Assignment 1

Assignment 1 1. Work through Example 1 of Chapter 4 (pp. 62-79) of the eBook: Housing Prices. Do not submit a solution to this problem though. The real estate company wants to develop a model to predict the selling price of a home based on the data collected. The resulting pricing model will be used to determine initial asking prices for homes in the company’s portfolio. Linear Equation Pred Price = 197.150171156985 + 59.208097328214 * : Baths + 0.0511232612829319 * :Square Feet + -3.79851039837821 * :Miles to Base + 5.00610916953334 * :Acres Response Price Whole Model Actual by Predicted Plot Effect Summary Source Logworth PValue Miles to Base 4.742 0.00002 Acres 2.931 0.00117 Baths 2.910 0.00123 Square Feet 1.534 0.02927

Residual by Predicted Plot Summary of Fit RSquare 0.801793 RSquare Adj 0.781972 Root Mean Square Error 61.91579 Mean of Response 391.1911 Observations (or Sum Wgts) 45 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 4 620305.34 155076 40.4523 Error 40 153342.58 3834 Prob > F C. Total 44 773647.92 <.0001* Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Lower 95% Upper 95% Intercept 197.15017 34.72253 5.68 <.0001* 126.97332 267.32702 Baths 59.208097 17.0208 3.48 0.0012* 24.807769 93.608426 Square Feet 0.0511233 0.022611 2.26 0.0293* 0.0054245 0.096822 Miles to Base -3.79851 0.780608 -4.87 <.0001* -5.376177 -2.220844 Acres 5.0061092 1.43194 3.50 0.0012* 2.112051 7.9001673 Effect Tests Source Nparm DF Sum of Squares F Ratio Prob > F Baths 1 1 46387.913 12.1005 0.0012* Square Feet 1 1 19597.284 5.1120 0.0293* Miles to Base 1 1 90774.517 23.6789 <.0001* Acres 1 1 46854.783 12.2222 0.0012*

Miles to Base Leverage Plot Acres Leverage Plot Prediction Profiler

2. Use the BankRevenue.jmp data provided with BBM book (posted on the Textbook Data page). Fit a full model to Log(Rev_Total) using Log(Bal_Total) and the other variables as model effects (using main effects only - no cross terms). Note, you may need to re-create these columns. Use the Minimum BIC stopping rule and stepwise regression to build your model. BIC Model Response Log[Rev_Total] Effect Summary Source Logworth PValue Log[Bal_Total] 1368.799 0.00000 Check 275.558 0.00000 CARD 235.456 0.00000 Offer 4.083 0.00008 Lack Of Fit Source DF Sum of Squares Mean Square F Ratio Lack Of Fit 5992 3932.2562 0.656251 0.9852 Pure Error 1423 947.8833 0.666116 Prob > F Total Error 7415 4880.1395 0.6431 Max RSq 0.9219 Summary of Fit RSquare 0.597695 RSquare Adj 0.597478 Root Mean Square Error 0.811261 Mean of Response 0.059558 Observations (or Sum Wgts) 7420 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 4 7250.315 1812.58 2754.075 Error 7415 4880.140 0.66 Prob > F C. Total 7419 12130.455 <.0001* Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -2.45907 0.025795 -95.33 <.0001* Log[Bal_Total] 0.4342763 0.004361 99.57 <.0001* Offer[0] -0.075493 0.019166 -3.94 <.0001* CARD[0] -0.765025 0.022471 -34.05 <.0001* Check[0] 0.6434943 0.017353 37.08 <.0001*

Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 6 7261.582 1210.26 1842.661 Error 7413 4868.873 0.66 Prob > F C. Total 7419 12130.455 <.0001* Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -2.538458 0.034835 -72.87 <.0001* Log[Bal_Total] 0.4424023 0.004923 89.86 <.0001* LOAN[0] 0.0572065 0.017386 3.29 0.0010* INSUR[0] 0.0400496 0.013363 3.00 0.0027* Offer[0] -0.069977 0.019193 -3.65 0.0003* CARD[0] -0.7964 0.023826 -33.43 <.0001* Check[0] 0.7049116 0.022894 30.79 <.0001* BIC AICc Number of Predictors 4 6 RSquare 0.597695 0.598624 RSquare Adj 0.597478 0.598299 Root Mean Square Error 0.811261 0.810433 c. Which is the "better" model? Explain. (Just do your best.) There isn't a definitive correct choice in this scenario. While the model with more predictor variables shows a slightly higher RSq Adj and a lower RMSE, the closeness of the RSq Adj and RMSE values suggests that selecting the model with fewer predictors might be a reasonable decision. In general, simple model often gives better outcomes.