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## 8th grade

### Unit 7: Lesson 2

Interpreting scatter plots# Example of direction in scatterplots

AP.STATS:

DAT‑1 (EU)

, DAT‑1.A (LO)

, DAT‑1.A.2 (EK)

, DAT‑1.A.3 (EK)

, DAT‑1.A.4 (EK)

Sal answers a question about scatter plots that show the relationship between study time, shoe size, and test score. Created by Sal Khan.

## Want to join the conversation?

- In1:32to2:19, when he is explaining the answers, one of them says there's a nonlinear relationship, and then it says there is no relationship in another answer. Do these things mean the same thing?(44 votes)
- No, these are not the same thing. "No relationship" is when the points are all over the place and there isn't any type of correlation like between your shoe size and how many computers you have in your house. But, a nonlinear relationship is when the points have a correlation but not a linear correlation, maybe it has a exponential correlation. For example, you are monitoring growth of a country's population, let's say on day one, the country has x amount of people. Each day, the amount of people doubles. If you plot it, you find it is not a linear relationship or a "no relationship", but it is an exponential equation. Nonlinear relationship is when it is a relationship, but not linear. No relationship is when there is not any relationship between the points what so ever.

I hope that helped!(71 votes)

- im a idiot please help me here how will we use this in our life(14 votes)
- You are not an idiot. You may use this in a situation where you need to make a prediction. In accounting, scatterplots can be used to see if there is a relationship between to variables, such as money spent of advertising and amount sold. The relationship is not linear and is more complex, but yo may have heard about scientists modeling COVID-19 infections.(15 votes)

- so if you can fit a line, the scatter plot would be considered positive?(6 votes)
- Not necessarily. A line which has a slope >0 is positive, a line with slope <0 is negative.(14 votes)

- how can u tell its a positive line or a negative line(6 votes)
- x is generally thought of as the independent variable that affects the y variable, thus you always consider how x moving forward affects y.(3 votes)

- what does this mean so confused(4 votes)
- you are just trying to see if there is a relationship , in the example the more you study the better grades so it makes sense. whereas shoe size will be random(3 votes)

- When Will I use this in real-life situations?(5 votes)
- How do you know if its independent or dependent(5 votes)
- If a variable is dependent, it cannot stand alone. If it is independent, it can stand alone. I hope this helps.(2 votes)

- Do I have to watch the whole video in order to go to the lesson(2 votes)
- You do not have to watch a video to go to the lesson, infact I only watch the video 70% of the time.(5 votes)

- Do scatter plots only show the average?(3 votes)
- Can someone walk me through this again, please?(2 votes)
- Hi!

In the problem, two graphs are shown: one showing the relationship between study time and grades (the first graph), the other showing the relationship between shoe size and grades (the second graph).

Here are the possible answers and why they or why they don't work:

1.*There's a negative linear relation between the study time and score, and a positive linear relationship between shoe size and score.*

A negative linear relation is one where the y-values of the dots are generally decreasing as x increases. Since this is the opposite of what's happening with the first graph, this is not the answer.

2.*There is a nonlinear relationship between study time and score and a negative linear relationship between shoe size and score.*

The first graph is linear, while the second plot is not linear at all. This is also incorrect.

3.*There is a positive linear relationship between study time and score and no relationship between shoe size and score.*

This is true. The y-values of the first chart are generally increasing, while the values of the second plot do not follow a line.

4.*Both graphs show positive linear trends of approximately equal strength.*

The second graph is not linear at all, so this is not true.

Hope this helps!😄(4 votes)

## Video transcript

The graphs below
show the test grades of the students
in Dexter's class. The first graph shows the
relationship between test grades and the amount of time
the students spent studying. So this is study
time on this axis and this is the test
grade on this axis. And the second graph
shows the relationship between test grades
and shoes size. So shoe size on this
axis and then test grade. Choose the best description
of the relationship between the graphs. So first, before looking
at the explanations, let's look at the actual graphs. So this one on the
left right over here, it looks like there is a
positive linear relationship right over here. I could almost fit a line
that would go just like that. And it makes sense
that there would be, that the more time
that you spend studying, the better score
that you would get. Now for a certain
amount of time studying, some people might do
better than others, but it does seem like
there's this relationship. Here it doesn't
seem like there's really much of a relationship. You see the shoe sizes,
for a given shoe size, some people do not so well
and some people do very well. Someone with a size 10
and 1/2, it looks like, someone it looks like
they flunked the exam. Someone else, looks like
they got A minus or a B plus on the exam. And it really would be hard
to somehow fit a line here. No matter how you draw
a line, these dots don't seem to form a trend. So let's see which of
these choices apply. There's a negative
linear relationship between study time and score. No, that's not true. It looks like there's a
positive linear relationship. The more you study, the
better your score would be. A negative linear relationship
would trend downwards like that. There is a non-linear
relationship between study time and score and a negative
linear relationship between shoe size and score. Well that doesn't
seem right either. A non-linear
relationship, it would not be easy to fit a line to it. And this one seems like a
line would be very reasonable. And it doesn't seem like
there's any type of relationship between shoe size and score. So I wouldn't pick
this one either. There's a positive
linear relationship between study time and score. That's right. And no relationship between
shoe size and score. Well, I'm going to
go with that one. Both graphs show
positive linear trends of approximately equal strength. No, not at all. This one doesn't show
a linear relationship of really any strength.