A researcher reports that the correlation between two quantitative variables is r = 0.8. Which of the following statements is correct? A) The average value of y changes by 0.8 when x is increased by 1. B) The average value of x changes by 0.8 when y is increased by 1. C) The explanatory variable (x) explains 0.8 or 80% of the variation in the response variable (y). D) The explanatory variable (x) explains (0.8)² = 0.64 or 64% of the variation in the response variable (y).

Question

Quizplus · Accepted Answer

The correct interpretation of a correlation coefficient (r = 0.8) is related to the coefficient of determination (r^2), which explains the proportion of the variance in the dependent variable that is predictable from the independent variable. In this case, r^2 = (0.8)^2 = 0.64 or 64%, indicating that 64% of the variation in the response variable (y) can be explained by the explanatory variable (x).

A Researcher Reports That the Correlation Between Two Quantitative Variables