Which of the following best describes the difference between the interpretation

Question

Which of the following best describes the difference between the interpretation of the correlation coefficient and the beta coefficient for a regression equation expressing the relationship between variables X and Y?

The beta coefficient represents the linear relationship between X and Y, whereas the correlation coefficient represents the percent variability in Y explained by X.

The beta coefficient represents the difference between observed and expected values of Y, whereas the correlation coefficient represents the linear relationship between X and Y.

The beta coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the correlation coefficient provides a unit-free measure of the strength of the relationship.

The correlation coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the beta coefficient provides a unit-free measure of the strength of the relationship.

Explanation / Answer

correct answer is

The beta coefficient predicts increases or decreases in Y with increases or decreases in X, whereas the correlation coefficient provides a unit-free measure of the strength of the relationship.

and Correlation coefficient measures the strength of the linear association between X and Y, while you can think of beta as an estimated slope of the regression line.

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