Question

select the most appropriate response.
if the correlation between a persons age and annual income is r = 0.60, then what does the coefficient of determination r² tell us about the explained variation?
36% of the variation in a persons annual income can be explained by the predictor variable age.
36% of a persons annual income can be explained by their age.
60% of the variation in a persons annual income can be explained by the predictor variable age
60% of a persons annual income can be explained by their age

Explanation:

Step1: Recall the formula for the coefficient of determination

The coefficient of determination \( r^{2}\) is calculated as \( r^{2}=(r)^{2}\), where \( r\) is the correlation coefficient.

Step2: Substitute the given value of \( r\)

Given \( r = 0.60\), then \( r^{2}=(0.60)^{2}=0.36\).

Step3: Interpret the coefficient of determination

The coefficient of determination \( r^{2}\) represents the proportion of the variation in the dependent variable (in this case, a person's annual income) that can be explained by the independent variable (age). So \( r^{2}=0.36\) means 36% of the variation in a person's annual income can be explained by the predictor variable age.

Answer:

36% of the variation in a person's annual income can be explained by the predictor variable age.