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# Interpreting a trend line

CCSS.Math:

## Video transcript

shira'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 she read you 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 studying in hours vertical axis is scores on the test and each of these blue dots represent the time and the score for a given student so this student right over here spent I don't know it looks like they spent about point 6 hours studying and they didn't do too well on the exam they look like they got below of 45 looks like a 43 or 44 on the exam this student over here spent almost 4 and a half hours studying and got looks like a 94 92 a 95 on the exam and what sheera did is try to draw a line that tries to fit this data it seems like it does a pretty good job of getting of at least showing the trend in the data now slope of 15 means that if I'm on the line so let's say I'm here and if I increase in the horizontal direction by 1 so they are increased by the horizontal direction by 1 I should be increasing in the vertical direction by 15 and you see that if we increase by 1 hour here we increase by 15 percent on the test now what that means is that the trend it shows is that in general along this trend if someone studies an extra hour then if we're going with that trend then hey you know it seems reasonable that they might expect to see a 15 percent gain on their test now let's see which of these are consistent in general students who didn't study at all got scores of about 15 on the test well let's see this is this is neither true we don't see that these are the people who didn't study at all and they didn't get 15 on the test and that's definitely not what this 15 implies this doesn't say what the what the people who didn't study at all get so this one is not true that one is not true if let's try this one if one student studied for 1 hour more than another student the student who studied more got eggs actly 15 more points on the test well this is getting closer to the spirit of 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's guarantee that if you study an hour extra that you'll get 15% more on the test this is just saying that this is a general trend that this line is seeing so it's not it's not guaranteed for example we could find this student here who studied exactly two hours and if if we look at the students who studied for three hours well there's no one exactly at three hours but some of them so this was listening to study the student who's at two hours you go to three hours there's no one exactly there but no one there's going to be students who got better than what would be expected and students who might get a little bit worse they've noticed there's points above the trend line and there's points below the trend line so this exactly you can't say it's guaranteed an hour more turns into 15% let's try this choice in general studying for one extra hour was associated with the 15-point improvement in test score that feels about right in general studying for 15 extra hours was associated with a one-point improvement in test score we know that would get the slope the other way around so that's definitely not the case let's check our answer we got it right