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Let (1, 2). Consider testing the hypotheses: = Ho:y=0, Hi:#0. (iia) Obtain the F-value for testing the hypotheses from the Analysis of Variance Table provided above. (iib) Obtain the F-value through the Wald statistic W = ³Û±¹â. (iic) Verify that W/2 follows a F2,135 distribution under the null hypothesis. (iid) Draw conclusion whether Ho should be rejected at level 0.05. 2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model below: 1 y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €. See Question 2, Tutorial 3 for the meaning of the variables in the above model. The following results are obtained: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.302e+03 4.320e+02 3.015 0.00307 x4 x6 x8 x4:x8 x6:x8 -1.442e+02 2.056e+01 -7.013 1.02e-10 6.340e-01 6.099e+00 0.104 0.91737 -9.455e-02 5.802e-02 -1.630 0.10550 2.882e-02 2.589e-03 11.132 1.673e-03 7.215e-04 2.319 < 2e-16 0.02191 Analysis of Variance Table 14595537 75.0499 1.244e-14 Df Sum Sq Mean Sq F value Pr(>F) x4 1 3486722 3486722 17.9286 4.214e-05 x6 1 14595537 x8 x4:x8 x6:x8 1 132.4836 < 2.2e-16 1045693 194478 5.3769 0.02191 1 1198603043 1198603043 6163.1900 < 2.2e-16 1 25765100 25765100 1045693 Residuals 135 26254490 Estimated variance matrix (Intercept) x4 x6 x8 x4:x8 x6:x8 (Intercept) x4 x6 x8 x4:x8 x6:x8 0.18875694 1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953 -5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013 -2.322825e+03 3.160915e+01 3.720077e+01 0.18297010 -0.00373435 -0.00266544 -1.625142e+01 6.162178e-01 1.829701e-01 0.00336601 -0.00012093 -0.00003820 5.718895e-01 -3.608028e-02 -3.734350e-03 -0.00012093 0.00000670 0.00000093 1.887569e-01 -4.450130e-03 -2.665440e-03 -0.00003820 0.00000093 0.00000052

Let (1, 2). Consider testing the hypotheses: = Ho:y=0, Hi:#0. (iia) Obtain the F-value for testing the hypotheses from the Analysis of Variance Table provided above. (iib) Obtain the F-value through the Wald statistic W = ³Û±¹â. (iic) Verify that W/2 follows a F2,135 distribution under the null hypothesis. (iid) Draw conclusion whether Ho should be rejected at level 0.05. 2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model below: 1 y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €. See Question 2, Tutorial 3 for the meaning of the variables in the above model. The following results are obtained: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.302e+03 4.320e+02 3.015 0.00307 x4 x6 x8 x4:x8 x6:x8 -1.442e+02 2.056e+01 -7.013 1.02e-10 6.340e-01 6.099e+00 0.104 0.91737 -9.455e-02 5.802e-02 -1.630 0.10550 2.882e-02 2.589e-03 11.132 1.673e-03 7.215e-04 2.319 < 2e-16 0.02191 Analysis of Variance Table 14595537 75.0499 1.244e-14 Df Sum Sq Mean Sq F value Pr(>F) x4 1 3486722 3486722 17.9286 4.214e-05 x6 1 14595537 x8 x4:x8 x6:x8 1 132.4836 < 2.2e-16 1045693 194478 5.3769 0.02191 1 1198603043 1198603043 6163.1900 < 2.2e-16 1 25765100 25765100 1045693 Residuals 135 26254490 Estimated variance matrix (Intercept) x4 x6 x8 x4:x8 x6:x8 (Intercept) x4 x6 x8 x4:x8 x6:x8 0.18875694 1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953 -5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013 -2.322825e+03 3.160915e+01 3.720077e+01 0.18297010 -0.00373435 -0.00266544 -1.625142e+01 6.162178e-01 1.829701e-01 0.00336601 -0.00012093 -0.00003820 5.718895e-01 -3.608028e-02 -3.734350e-03 -0.00012093 0.00000670 0.00000093 1.887569e-01 -4.450130e-03 -2.665440e-03 -0.00003820 0.00000093 0.00000052

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Let (1, 2). Consider testing the hypotheses: = Ho:y=0, Hi:#0. (iia) Obtain the F-value for testing the hypotheses from the Analysis of Variance Table provided above. (iib) Obtain the F-value through the Wald statistic W = ³Û±¹â. (iic) Verify that W/2 follows a F2,135 distribution under the null hypothesis. (iid) Draw conclusion whether Ho should be rejected at level 0.05.
