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Interpreting a trend line

Sal interprets a trend line that shows the relationship between study time and math test score for Shira. Created by Sal Khan.

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  • leaf orange style avatar for user Pjeirefretter
    Can someone please explain what bivariate data is ?
    (2 votes)
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  • mr pants teal style avatar for user Wrath Of Academy
    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?
    (6 votes)
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    • purple pi purple style avatar for user Hannah Elaine
      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.
      (1 vote)
  • duskpin sapling style avatar for user ravza
    This isn't exactly a question about the video, but is it possible to determine the line of best fit without a graph? If you have several points, and no graph, how would you determine the equation of the line of best fit?
    Thanks.
    (3 votes)
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    • duskpin ultimate style avatar for user Zingo
      If you had no graph, then you wouldn't be able to calculate the slope. So, I'd say your best bet is to eyeball it, and try to keep the line in the center of the data trend. If you're answering a question on paper, then definitely use a ruler. If you really wanted to calculate slope, then you could make a graph and plot the points on the graph. I find that calculating the slope is really helpful when determining the line.
      (3 votes)
  • blobby green style avatar for user tyaine danclair
    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........
    (3 votes)
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  • female robot ada style avatar for user sarnow7294
    when would i use a scatter plot? Why would i need to know the trend?
    (2 votes)
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  • blobby green style avatar for user maryama egal
    Why is it important that for a best-fit line be drawn with an equal number of data points above and below the line?
    (2 votes)
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  • aqualine ultimate style avatar for user Hannarsawr
    At , what does Sal mean?
    (3 votes)
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  • leaf orange style avatar for user Click here
    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?
    (3 votes)
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  • male robot hal style avatar for user Mukunda
    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.
    (3 votes)
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  • female robot grace style avatar for user ccwong
    In the video, Sal mentions that the slope of the line on the graph, which is 15, means that for every hour a student studies, there is a 15 point improvement on their test.
    Does this work every time? Is it always going to be increasing on the x-axis by one? Or does it just depend on the graph you are working with?
    Also, to find the slope and analyze what it is saying (just like the question Sal is solving in the video) do you just start at a "whole number point" on the line and then travel vertically until you reach another "whole number" in order to see the change? For example, Sal first begins at point (0.5, 45) and travels horizontally to point (1.5, 60) to find the meaning in the change of slope.

    Well, that was a mouthful! Thanks for anyone who helps, and I hope this helped other viewers too! :)
    (3 votes)
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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.