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### Course: AP®︎/College Statistics>Unit 5

Lesson 1: Representing the relationship between two quantitative variables

# Example of direction in scatterplots

There are two graphs. One shows the relationship between study time and test grades. Do you get better grades if you study more? The other graph shows the relationship between shoe size and grades. Do you get better grades if you wear larger shoes? Created by Sal Khan.

## Want to join the conversation?

• In to , 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?
(54 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!
(86 votes)
• im a idiot please help me here how will we use this in our life
(26 votes)
• Yeah, scatterplots are used to show raw data and the direction in them shows trends, which can be used to make decisions.
(7 votes)
• so if you can fit a line, the scatter plot would be considered positive?
(12 votes)
• Not necessarily. A line which has a slope >0 is positive, a line with slope <0 is negative.
(17 votes)
• When Will I use this in real-life situations?
(16 votes)
• Well obviously, you need to be in school more because that capital W is not grammatically correct.
(8 votes)
• how can u tell its a positive line or a negative line
(9 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.
(6 votes)
• Can someone walk me through this again, please?
(7 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!😄
(11 votes)
• what does this mean so confused
(7 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
(7 votes)
• How do you know if its independent or dependent
(8 votes)
• If a variable is dependent, it cannot stand alone. If it is independent, it can stand alone. I hope this helps.
(4 votes)
• ?what i s the meaning of scatter plots
(6 votes)
• Scatter plots are graphical representations of data points where each point represents the values of two different variables. The position of each point on the plot corresponds to the values of the two variables. Scatter plots are used to visually inspect the relationship between the variables, such as whether they are positively or negatively correlated, or if there is any pattern or trend between them. They are commonly used in statistics and data analysis to understand the association between variables and to identify any outliers or patterns in the data.
(2 votes)
• yall the got me learning more than the actual assignments plus its funny
(6 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.