B. The house on the east side is $13073 more than the one on the west side.C. The house on the east side is $7563 less than the one on the west side.D. The house on the east side is $7563 more than the one on the west side.E. There is no sales price difference between the areas.A. 16.421B. 9.07C. 10.996D. 136.97E. 4.452A. The group of independent variables do not explain sales price.B. The group of independent variables explains sales price.C. The group of dependent variables do not explain sales price.D. The independent variables have the same coefficients.E. Inconclusive since the group of variables appears to be homogeneous.MSCI 3710Multiple Regression (Chapter 15): Sample Exam Problem 13Note: The following problem is taken from the Final Exam in Spring 2002, questions 24-27.Use the following information to answer the next four questions. (Kvanli Chapter 15)A real estate association in a suburban community would like to develop a model to predict selling price (in $1,000) of a house from size (in 100 square-foot), number of rooms, for two different neighborhoods – one on the east side of the community and the other on the west side.A random sample of 20 houses was selected with the following results.obsPrice ($1000) sq.ft (100) Rooms East1125 42 5 12112.4 40 4 1(etc.)SUMMARY OUTPUTRegression StatisticsMultiple R 0.821R Square 0.673Adjusted R Square 0.612Standard Error 11.673Observations 20ANOVA df SS MS F Significance FRegression 3 4495.39 1498.46 ----- 0.00036Residual 16 2180.32 136.27Total 19 6675.71 Coefficients Standard Error t Stat P-valueIntercept 70.097 16.421 4.269 0.001sq.ft (100) 0.843 0.411 2.048 0.057Rooms 7.564 4.452 1.699 0.109East -13.073 5.351 -2.443 0.027RESIDUAL OUTPUTObservation Predicted Price ($1000) Residuals Standard Residuals1 130.241 -5.241 -0.4892 120.991 -8.591 -0.8023 114.249 31.051 2.8994 139.511 6.989 0.6525 103.314 -0.114 -0.0116 141.196 -3.396 -0.3177 126.890 2.210 0.2068 122.676 -9.476 -0.8859 146.232 -13.432 -1.25410 147.527 -2.527 -0.23611 126.499 -12.999 -1.21312 161.854 19.446 1.81513 147.527 -5.127 -0.47914 142.491 3.709 0.34615 151.741 -4.341 -0.40516 134.064 -10.364 -0.96717 128.165 6.435 0.60118 139.943 3.657 0.34119 163.519 2.181 0.20420 148.370 -0.070 -0.0071. According to the least squares regression from this sample, for a fixed size (sq. ft.) and number of rooms, how will sales price for a house in the East compare to a house in the West?A. The house on the east side is $13073 less than the one on the west side.B. The house on the east side is $13073 more than the one on the west side.C. The house on the east side is $7563 less than the one on the west side.D. The house on the east side is $7563 more than the one on the west side.E. There is no sales price difference between the areas.2. Which set of independent variables are found to be significant predictor of house sales price at 0.05 significance level?A. Size (sq. ft.) and Number of roomsB. Number of roomsC. Neighborhood D. Size (sq. ft.) and NeighborhoodE. Size (sq. ft.) and Number of rooms3. The calculated value of the test statistic to test the complete regression model (i.e., for the Ho:β1 = β2 = β3 = 0 ) is:A. 16.421B. 9.07C. 10.996D. 136.97E. 4.4524. At the 5% level of significance, what is your conclusion about the test of the regression model?A. The group of independent variables do not explain sales price.B. The group of independent variables explains sales price.C. The group of dependent variables do not explain sales price.D. The independent variables have the same coefficients.E. Inconclusive since the group of variables appears to be
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