Refer to the ANOVA table for this regression Source Regressi

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)

Solution

b) From the table F value is = 1.95

c-1) F-statistic = (ESS/df)/(RSS/df)

F= 59601/35615 = 1.67

c-2) No, the overall regression is not significant because the F-calculated < F-critical.

c-3) The correct option is a)

d) R² = ESS/TSS = (1192019/2794688) = 0.426

Adjusted R² = 1 –[(1-R2)(N-1)/(N-k-1)] = 1-[(1-0.426)(65)/45]

Adjusted R² = 1-(0.829) = 0.171