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### Course: Integrated math 1>Unit 9

Lesson 2: Estimating with trend lines

# Interpreting a trend line

The graph shows how studying affects test scores. The line slope of 15 means that for each extra hour of studying, there is usually a 15-point increase in test score. But it's not a guarantee. Some students may do better or worse than the trend. Created by Sal Khan.

## Want to join the conversation?

• Can someone please explain what bivariate data is ?
• Same as above, but maybe a better way to understand vocab:
bi = 2
variate = variables
• According to that line, if someone studied about 7 hours, then their score should be ~125 - which is off the chart. The maximum score appears to be 100, so what's going on? How can the line show that 7 hours is a score of ~125?
• The line doesn't go on infinitely (I guess it is technically a line segment). If you plotted more and more points and the hours went up and up the line would just level off. Remember that this is data taken from the real world. It doesn't have the precision most math has. If you have a line that is plotting the amount of money you pay for flowers and one flower is 2 dollars you can have an exact, perfect line. This type of data is not like that. If you have a student who studies for 10 hours he'll probably get in the 90s but it's not definite. The line is just an estimate.
• Hi moderators,

i noticed that the content in this video is repeated in another video in the same module "interpreting slope of a line". the content is same in both the videos.
• Imagine studying for 15 hours and only getting 1/100 on your test
• i understand nothing. literally.
• The more time is the more score
• I am not sure if there is an easier way to go about this but there has to be some sort of formula. It is hard eyeballing the line and then it is even more difficult trying to measure a line on a computer screen........
• why do we have to interpret the line.
• Who is Lugi?
• At , what does Sal mean?
• if the first statement were true, at x=0 (did not study), you would have seen a score of 15 --> (0,15) -> but there is no datapoint to indicate this, so this first statement is false/incorrect.
• How ill this help me pay off my multi million debt.🇯🇵🇩🇪🇮🇹
• Does line of best fit have to be exact? The line of best fit can also be used to find slope, so if you don't place the line of best fit perfectly, the actual slope maybe a bit off. How can I fix this kind of problem?

## 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. 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.