Tutorial 6_Questions &amp; Solutions

# Tutorial 6_Questions & Solutions - 1 Tutorial 6...

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Unformatted text preview: 1 Tutorial 6 Exercises for Lecture 6 MULTIPLE REGRESSION B At the end of this tutorial you should be able to • state the assumptions behind the normal multiple regression model • use a scatter plot to assess whether the homoskedasticity assumption is violated • use residual plots and the Durbin-Watson statistic to assess the assumption that the errors are serially uncorrelated • use a residual histogram to assess whether the normality assumption is violated • use the VIF to measure collinearity • use and understand the role of dummy variables in regression analysis b Reading : Black et al , Sections 13.3, 15.4, 16.5, 15.2. Q1. The data file Multiple Regression B Q1.XLS contains data on 90 homes in the towns of Glen Cove, Freeport and Roslyn. Variables in the file include appraised value (\$’000), land area of the property (acres), number of cars that can be parked in the garage, interior size (sq. ft.), age in years, number of rooms and number of bathrooms. A subset of the data is reported in the table below. Home Appraised Value Land House Size Rooms Bathrooms 1 466 0.2297 2448 7 3.5 2 364 0.2192 1942 7 2.5 3 429 0.163 2073 5 3 4 548.4 0.4608 2707 8 2.5 5 405.9 0.2549 2042 7 1.5 6 374.1 0.229 2089 7 2 7 315 0.1808 1433 7 2 8 749.74 0.5015 2991 9 2.5 9 217.7 0.2229 1008 5 1 10 635.7 0.13 3202 8 2.5 11 350.7 0.1763 2230 8 2 12 : 455 : 0.42 : 1848 : 7 : 2 : A researcher interested in explaining variations in appraisal value has used all 90 observations in the data file to estimate a multiple regression model and has obtained the following results: Regression Statistics Multiple R 0.824482489 R Square 0.679771374 Adjusted R Square 0.664701792 Standard Error 108.6788729 Observations 90 ANOVA df SS MS F Regression 4 2131139.591 532784.8978 45.10883954 Residual 85 1003943.28 11811.09741 Total 89 3135082.871 Coefficients Standard Error t Stat P-value Intercept 18.88 56.63889878 0.333355631 0.73968676 Land (acres) 474.15 114.0854645 4.156122453 7.68592E-05 2 House Size(sq ft) 0.11 0.02319095 4.653565649 1.18945E-05 Rooms -13.65 8.658722529 -1.576290318 0.11867366 Baths 84.46 18.60261262 4.540483581 1.83609E-05 RESIDUAL OUTPUT Observation Predicted Appraised Value Residuals 1 592.07 -126.07 2 448.02 -84.02 3 505.04 -76.04 4 631.48 -83.08 5 391.27 14.63 6 : 426.30 : -52.20 : Durbin-Watson Statistic 0.842 House Size(sq ft) Residual Plot-400-300-200-100 100 200 300 500 1000 1500 2000 2500 3000 3500 4000 4500 House Size(sq ft) Residuals Rooms Residual Plot-400-300-200-100 100 200 300 2 4 6 8 10 12 14 Rooms Residuals Values of the Variance Inflation Factor (VIF) were obtained from the following auxiliary regressions....
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## This note was uploaded on 10/21/2009 for the course ECON 1320 taught by Professor John during the Three '08 term at Queensland.

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Tutorial 6_Questions & Solutions - 1 Tutorial 6...

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