Regression

Descriptive Statistics

Mean Std. Deviation N
selling price in $1000s 99.53 44.18 93
size in 1000s sq ft 1.65 .53 93
number bathrooms 1.96 .41 93

Correlations

selling price in $1000s size in 1000s sq ft number bathrooms
Pearson Correlation selling price in $1000s 1.000 .899 .714
size in 1000s sq ft .899 1.000 .662
number bathrooms .714 .662 1.000

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 number bathrooms, size in 1000s sq ft(a) . Enter
a All requested variables entered.
b Dependent Variable: selling price in $1000s

Model Summary(b)
Model R R Square Adjusted R Square Std. Error of the Estimate Durbin-Watson
1 .913(a) .833 .829 18.27 2.015
a Predictors: (Constant), number bathrooms, size in 1000s sq ft
b Dependent Variable: selling price in $1000s

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 149573.058 2 74786.529 224.114 .000(a)
Residual 30032.809 90 333.698

Total 179605.867 92


a Predictors: (Constant), number bathrooms, size in 1000s sq ft
b Dependent Variable: selling price in $1000s

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. Correlations Collinearity Statistics
Model B Std. Error Beta

Zero-order Partial Part Tolerance VIF
1 (Constant) -49.752 9.183
-5.418 .000




size in 1000s sq ft 63.863 4.840 .759 13.194 .000 .899 .812 .569 .561 1.782
number bathrooms 22.448 6.130 .211 3.662 .000 .714 .360 .158 .561 1.782
a Dependent Variable: selling price in $1000s

Casewise Diagnostics(a)
Case Number Std. Residual selling price in $1000s
5 4.437 309
a Dependent Variable: selling price in $1000s

Residuals Statistics(a)

Minimum Maximum Mean Std. Deviation N
Predicted Value -1.76 263.47 99.53 40.32 93
Residual -41.16 81.06 4.17E-14 18.07 93
Std. Predicted Value -2.512 4.066 .000 1.000 93
Std. Residual -2.253 4.437 .000 .989 93
a Dependent Variable: selling price in $1000s

Outlier Statistics(a)

Case Number Statistic
Std. Residual 1 5 4.437
2 41 -2.253
3 89 -2.240
4 30 -2.040
5 7 -1.907
6 91 1.865
7 4 -1.854
8 32 -1.377
9 59 -1.367
10 76 -1.337
a Dependent Variable: selling price in $1000s

Charts

*zresid histogram

*zresid normal p-p plot

P by s scatterplot

P by ba scatterplot

*resid by s scatterplot

*resid by ba scatterplot

*resid by *pred scatterplot

Regression

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 size in 1000s sq ft(a) . Enter
2 number bathrooms(a) . Enter
a All requested variables entered.
b Dependent Variable: selling price in $1000s

Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics
Model



R Square Change F Change df1 df2 Sig. F Change
1 .899(a) .808 .806 19.47 .808 382.628 1 91 .000
2 .913(b) .833 .829 18.27 .025 13.412 1 90 .000
a Predictors: (Constant), size in 1000s sq ft
b Predictors: (Constant), size in 1000s sq ft, number bathrooms

ANOVA(c)
Model Sum of Squares df Mean Square F Sig.
1 Regression 145097.464 1 145097.464 382.628 .000(a)
Residual 34508.402 91 379.213

Total 179605.867 92


2 Regression 149573.058 2 74786.529 224.114 .000(b)
Residual 30032.809 90 333.698

Total 179605.867 92


a Predictors: (Constant), size in 1000s sq ft
b Predictors: (Constant), size in 1000s sq ft, number bathrooms
c Dependent Variable: selling price in $1000s

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. Correlations
Model B Std. Error Beta

Zero-order Partial Part
1 (Constant) -25.194 6.688
-3.767 .000


size in 1000s sq ft 75.607 3.865 .899 19.561 .000 .899 .899 .899
2 (Constant) -49.752 9.183
-5.418 .000


size in 1000s sq ft 63.863 4.840 .759 13.194 .000 .899 .812 .569
number bathrooms 22.448 6.130 .211 3.662 .000 .714 .360 .158
a Dependent Variable: selling price in $1000s

Regression

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 number bathrooms(a) . Enter
2 size in 1000s sq ft(a) . Enter
a All requested variables entered.
b Dependent Variable: selling price in $1000s

Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics
Model



R Square Change F Change df1 df2 Sig. F Change
1 .714(a) .509 .504 31.12 .509 94.473 1 91 .000
2 .913(b) .833 .829 18.27 .323 174.076 1 90 .000
a Predictors: (Constant), number bathrooms
b Predictors: (Constant), number bathrooms, size in 1000s sq ft

ANOVA(c)
Model Sum of Squares df Mean Square F Sig.
1 Regression 91484.398 1 91484.398 94.473 .000(a)
Residual 88121.469 91 968.368

Total 179605.867 92


2 Regression 149573.058 2 74786.529 224.114 .000(b)
Residual 30032.809 90 333.698

Total 179605.867 92


a Predictors: (Constant), number bathrooms
b Predictors: (Constant), number bathrooms, size in 1000s sq ft
c Dependent Variable: selling price in $1000s

