Exercise 15.11 (Algo) THE FUEL CONSUMPTION CASEUsing the appropriate model, sample size n, and output below: Model: y = β0 + β1x1 + β2x2 + β3x3 + ε Sample size: n = 8 S = .5561 Sq = 93.1% Sq(adj) = 90.3% Analysis of VarianceSource DF SS MS F PRegression 2 20.8141 10.4070 33.66 0.0013Residual Error 5 1.5459 0.3092 Total 7 22.3600 (1) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round your answers to 3 decimal places.) (2) Report R2 and as shown on the output. (Round your answers to 3 decimal places.) (3) Report SSE, s2, and s as shown on the output. Calculate s2 from SSE and other numbers. (Round your answers to 4 decimal places.) (4) Calculate the F(model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. (Round your answer to 2 decimal places.)(5) Use the F(model) statistic and the appropriate critical value to test the significance of the linear regression model under consideration by setting α equal to .05. (6) 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. (Round your answer to 4 decimal places.)
Question
Exercise 15.11 (Algo) THE FUEL CONSUMPTION CASEUsing the appropriate model, sample size n, and output below: Model: y = β0 + β1x1 + β2x2 + β3x3 + ε Sample size: n = 8 S = .5561 Sq = 93.1% Sq(adj) = 90.3% Analysis of VarianceSource DF SS MS F PRegression 2 20.8141 10.4070 33.66 0.0013Residual Error 5 1.5459 0.3092 Total 7 22.3600 (1) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round your answers to 3 decimal places.) (2) Report R2 and as shown on the output. (Round your answers to 3 decimal places.) (3) Report SSE, s2, and s as shown on the output. Calculate s2 from SSE and other numbers. (Round your answers to 4 decimal places.) (4) Calculate the F(model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. (Round your answer to 2 decimal places.)(5) Use the F(model) statistic and the appropriate critical value to test the significance of the linear regression model under consideration by setting α equal to .05. (6) 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. (Round your answer to 4 decimal places.)
Solution
(1) The total variation is 22.3600, the unexplained variation is 1.5459, and the explained variation is 20.8141.
(2) R2 is 93.1% and R2(adj) is 90.3%.
(3) SSE is 1.5459, s2 is 0.3092, and s is 0.5561. To calculate s2, divide SSE by the degrees of freedom.
(4) To calculate the F(model) statistic, divide the explained variation by the unexplained variation. The F(model) statistic is 33.66.
(5) To test the significance of the linear regression model, compare the F(model) statistic with the critical value at α = 0.05.
(6) The p-value related to F(model) is not provided in the given output.
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