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A bivariate relationship has a correlation coefficient ( � ) (r) of 0.7. 0.7. Identify the % of variation in the response variable that can be explained by response in the explanatory variable:

Question

A bivariate relationship has a correlation coefficient ( � ) (r) of 0.7. 0.7.

Identify the % of variation in the response variable that can be explained by response in the explanatory variable:

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Solution

The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship.

The square of the correlation coefficient (r^2), also known as the coefficient of determination, is a measure of the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is a key output of regression analysis.

In this case, the correlation coefficient (r) is 0.7. To find the coefficient of determination (r^2), we square the correlation coefficient:

r^2 = (0.7)^2 = 0.49

Therefore, 49% of the variation in the response variable can be explained by the response in the explanatory variable.

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