Question #92
Reading: Reading 1 Multiple Regression
PDF File: Reading 1 Multiple Regression.pdf
Page: 44
Status: Unattempted
Correct Answer: B
Part of Context Group: Q92-93
First in Group
Shared Context
Question
Which of the following statements best describes the explanatory power of the estimated regression?
Answer Choices:
A. The residual standard error of only 0.3 indicates that the regression equation is a good fit for the sample data
B. The independent variables explain 61.58% of the variation in housing starts
C. The large F-statistic indicates that both independent variables help explain changes in housing starts
Explanation
The coefficient of determination is the statistic used to identify explanatory power. This
can be calculated from the ANOVA table as 3.896 / 6.327 × 100 = 61.58%.
The residual standard error of 0.3 indicates that the standard deviation of the residuals is
0.3 million housing starts. Without knowledge of the data for the dependent variable, it is
not possible to assess whether this is a small or a large error.
The F-statistic does not enable us to conclude on both independent variables. It only
allows us the reject the hypothesis that all regression coefficients are zero and accept the
hypothesis that at least one isn't.