Please note that the filled in answers have been verified as being correct. Here

Question

Please note that the filled in answers have been verified as being correct. Here is the problem:

Refer to the ANOVA table for this regression Source Regression Residual 1,192,019 20 1,602,669 45 2,794,688 65 MS 59,601 35,615 Total (a) State the degrees of freedom for the F test for overall significance The degrees of freedom for regression are 20 and for error 45 (b) Use Appendix F to look up the critical value of F for = .05. (Round your answer to 2 decimal places.) 05 (c-1) Calculate the F statistic. (Round your answer to 4 decimal places.) F statistic (c-2) The overall regression is significant. No O Yes (c-3) The hypotheses is a. HO All the coefficients are zero (81 = 2-3-0) vs. H1: At least one coefficient is not zero b. HO At least one coefficient is non-zero vs. H1: All the coefficients are zero (81 2-3-0) (d) Calculate R2 and R2adj (Round your answers to 4 decimal places.)

Explanation / Answer

a. 20 and 45
b. For 5 % significance, at numerator degrees of freedom 20 and denominator degrees of freedom 45 the critical table F-value is 2.049
c. c-1, F statistic = MSR/MSE = 59601/35615 = 1.67
c-2, No as the calculated F -value is less than table F-value
c-3 Option a
d. R^2 = (1-SSE/SST) = 1-(1602669/2794688) = 0.426
adj.R^2 = (1-MSE/MST)
MSE = SSE/ (n-2) = 1602669/(66-2) = 25041.7
MST = SST/ (n-1) = 2794688/(65) = 42995.2
So, (1-MSE/MST) = 1-(25041.7/42995.2) = 0.4175

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