5. An appraisal specialist has applied multiple regression analysis to prepare a mass appraisal model for this Edmonton data. Four variations of this model have been prepared, all using PRICE as the dependent variable. The model results are provided in the "MRA" worksheet in the "Project 2: Assessment Database" file. (a) Compare the results of Regression 1 with the results obtained in Question 4. What are the main differences? Which results are better? (Hint: consider the descriptive statistics for the two regression results). (5 marks) (b) Using the results for Regressions 1, 2, and 3, obtain a predicted value for a property with 2,500 square feet of living area, a 7,200 square foot lot, 3 bedrooms, 2 bathrooms, 2 fireplaces, and 1 family room. Why are they different? (4 marks) (c) Which variables in Regression 3 are the most important? Why? List the top five variables in decreasing order of importance. (2 marks) (d) In Regression 4 there are two variables that are related to the lot - LOT_SIZE and either WIDTH or DEPTH. How would you explain the coefficient for the WIDTH or DEPTH variable? If the results are different than expected, explain why. (4 marks) (e) Which of the four regression results do you consider to be the best and why? In your answer, consider the statistics for each regression (R, SEE, F-value, and COV) and the coefficients and t- statistics for each variable. Include a table summarizing your comparison of the four regression results. (Hint: calculate the COV for each regression). (10 marks) Regression 1 Descriptive Statistics Regression 2 Descriptive Statistics Mean Mean Std. Deviation N Std. Deviation N PRICE LIVAREA 411958.46 84165.255 260 PRICE 411958.46 84165.255 260 1640.57 428.507 260 BEDROOMS 2.85 .507 260 LOT_SIZE 7411.02 1688.431 260 BATHS 1.6798 55414 260 LIVAREA 1640.57 428.507 260 LOT_SIZE 7411.02 1688.431 260 Variables Entered/Removed Variables Entered/Removed" Model Variables Entered Variables Removed Method Model Variables Entered Variables Removed Method LOT_SIZE, Enter BEDROOMS, Enter LOT_SIZE, LIVAREA a. Dependent Variable: PRICE b. All requested variables entered. BATHS, LIVAREA a. Dependent Variable: PRICE b. All requested variables entered. Model Summary Model 1 R R Square Adjusted R Square Std. Error of the Estimate Model .772 595 592 53755.818 2 a. Predictors: (Constant), LOT_SIZE, LIVAREA Model Summary R R Square Adjusted R Square Std. Error of the Estimate 797 636 630 51175.836 a. Predictors: (Constant), LOT_SIZE, BEDROOMS, BATHS, LIVAREA Regression Residual Total nt Variable: PRICE ANOVA Sum of Squares ANOVA df Mean Square F Sig. Model Sum of Squares df Mean Square F Sig. 1092051816307.490 2 546025908153.745 188.957 000 12 Regression 1166865262226.340 4 291716315556.586 111.386 000 742649815077.126 257 2889687996.409 Residual 667836369158.271 255 2618966153.562 1834701631384.620 259 Total 1834701631384.620 259 s: (Constant), LOT SIZE, LIVAREA a. Dependent Variable: PRICE b. Predictors: (Constant), LOT_SIZE, BEDROOMS, BATHS, LIVAREA Coefficients Coefficients Standardized Unstandardized Coefficients Coefficients Unstandardized Coefficients Standardized Coefficients B Std. Error Beta t Sig Model B Std. Error Beta t Sig. (Constant) 125149.348 17271.167 7.246 000 12 (Constant) 53872.716 22107.531 2.437 016 LIVAREA 138.103 8.239 703 16.762 .000 BEDROOMS 31404.828 6841.387 189 4.590 000 LOT_SIZE 8.129 2.091 163 3.888 000 BATHS 23892.937 7836.937 157 3.049 003 ht Variable: PRICE LIVAREA 102.683 10.979 523 9.353 000 LOT_SIZE 8.078 1.994 162 4.052 .000 a. Dependent Variable: PRICE Regression 3 Descriptive Statistics Regression 4 Descriptive Statistics Mean Std. Deviation N Mean Std. Deviation N PRICE 411958.46 84165.255 260 BEDROOMS 2.85 507 260 PRICE BEDROOMS 411958.46 84165.255 260 2.85 507 260 BATHS 1.6798 55414 260 BATHS 1.6798 55414 260 FAMILYRM .80 535 260 FAMILYRM .80 535 260 FIREPLCS 1.15 .730 260 FIREPLCS 1.15 .730 260 LIVAREA 1640.57 428.507 260 LIVAREA 1640.57 428.507 260 LOT_SIZE 7411.02 1688.431 260 LOT_SIZE 7411.02 1688.431 260 DEPTH 117.819 11.1583 260 Variables Entered/Removed Variables Entered/Removed Variables Entered Variables Removed Method Model Variables Entered Variables Removed Method Model 3 LOT_SIZE DEPTH, BEDROOMS, BEDROOMS, FAMILYRM, Enter FAMILYRM, FIREPLCS, BATHS, LIVAREA a. Dependent Variable: PRICE b. All requested variables entered. FIREPLCS, BATHS, LIVAREA, LOT SIZE a. Dependent Variable: PRICE b. All requested variables entered. Enter Model Summary Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate Model R R Square Adjusted R Square Std. Error of the Estimate 3 806 .650 642 50359.390 4 808 652 643 50305.898 a. Predictors: (Constant), LOT_SIZE, BEDROOMS, FAMILYRM, FIREPLCS, BATHS, LIVAREA a. Predictors: (Constant), DEPTH, BEDROOMS, BATHS, LOT_SIZE, FAMILYRM, FIREPLCS, LIVAREA Regression Residual Total ariable: PRICE ANOVA ANOVA Sum of Squares df Mean Square F Sig. Model Sum of Squares df Mean Square F Sig 1193076384331.620 6 198846064055.270 78.407 000 14 Regression 1196969432620.860 7 170995633231.552 67.569 000 641625247052.997 253 2536068170.170 Residual 637732198763.751 252 2530683328.428 1834701631384.620 259 Total 1834701631384.620 259 Constant), LOT SIZE, BEDROOMS, FAMILYRM, FIREPLCS, BATHS, LIVAREA a. Dependent Variable: PRICE b. Predictors: (Constant), DEPTH, BEDROOMS, BATHS, LOT_SIZE, FAMILYRM, FIREPLCS, LIVAREA Coefficients Coefficients Unstandardized Coefficients Standardized Coefficients Standardized Unstandardized Coefficients Coefficients B Std. Error Beta t Sig. Model B Std. Error Beta t Sig. (Constant) BEDROOMS 72552.135 22582.761 3.213 .001 30394.954 6740.116 183 4.510 .000 (Constant) BEDROOMS 109742.509 37523.333 2.925 004 30882.849 6744.438 186 4.579 000 BATHS 18299.725 8088.722 120 2.262 .025 BATHS 18055.867 8082.522 119 2.234 .026 FAMILYRM 4229.055 7228.230 .027 585 559 FAMILYRM 5093.574 7254.117 032 702 483 FIREPLCS 17499.728 5576.331 152 3.138 .002 FIREPLCS 17793.825 5575.452 154 3.191 002 LIVAREA 87.852 11.946 447 7.354 000 LIVAREA 86.965 11.954 443 7.275 000 LOT_SIZE 7.319 1.978 147 3.700.000 LOT_SIZE 8.625 2.239 173 3.852.000 ariable: PRICE DEPTH -402.550 324.559 -.053 -1.240 216 a. Dependent Variable: PRICE