Question

Assume that you have paired values consisting of heights (in inches) and weights (in lb) from 40 randomly selected men. The linear correlation coefficient r is 0.464. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide?

A.) The coefficient of determination is 0.215. 78.5% of the variation is explained by the linear correlation, and 21.5% is explained by other factors.
B.) The coefficient of determination is 0.785. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.
C.) The coefficient of determination is 0.215. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.
D.) The coefficient of determination is 0.785. 78.5% of the variation is explained by the linear correlation, and 21.5% is explained by other factors.

Answer 1

Answer: C.) The coefficient of determination is 0.215. 21.5% of the variation is explained by the linear correlation, and 78.5% is explained by other factors.

Explanation:

Given that :

Number of observations = 40

Linear Correlation Coefficient (R) = 0.464

The Coefficient of determination ( R^2) =?

The Coefficient of determination (R^2) is the squared value of the linear correlation Coefficient value (R) . The value value ranges from 0 to 1 and depicts the proportion of the variation in the dependent variable that can be accounted for by the independent variable.

For the scenario given above,

The Coefficient of determination (R^2) = 0.464^2 = 0.215296 = (0.215296 * 100%) = 21.5%

This means that 21.5% of the variation can be explained by the relationship between both variables while (100% - 21.5% = 78.5%) can be explained by other factors.