Question #20
Reading: Reading 1 Multiple Regression
PDF File: Reading 1 Multiple Regression.pdf
Page: 9
Status: Unattempted
Correct Answer: A
Question
An analyst runs a regression of monthly value-stock returns on five independent variables over 48 months. The total sum of squares is 430, and the sum of squared errors is 170. Test the null hypothesis at the 2.5% and 5% significance level that all five of the independent variables are equal to zero.
Answer Choices:
A. Rejected at 5% significance only
B. Not rejected at 2.5% or 5.0% significance
C. Rejected at 2.5% significance and 5% significance
Explanation
The F-statistic is equal to the ratio of the mean squared regression (MSR) to the mean
squared error (MSE).
RSS = SST – SSE = 430 – 170 = 260
MSR = 260 / 5 = 52
MSE = 170 / (48 – 5 – 1) = 4.05
F = 52 / 4.05 = 12.84
The critical F-value for 5 and 42 degrees of freedom at a 5% significance level is
approximately 2.44. The critical F-value for 5 and 42 degrees of freedom at a 2.5%
significance level is approximately 2.89. Therefore, we can reject the null hypothesis at
either level of significance and conclude that at least one of the five independent variables
explains a significant portion of the variation of the dependent variable.