Question

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

Answer 1

here the null hypothesis

H0: $\beta$Lot.Size=$\beta$Square.Feet=$\beta$Num.Bath=$\beta$API.2011=$\beta$dis_coast=$\beta$dis_fwy=$\beta$dis_down=$\beta$I(dis_fwy*dis_down)=$\beta$Pool=0

Ha: atleast one of the $\beta$ 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.