Practice Correlation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Correlation measures the strength and direction of the linear relationship between two quantitative variables, ranging from −1 to +1.

Do two things go up and down together? r=+1 means perfectly together, r=−1 means perfectly opposite.

Showing a random 20 of 50 problems.

Example 1

easy
Does a correlation of r=0.05 indicate a strong or weak linear relationship?

Example 2

easy
If r=−0.95, describe the direction and strength of the linear relationship.

Example 3

medium
If you add the same constant to every x-value, how does r change?

Example 4

hard
Data (0,0),(1,1),(2,4),(3,9),(4,16) follow y=x2. Is r near 0 or near 1?

Example 5

challenge
Variable A correlates with B at r=0.9, and B correlates with C at r=0.9. Must A and C be strongly correlated?

Example 6

medium
Why can r be near 0 even for a tight non-linear (e.g., parabolic) relationship?

Example 7

easy
Can you compute a correlation between eye color and favorite number?

Example 8

medium
A study reports r=0.7 between exercise frequency and happiness. Can you conclude exercising more will make a specific person happier?

Example 9

medium
If you swap x and y in a dataset, does r change?

Example 10

medium
If every y value is multiplied by 3 (a positive constant), how does r between x and y change?

Example 11

hard
Calculate r for the data (1,2),(2,3),(3,5),(4,4),(5,6).

Example 12

medium
A relationship is described by y=−0.5x+4 exactly. What is r?

Example 13

hard
If the points (xi,yi) all lie on the line y=5, what is r?

Example 14

medium
Data points are (1,10),(2,7),(3,4),(4,1). What is r?

Example 15

easy
A correlation coefficient is r=+1. What does this mean?

Example 16

hard
A researcher reports r=0.95 from a sample of size 4. Why is this fragile evidence of a real relationship?

Example 17

challenge
Anscombe's quartet shows four datasets with identical mean, SD, and r=0.816 but radically different shapes. What lesson does this teach about r?

Example 18

easy
What is the range of possible values for the correlation coefficient r?

Example 19

medium
Data shows r=0.9 between shoe size and reading ability among children aged 5–12. Why might this be misleading as evidence of causation?

Example 20

easy
A correlation of r=0 means what about the linear relationship?
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