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Lesson_12n13_Workbook_F12_Version_Space_

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Unformatted text preview: ______________________________________________________________________________________ _________________________________________________________________________________________ PROBLEM # 12.8 In simple linear regression, the regression equation is a straight line. In multiple regressions, what geometric form is taken by the regression equation when there are two independent variables? When there are three or more independent variables? When there are two independent variables, the regression equation can be thought of in terms of a_____________________________________. When there are three or more independent variables, the regression equation becomes a mathematical entity called a _______________________________________; _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ _________________________________________________________________________ PROBLEM # 12.9 What assumptions are required in using the multiple regression models? In terms of the residual component of the model, the assumptions underlying multiple regression are: 1. For any __________________________________ for the __________________________________, the population of residuals will be __________________________________ with a mean of _________ and a standard deviation of σ. 7 2. The standard deviation of the error terms is the _____________regardless of the combination of values taken on by the independent variables. 3. The error terms are statistically _____________________________________________________. PROBLEM # 12.10- The following data have been reported for a sample of 10 major U.S. zoological parks: City Y=Budget X1= Attendance X2= Acres 1 2 3 4 5 6 7 8 9 10 $19.5 million 40.0 11.9 14.0 11.6 22.2 20.5 26.0 17.0 14.6 0.6 million 2.0 0.4 1.0 1.5 1.3 1.3 2.5 0.9 1.1 210 216 70 125 55 80 42 91 125 92 X3= Number of Species 271 400 377 277 721 400 437 759 270 260 a. Determine the least squares multiple regression equation. G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 H I SUMMARY OUTPUT Regression Statistics Multiple R 0.8817 R Square 0.7774 Adjusted R Square 0.6662 Standard Error 4.9139 Observations 10 Budget 19.5 40.0 11.9 14.0 11.6 22.2 20.5 26.0 17.0 14.6 J Attend 0.6 2.0 0.4 1.0 1.5 1.3 1.3 2.5 0.9 1.1 K Acres 210 216 70 125 55 80 42 91 125 92 L Species 271 400 377 277 721 400 437 759 270 260 M ANOVA df Regression Residual Total Intercept Attend Acres Species 3 6 9 SS 506.06 144.88 650.94 Coefficients Standard Error 4.31855 6.600 11.95568 4.142 0.06115 0.033 -0.01538 0.016 MS 168.69 24.15 F Significance F 6.99 0.022 t Stat P-value 0.654 0.537 2.887 0.028 1.829 0.117 -0.984 0.363 Lower 95% Upper 95% -11.8314 20.4685 1.8209 22.09...
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