Question

The correlation between a respondent's years of education and his or her annual income is r = 0.87 Which of the following statements is true? a. 76% of the variance in annual income can be explained by respondents' years of education. b. 13% of the variance in annual income can be explained by respondents' years of education. c. 87% of the variance in annual income can be explained by respondents' years of education. d. 24% of the variance in annual income can be explained by respondents' years of education.

Answer 1

A) 76% of the variance in annual income can be explained by respondents' years of education.

Explanation:

Given our correlation coefficient, r=0.87, we can calculate R²=0.7569, which helps show a proportion of the variance for a dependent variable that's explained by the independent variable.

In this case, 76% of the variance in annual income, our dependent variable, can be explained by respondents' years of education, the independent variable.