Which statistic is commonly used to evaluate how well the sample regression equation fits the data?

• A. The coefficient of determination $R^2$
• B. The correlation coefficient $r$
• C. The standard deviation of the independent variable
• D. The mean of the residuals

Answer: (A)

Verified step by step guidance

1. Understand that the question asks for the statistic that measures how well the sample regression equation fits the data, which means it evaluates the proportion of variability in the dependent variable explained by the independent variable(s).
2. Recall that the coefficient of determination, denoted as \(R^{2}\), quantifies the proportion of the total variation in the dependent variable that is explained by the regression model.
3. Recognize that the correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables but does not directly indicate the goodness of fit of the regression model.
4. Note that the standard deviation of the independent variable and the mean of the residuals do not provide a measure of how well the regression equation fits the data; the mean of residuals is always zero in ordinary least squares regression.
5. Conclude that the coefficient of determination \(R^{2}\) is the most appropriate statistic to evaluate the fit of the sample regression equation.