Practice Correlation in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

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

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

Showing a random 20 of 50 problems.

Example 1

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

Example 2

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

Example 3

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

Example 4

hard
Data (0,0),(1,1),(2,4),(3,9),(4,16)(0,0), (1,1), (2,4), (3,9), (4,16) follow y=x2y = x^2. Is rr near 00 or near 11?

Example 5

challenge
Variable AA correlates with BB at r=0.9r=0.9, and BB correlates with CC at r=0.9r=0.9. Must AA and CC be strongly correlated?

Example 6

medium
Why can rr be near 00 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=0.7r = 0.7 between exercise frequency and happiness. Can you conclude exercising more will make a specific person happier?

Example 9

medium
If you swap xx and yy in a dataset, does rr change?

Example 10

medium
If every yy value is multiplied by 33 (a positive constant), how does rr between xx and yy change?

Example 11

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

Example 12

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

Example 13

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

Example 14

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

Example 15

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

Example 16

hard
A researcher reports r=0.95r = 0.95 from a sample of size 44. Why is this fragile evidence of a real relationship?

Example 17

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

Example 18

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

Example 19

medium
Data shows r=0.9r = 0.9 between shoe size and reading ability among children aged 55–1212. Why might this be misleading as evidence of causation?

Example 20

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