A global logistics company calculates the correlation coefficient (r) between the distance a delivery truck travels and its maintenance costs to be +0.90.

What is the coefficient of determination, and what does it signify?

Answer options:

0.90; 90% of the variation in maintenance costs is explained by the distance traveled.

0.81; 81% of the variation in maintenance costs is explained by the distance traveled.

0.81; 81% of the variation in distance traveled is caused by maintenance costs.

1.80; Maintenance costs increase by 1.80 for every mile traveled.

How to approach this question

Square the correlation coefficient (r) to find the coefficient of determination (r^2). Interpret it as the percentage of variation in the dependent variable explained by the independent variable.

Full Answer

B.0.81; 81% of the variation in maintenance costs is explained by the distance traveled.✓ Correct

The coefficient of determination is calculated by squaring the correlation coefficient (r). Here, r = 0.90, so r^2 = 0.81 or 81%. This means that 81% of the total variation in the dependent variable (maintenance costs) can be explained by changes in the independent variable (distance traveled).

Common mistakes

Confusing r with r^2, or misinterpreting the direction of causality.

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