A researcher is examining the effects of income (X 1) and number of friends (X 2) on personal happiness (Y) and finds an R of 0.45. Which of the following is a correct interpretation of this result?
A) Money CAN buy happiness.
B) Friends are more important than money for happiness.
C) Taken together, income and number of friends explain 45% of the variance in happiness.
D) Taken together, income and number of friends explain 0.45% of the variance in happiness.

Question

A researcher is examining the effects of income (X 1) and number of friends (X 2) on personal happiness (Y) and finds an R of 0.45. Which of the following is a correct interpretation of this result?
A) Money CAN buy happiness.
B) Friends are more important than money for happiness.
C) Taken together, income and number of friends explain 45% of the variance in happiness.
D) Taken together, income and number of friends explain 0.45% of the variance in happiness.

Quizplus · Accepted Answer

An R of 0.45 means that income and number of friends are positively related to happiness, but it does not indicate causation. Additionally, the R-squared value (0.2025) shows that income and number of friends together can explain 20.25% of the variance in happiness, not 45% or 0.45%. Therefore, the correct interpretation is that taken together, income and number of friends explain 20.25% of the variance in happiness.

A Researcher Is Examining the Effects of Income (X 1)