Question

You have just run a multiple regression of EARNINGS on years of schooling S, years of experience EXP, and a dummy variable for MALE on 34 observations, and the value of the coefficient of determination is 0.65 . Assume our regression includes a constant if not otherwise specified. To determine if this indicates that ALL of the independent variables explain a significant portion of the variation in the dependent variable at alpha=5\%, you would perform a

HINT:
Ask yournelf What is n ?
What is k ?
What is g?
A. b-test with a critical value of 1(30,0.025)=2.042
B. F-test with a critical value of F(3,30,0.05)=2.92
C.t-test with a critical value of t(30,0.05)
D. Ftest with a critical value of F 3,31,0.05
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Answer 1

To determine if the independent variables significantly explain the variation in EARNINGS in a multiple regression, an F-test is used with degrees of freedom (df1=3, df2=30) and an alpha level of 5%. The critical value from an F-distribution table is F(3,30,0.05)=2.92.

Step-by-step explanation:

To determine if all of the independent variables in the multiple regression explain a significant portion of the variation in the dependent variable EARNINGS, you would perform an F-test. Since the regression has 34 observations and includes three independent variables (years of schooling S, years of experience EXP, and a dummy variable for MALE) and a constant, we have:

• n (number of observations) = 34
• k (number of independent variables) = 3
• The degrees of freedom for the regression is df1 = k = 3
• The degrees of freedom for the error is df2 = n - k - 1 = 34 - 3 - 1 = 30

With an alpha level of 5%, the critical value for the F-test can be found using an F-distribution table, which yields F(3,30,0.05)=2.92. If the calculated F-statistic from the regression output is greater than this critical value, we would reject the null hypothesis that the independent variables do not explain a significant amount of variation in EARNINGS.