Question

Using the appropriate model, sample size n, and output below: Model: y = β0 + β1x1 + β2x2 + β3x3 + ε Sample size: n = 16 Regression Statistics Multiple R .9979 R Square .9958 Adjusted R Square .9947 Standard Error 403.4885 Observations 16 ANOVA DF SS MS F Significance F Regression 3 462,169,641.8709 154,056,547.2903 946.2760 .0000 Residual 12 1,953,635.6197 162,802.9683 Total 15 464,123,277.4907 (1) Report SSE, s2, and s as shown on the output. (Round your answers to 4 decimal places.) SSE s2 s (2) Report R2 and R⎯⎯⎯2 as shown on the output. (Round your answers to 4 decimal places.) R2 Picture (3) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round your answers to 4 decimal places.) Total variation Unexplained variation Explained variation (4) Calculate the F(model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. (Round your answer to 3 decimal places.) F(model) (5) Use the F(model) statistic and the appropriate rejection point to test the significance of the linear regression model under consideration by setting α equal to .05. H0: β1 = β2 = β3 = 0 by setting α = .05. (6) Use the F(model) statistic and the appropriate rejection point to test the significance of the linear regression model under consideration by setting α equal to .01. H0: β1 = β2 = β3 = 0 by setting α = .01. (7) Find the p-value related to F(model) on the output. Using the p-value, test the significance of the linear regression model by setting α = .10, .05, .01, and .001. p-value = .000. H0 at α = .05, .01, and .001.

Answer 1

(1) Report SSE, s2, and s as shown on the output. (Round your answers to 4 decimal places.)

SSE= 1,953,635.6197 , s2=162,802.9683 , s =403.4885

(2) Report R2 and R⎯⎯⎯2 as shown on the output. (Round your answers to 4 decimal places.)

R2=.9958

(3) Report the total variation=, unexplained variation, and explained variation as shown on the output. (Round your answers to 4 decimal places.) Total variation=15 464,123,277.4907

Unexplained variation=1,953,635.6197

Explained variation =462,169,641.8709

(4) Calculate the F(model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. (Round your answer to 3 decimal places.) F(model)

F=946.2760

(5) Use the F(model) statistic and the appropriate rejection point to test the significance of the linear regression model under consideration by setting α equal to .05. H0: β1 = β2 = β3 = 0 by setting α = .05.

rejection region=3.49

(6) Use the F(model) statistic and the appropriate rejection point to test the significance of the linear regression model under consideration by setting α equal to .01. H0: β1 = β2 = β3 = 0 by setting α = .01.

reject the H0 as the p-value of regression is less than alpha=0.01

or calcuateld F=946.276 is more than critical F(0.01)=5.9525

(7) Find the p-value related to F(model) on the output. Using the p-value, test the significance of the linear regression model by setting α = .10, .05, .01, and .001. p-value = .000. H0 at α = .05, .01, and .001

p-vaue=0.000
.