Multiple Linear RegressionMultiple Linear Regression ModelingIssues for MLRAnalysis of Real Estate DataSummary StatisticsStatistical InferencesResidual Analysis and Model GoodnessMultiple Linear Regression Analysis of Real Estate DataChapter 11. Linear RegressionMultiple Linear RegressionJ.C. WangJC Wang (WMU) Stat2160 S2160, Chapter 11 1 / 25Multiple Linear Regression Analysis of Real Estate DataOutline1Multiple Linear RegressionMultiple Linear Regression ModelingIssues for MLR2Analysis of Real Estate DataSummary StatisticsStatistical InferencesResidual Analysis and Model GoodnessJC Wang (WMU) Stat2160 S2160, Chapter 11 2 / 25Multiple Linear Regression Analysis of Real Estate DataOutline1Multiple Linear RegressionMultiple Linear Regression ModelingIssues for MLR2Analysis of Real Estate DataSummary StatisticsStatistical InferencesResidual Analysis and Model GoodnessJC Wang (WMU) Stat2160 S2160, Chapter 11 3 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear RegressionThe multiple linear regression analysis concentrates on a model thathas more than one independent (explantaory) variable. Theindependent variables are used to predict the dependent variable.JC Wang (WMU) Stat2160 S2160, Chapter 11 4 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear Regression ModelingPurpose of multiple regression analysis is predictionModel: y = b0+ b1x1+ ... + bnxn; where biare the slopes, y is adependent variable and xiis an independent variable.Correlation coefficient, rij.Coefficient of determination, R2(or multiple R2).JC Wang (WMU) Stat2160 S2160, Chapter 11 5 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear Regression ModelingPurpose of multiple regression analysis is predictionModel: y = b0+ b1x1+ ... + bnxn; where biare the slopes, y is adependent variable and xiis an independent variable.Correlation coefficient, rij.Coefficient of determination, R2(or multiple R2).JC Wang (WMU) Stat2160 S2160, Chapter 11 5 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear Regression ModelingPurpose of multiple regression analysis is predictionModel: y = b0+ b1x1+ ... + bnxn; where biare the slopes, y is adependent variable and xiis an independent variable.Correlation coefficient, rij.Coefficient of determination, R2(or multiple R2).JC Wang (WMU) Stat2160 S2160, Chapter 11 5 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear Regression ModelingPurpose of multiple regression analysis is predictionModel: y = b0+ b1x1+ ... + bnxn; where biare the slopes, y is adependent variable and xiis an independent variable.Correlation coefficient, rij.Coefficient of determination, R2(or multiple R2).JC Wang (WMU) Stat2160 S2160, Chapter 11 5 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear Regression ModelingcontinuedStandard error of the estimated regr. line, s.Test hypothesis of slopes, p-value.Slope confidence intervals.Residual calculation.JC Wang (WMU) Stat2160 S2160, Chapter 11 6 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear Regression ModelingcontinuedStandard error of the estimated regr. line, s.Test hypothesis of slopes, p-value.Slope confidence intervals.Residual calculation.JC Wang (WMU) Stat2160 S2160, Chapter 11 6 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear Regression ModelingcontinuedStandard error of the estimated regr. line, s.Test hypothesis of slopes, p-value.Slope confidence intervals.Residual calculation.JC Wang (WMU) Stat2160 S2160, Chapter 11 6 / 25Multiple Linear Regression Analysis of Real Estate DataMultiple Linear Regression ModelingcontinuedStandard error of the estimated regr. line, s.Test hypothesis of slopes, p-value.Slope confidence intervals.Residual calculation.JC Wang (WMU) Stat2160 S2160, Chapter 11 6 / 25Multiple Linear Regression Analysis of Real Estate DataMLRReal Estate ExampleA realtor in a suburban town would like to study the relationshipbetween the size of a single-family house (as measured by the numberof rooms) and the selling price of the house. The study is to be carriedout in two different neighborhood, one on the east side (code=0) of thetown and the other on the west side (code=1). A random sample of 8houses was selected with the following results:JC Wang (WMU) Stat2160 S2160, Chapter 11 7 / 25Multiple Linear Regression Analysis of Real Estate DataMLR: Real Estate ExamplecontinuedSelling Price # of Rooms Neighborhood98.2 6 0109.6 7 0119.3 8 0135.3 9 0108.5 6 1126.7 8 1138.8 9 1143.8 10 1JC Wang (WMU) Stat2160 S2160, Chapter 11 8 / 25Multiple Linear Regression Analysis of Real Estate DataThings to Consider in MLRScatter plotsCorrelationMLR equation, R2, CIs of slopes, and residualsJC Wang (WMU) Stat2160 S2160, Chapter 11 9 / 25Multiple Linear Regression Analysis of Real Estate DataThings to Consider in MLRScatter plotsCorrelationMLR equation, R2, CIs of slopes, and residualsJC Wang (WMU) Stat2160 S2160, Chapter 11 9 / 25Multiple Linear Regression Analysis of Real Estate DataThings to Consider in MLRScatter plotsCorrelationMLR equation, R2, CIs of slopes, and residualsJC Wang (WMU) Stat2160 S2160, Chapter 11 9 / 25Multiple Linear Regression Analysis of Real Estate DataOutline1Multiple Linear RegressionMultiple Linear Regression ModelingIssues for MLR2Analysis of Real Estate DataSummary StatisticsStatistical InferencesResidual Analysis and Model GoodnessJC Wang (WMU) Stat2160 S2160, Chapter 11 10 / 25Multiple Linear Regression Analysis of Real Estate DataCorrelationsCorrelation Coefficientsprice rooms hoodprice 1rooms 0.9682 1hood 0.4537 0.2750 1correlation coefficient of price and rooms is 0.9682 and sign ispositive.correlation coefficient of price and hood is 0.4537 and sign ispositive.correlation coefficient of rooms and hood is 0.2750 and sign ispositive.There is no multi-collinearity.JC Wang (WMU) Stat2160 S2160, Chapter 11 11 / 25Multiple Linear Regression Analysis of Real Estate DataCorrelationsCorrelation Coefficientsprice rooms hoodprice 1rooms 0.9682 1hood 0.4537 0.2750 1correlation coefficient of price and rooms is 0.9682 and sign ispositive.correlation coefficient of price and hood is 0.4537 and sign ispositive.correlation coefficient of rooms and hood is 0.2750 and sign ispositive.There is no multi-collinearity.JC Wang (WMU) Stat2160 S2160, Chapter 11 11 / 25Multiple Linear Regression Analysis of Real Estate DataCorrelationsCorrelation Coefficientsprice
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