A dataset contains the heights/weights of students. What's the best way to find if these two variables are correlated?

Create a scatter plot and calculate the correlation coefficient.

A researcher finds that students who take more math classes tend to score higher on the SAT. Reasonable conclusion?

More math classes may equal stronger math skills, which may help with SAT

What does the correlation coefficient (r) measure?

The strength and direction of a linear relationship between two variables

There's a strong correlation between hours of studying and students' final grades. What's a valid conclusion?

More studying is linked to higher grades, but other factors may contribute.

If two variables are correlated, one must cause the other.

Even correlated, other factors may be responsible for their relationship.

What does it mean if a dataset has a correlation coefficient of r=0?

There is no linear relationship between the variables.

There's a strong correlation between the number of people at the beach and ice cream sales. What's a good explanation?

A third variable, such as hot weather, is affecting both factors.

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3.16 Sample Work

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Answers

1
A scatter plot shows that as study time increases, test scores tend to increase. What correlation does this represent?
Positive correlation
No correlation
Causal relationship
Negative correlation
2
A dataset contains the heights/weights of students. What's the best way to find if these two variables are correlated?
Compare the tallest and shortest students.
Create a scatter plot and calculate the correlation coefficient.
Find the average height and weight.
Count how many students have the same height and weight.
3
A researcher finds that students who take more math classes tend to score higher on the SAT. Reasonable conclusion?
Taking math classes causes higher SAT scores.
More math classes may equal stronger math skills, which may help with SAT
There is no relationship between math classes and SAT scores.
SAT scores determine how many math classes a student takes.
4
What does the correlation coefficient (r) measure?
The total number of data points in a set
The strength and direction of a linear relationship between two variables
The cause-and-effect relationship between two variables
The average of all values in a dataset
5
There's a strong correlation between hours of studying and students' final grades. What's a valid conclusion?
More studying is linked to higher grades, but other factors may contribute.
The final grade determines how many hours a student will study.
Studying more always guarantees a better grade.
There is no relationship between studying and grades.
6
Which correlation coefficient shows the strongest linear relationship?
r=−0.92
r=0.50
r=−0.30
r=0.85
7
If two variables are correlated, one must cause the other.
If two variables are correlated, they are always unrelated.
If two variables are correlated, one must cause the other.
Even correlated, other factors may be responsible for their relationship.
Correlation means the variables will always have the same values.
8
What does it mean if a dataset has a correlation coefficient of r=0?
There is no linear relationship between the variables.
The variables are strongly negatively correlated.
The variables are strongly positively correlated.
The variables are directly proportional.
9
If a dataset has a correlation coefficient of r=0.89, what does this indicate?
A perfect negative correlation
A weak negative correlation
A strong positive correlation
No correlation
10
There's a strong correlation between the number of people at the beach and ice cream sales. What's a good explanation?
Ice cream companies advertise more at the beach, creating demand.
Eating ice cream causes more people to go to the beach.
More people at the beach cause ice cream sales to increase.
A third variable, such as hot weather, is affecting both factors.

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