# Interpreting a trend line | Data and modeling | 8th grade | Khan Academy

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. Shira drew 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. The 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 spend

about 0.6 hours studying. And they didn’t do

too well on the exam. They look like they got

below a 45, looks like a 43 or a 44 on the exam. This student over here spent

almost 4 and 1/2 hours studying and got, looks like, a 94,

close to a 95 on the exam. And what Shira

did is try to draw a line that tries

to fit this data. And it seems like it

does a pretty good job 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 there, I increase the horizontal

direction by 1– I should be increasing in

the vertical direction by 15. And you see that. If we increase by one hour here,

we increase by 15% 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, 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, students

who didn’t study at all got scores of about

15 on the test. Well, let’s see. This is neither true–

these are the people who didn’t study at all, and they

didn’t get a 15 on the test. And that’s definitely

not what this 15 implies. This doesn’t say what the people

who didn’t study at all get. So this one is not true. That one is not true. Let’s try this one. If one student studied for one

hour more than another student, the student who studied

more got exactly 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

it’s a guarantee that if you study an hour extra that you’ll

get 15% more on the test. This is just saying that

this is the general trend that this line is seeing. So it’s not guaranteed. For example, we could

find this student here who studied exactly two hours. And 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, let’s see, the student who

was at two hours. You go to three hours,

there’s no one exactly there. But there’s going to be

students who got better than what would be

expected and students who might get a

little bit worse. Notice, 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 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. So that’s definitely

not the case. So let’s check our answer. And we got it right.

nice vid

thanks khan

how do I connect the trend line to x axis so it will lie on the x axis?