Please note that the filled in answers have been verified as being correct. Here
ID: 1147133 • Letter: P
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