In: Statistics and Probability
1.-Interpret the following regression model Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -7.819e+05 7.468e+04 -10.470 < 2e-16 *** Lot.Size -5.359e-01 1.163e-01 -4.610 4.67e-06 *** Square.Feet 1.108e+02 1.109e+01 9.986 < 2e-16 *** Num.Baths 2.985e+04 9.650e+03 3.094 0.00204 ** API.2011 1.226e+03 9.034e+01 13.568 < 2e-16 *** dis_coast -7.706e+00 2.550e+00 -3.022 0.00259 ** dis_fwy 1.617e+01 1.232e+01 1.312 0.18995 dis_down 5.364e+00 3.299e+00 1.626 0.10429 I(dis_fwy * dis_down) -4.414e-04 5.143e-04 -0.858 0.39098 Pool 1.044e+05 2.010e+04 5.194 2.59e-07 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 141400 on 832 degrees of freedom Multiple R-squared: 0.554, Adjusted R-squared: 0.5492 F-statistic: 114.8 on 9 and 832 DF, p-value: < 2.2e-16
here the null hypothesis
H0: Lot.Size=Square.Feet=Num.Bath=API.2011=dis_coast=dis_fwy=dis_down=I(dis_fwy*dis_down)=Pool=0
Ha: atleast one of the is different from zero
since the F-statisitc has p-value is less than typical level of significance alpha=0.05, so we reject H0 and conclude that atleast one of the regression coefficient is different from zero.
Lot.Size, Square.Feet, Num.Bath, API.2011, dis_coast are significant to explain the dependent variables but
dis_fwy , dis_down and I(dis_fwy * dis_down) are not significant, so these three may be removed from the model and re-analyze the data.