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Unformatted text preview: Chapter 12: Additional Topics in Regression Analysis 247 Chapter 12: Additional Topics in Regression Analysis 121 1 1 2 2 3 3 4 4 i i i i i i Y X X X X β β β β β ε = + + + + + where Y i = College GPA X 1 = SAT score X 2 = 1 for sophomore, 0 otherwise X 3 = 1 for junior, 0 otherwise X 4 = 1 for senior, 0 otherwise The excluded category is first year 122 1 1 2 2 3 3 4 4 5 5 i i i i i i i Y X X X X X β β β β β β ε = + + + + + + where Y i = wages X 1 = Years of experience X 2 = 1 for Germany, 0 otherwise X 3 = 1 for Great Britain, 0 otherwise X 4 = 1 for Japan, 0 otherwise X 5 = 1 for Turkey, 0 otherwise The excluded category consists of wages in the United States 123 1 1 2 2 3 3 4 4 i i i i i i Y X X X X β β β β β ε = + + + + + where Y i = cost per unit X 1 = 1 for computer controlled machines, 0 otherwise X 2 = 1 for computer controlled machines & computer controlled material handling, 0 otherwise X 3 = 1 for South Africa, 0 otherwise X 4 = 1 for Japan, 0 otherwise The excluded category is Colombia 12.4 a. For any observation, the values of the dummy variables sum to one. Since the equation has an intercept term, there is perfect multicollinearity and the existence of the “dummy variable trap”. b. 3 β measures the expected difference between demand in the first and fourth quarters, all else equal. 4 β measures the expected difference between demand in the second and fourth quarters, all else equal. 5 β measures the expected difference between demand in the third and fourth quarters, all else equal. 12.5 a. 2 1 2 : 0, : H H β β = 21,.05 .027 1.286; 1.721 .021 t t = = = , therefore, do not reject H at the 5% level b. 21,.025 2.08 t = , 95% CI: .142 ± 2.08(.047), (.0442, .2398) c. Total effect: .142 .25 1 .432 = 248 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition A $.25 increase in clothing expenditures 126 Regression Analysis: Y Retail Sales versus X Income, Ylag1 The regression equation is Y Retail Sales = 1752 + 0.367 X Income + 0.053 Ylag1 21 cases used 1 cases contain missing values Predictor Coef SE Coef T P Constant 1751.6 500.0 3.50 0.003 X Incom 0.36734 0.08054 4.56 0.000 Ylag1 0.0533 0.2035 0.26 0.796 S = 153.4 RSq = 91.7% RSq(adj) = 90.7% 18,.10 .0533 .2619; 1.33 .2035 t t = = = , therefore, do not reject H at the 20% level 127 Regression Analysis: Y_money versus X1_income, X2_ir, Y_lagmoney The regression equation is Y_money =  2309 + 0.158 X1_income  14126 X2_ir + 1.06 Y_lagmoney 27 cases used 1 cases contain missing values Predictor Coef SE Coef T P Constant 2309 1876 1.23 0.231 X1_incom 0.1584 0.2263 0.70 0.491 X2_ir 14126 6372 2.22 0.037 Y_lagmon 1.0631 0.1266 8.40 0.000 S = 456.1 RSq = 97.6% RSq(adj) = 97.3% Analysis of Variance Source DF SS MS F P Regression 3 194108213 64702738 311.02 0.000 Residual Error 23 4784762 208033 Total 26 198892975 Source DF Seq SS X1_incom 1 167714527 X2_ir 1 11728933 Y_lagmon 1 14664753 Unusual Observations Obs X1_incom Y_money...
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 Spring '09
 StevenJordan
 Regression Analysis, Errors and residuals in statistics, Source Regression Residual, Regression Residual Error, Variance Source Regression, Residual Error Total

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