Transcribed Image Text:Let (1, 2). Consider testing the hypotheses: = Ho:y=0, Hi:#0. (iia) Obtain the F-value for testing the hypotheses from the Analysis of Variance Table provided above. (iib) Obtain the F-value through the Wald statistic W = ³Û±¹â. (iic) Verify that W/2 follows a F2,135 distribution under the null hypothesis. (iid) Draw conclusion whether Ho should be rejected at level 0.05.
2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model below: 1 y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €. See Question 2, Tutorial 3 for the meaning of the variables in the above model. The following results are obtained: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.302e+03 4.320e+02 3.015 0.00307 x4 x6 x8 x4:x8 x6:x8 -1.442e+02 2.056e+01 -7.013 1.02e-10 6.340e-01 6.099e+00 0.104 0.91737 -9.455e-02 5.802e-02 -1.630 0.10550 2.882e-02 2.589e-03 11.132 1.673e-03 7.215e-04 2.319 < 2e-16 0.02191 Analysis of Variance Table 14595537 75.0499 1.244e-14 Df Sum Sq Mean Sq F value Pr(>F) x4 1 3486722 3486722 17.9286 4.214e-05 x6 1 14595537 x8 x4:x8 x6:x8 1 132.4836 < 2.2e-16 1045693 194478 5.3769 0.02191 1 1198603043 1198603043 6163.1900 < 2.2e-16 1 25765100 25765100 1045693 Residuals 135 26254490 Estimated variance matrix (Intercept) x4 x6 x8 x4:x8 x6:x8 (Intercept) x4 x6 x8 x4:x8 x6:x8 0.18875694 1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953 -5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013 -2.322825e+03 3.160915e+01 3.720077e+01 0.18297010 -0.00373435 -0.00266544 -1.625142e+01 6.162178e-01 1.829701e-01 0.00336601 -0.00012093 -0.00003820 5.718895e-01 -3.608028e-02 -3.734350e-03 -0.00012093 0.00000670 0.00000093 1.887569e-01 -4.450130e-03 -2.665440e-03 -0.00003820 0.00000093 0.00000052
Transcribed Image Text:2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model below: 1 y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €. See Question 2, Tutorial 3 for the meaning of the variables in the above model. The following results are obtained: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.302e+03 4.320e+02 3.015 0.00307 x4 x6 x8 x4:x8 x6:x8 -1.442e+02 2.056e+01 -7.013 1.02e-10 6.340e-01 6.099e+00 0.104 0.91737 -9.455e-02 5.802e-02 -1.630 0.10550 2.882e-02 2.589e-03 11.132 1.673e-03 7.215e-04 2.319 < 2e-16 0.02191 Analysis of Variance Table 14595537 75.0499 1.244e-14 Df Sum Sq Mean Sq F value Pr(>F) x4 1 3486722 3486722 17.9286 4.214e-05 x6 1 14595537 x8 x4:x8 x6:x8 1 132.4836 < 2.2e-16 1045693 194478 5.3769 0.02191 1 1198603043 1198603043 6163.1900 < 2.2e-16 1 25765100 25765100 1045693 Residuals 135 26254490 Estimated variance matrix (Intercept) x4 x6 x8 x4:x8 x6:x8 (Intercept) x4 x6 x8 x4:x8 x6:x8 0.18875694 1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953 -5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013 -2.322825e+03 3.160915e+01 3.720077e+01 0.18297010 -0.00373435 -0.00266544 -1.625142e+01 6.162178e-01 1.829701e-01 0.00336601 -0.00012093 -0.00003820 5.718895e-01 -3.608028e-02 -3.734350e-03 -0.00012093 0.00000670 0.00000093 1.887569e-01 -4.450130e-03 -2.665440e-03 -0.00003820 0.00000093 0.00000052
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