Question

A researcher determines that the correlation between the a predictor and response variable is -0.4. What percentage of variation in the response variable can be explained by its relationship with the predictor variable?

Answer 1

We have been given the value of r.

The coefficient of determination, r² is the square of the correlation coefficient, r.

The coefficient of determination, or the r-squared value is equal to the percent of variation in the dependent/ response variable that is accounted for (predicted) by the independent/ predictor variable.

Though the correlation coefficient is useful to determine the degree of linear relationship between tow variables,  the coefficient of determination allows us to interpret the relationships in terms of variations.

Thus, the percentage of variation in the response variable can be explained by its relationship with the predictor variable is -0.4² which is equal to 0.16. Thus, 16% is the required answer.