the other way around, that's definitely not the case so let's check our answer and we got it right。