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. Correlations
Model B Std. Error Beta

Zero-order Partial Part
1 (Constant) -49.248 15.644
-3.148 .002


number bathrooms 76.026 7.822 .714 9.720 .000 .714 .714 .714
2 (Constant) -49.752 9.183
-5.418 .000


number bathrooms 22.448 6.130 .211 3.662 .000 .714 .360 .158
size in 1000s sq ft 63.863 4.840 .759 13.194 .000 .899 .812 .569
a Dependent Variable: selling price in $1000s

Regression

Correlations

selling price in $1000s size in 1000s sq ft number bathrooms number bedrooms
Pearson Correlation selling price in $1000s 1.000 .899 .714 .590
size in 1000s sq ft .899 1.000 .662 .669
number bathrooms .714 .662 1.000 .334
number bedrooms .590 .669 .334 1.000

Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 size in 1000s sq ft . Forward (Criterion: Probability-of-F-to-enter <= .050)
2 number bathrooms . Forward (Criterion: Probability-of-F-to-enter <= .050)
a Dependent Variable: selling price in $1000s

Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics
Model



R Square Change F Change df1 df2 Sig. F Change
1 .899(a) .808 .806 19.47 .808 382.628 1 91 .000
2 .913(b) .833 .829 18.27 .025 13.412 1 90 .000
a Predictors: (Constant), size in 1000s sq ft
b Predictors: (Constant), size in 1000s sq ft, number bathrooms

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. Collinearity Statistics
Model B Std. Error Beta

Tolerance VIF
1 (Constant) -25.194 6.688
-3.767 .000

size in 1000s sq ft 75.607 3.865 .899 19.561 .000 1.000 1.000
2 (Constant) -49.752 9.183
-5.418 .000

size in 1000s sq ft 63.863 4.840 .759 13.194 .000 .561 1.782
number bathrooms 22.448 6.130 .211 3.662 .000 .561 1.782
a Dependent Variable: selling price in $1000s

Excluded Variables(c)

Beta In Collinearity Statistics
Model
VIF Minimum Tolerance
1 number bathrooms .211(a) 1.782 .561
number bedrooms -.020(a) 1.811 .552
2 number bedrooms .022(b) 1.884 .335
a Predictors in the Model: (Constant), size in 1000s sq ft
b Predictors in the Model: (Constant), size in 1000s sq ft, number bathrooms
c Dependent Variable: selling price in $1000s

Regression

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 number bedrooms, number bathrooms, size in 1000s sq ft(a) . Enter
2 . number bedrooms Backward (criterion: Probability of F-to-remove >= .100).
a All requested variables entered.
b Dependent Variable: selling price in $1000s

Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics
Model



R Square Change F Change df1 df2 Sig. F Change
1 .913(a) .833 .827 18.36 .833 148.034 3 89 .000
2 .913(b) .833 .829 18.27 .000 .143 1 91 .706
a Predictors: (Constant), number bedrooms, number bathrooms, size in 1000s sq ft
b Predictors: (Constant), number bathrooms, size in 1000s sq ft

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta

1 (Constant) -53.382 13.319
-4.008 .000
size in 1000s sq ft 62.354 6.292 .741 9.910 .000
number bathrooms 22.915 6.282 .215 3.648 .000
number bedrooms 1.636 4.327 .022 .378 .706
2 (Constant) -49.752 9.183
-5.418 .000
size in 1000s sq ft 63.863 4.840 .759 13.194 .000
number bathrooms 22.448 6.130 .211 3.662 .000
a Dependent Variable: selling price in $1000s

Regression

Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 size in 1000s sq ft . Stepwise (Criteria: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).
2 number bathrooms . Stepwise (Criteria: Probability-of-F-to-enter <= .050, Probability-of-F-to-remove >= .100).
a Dependent Variable: selling price in $1000s

Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics
Model



R Square Change F Change df1 df2 Sig. F Change
1 .899(a) .808 .806 19.47 .808 382.628 1 91 .000
2 .913(b) .833 .829 18.27 .025 13.412 1 90 .000
a Predictors: (Constant), size in 1000s sq ft
b Predictors: (Constant), size in 1000s sq ft, number bathrooms

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig.
Model B Std. Error Beta

1 (Constant) -25.194 6.688
-3.767 .000
size in 1000s sq ft 75.607 3.865 .899 19.561 .000
2 (Constant) -49.752 9.183
-5.418 .000
size in 1000s sq ft 63.863 4.840 .759 13.194 .000
number bathrooms 22.448 6.130 .211 3.662 .000
a Dependent Variable: selling price in $1000s

Regression

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 number bedrooms, number bathrooms, size in 1000s sq ft(a) . Enter
a All requested variables entered.
b Dependent Variable: selling price in $1000s

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .913(a) .833 .827 18.36
a Predictors: (Constant), number bedrooms, number bathrooms, size in 1000s sq ft

Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. Correlations Collinearity Statistics
Model B Std. Error Beta

Zero-order Partial Part Tolerance VIF
1 (Constant) -53.382 13.319
-4.008 .000




size in 1000s sq ft 62.354 6.292 .741 9.910 .000 .899 .724 .429 .335 2.983
number bathrooms 22.915 6.282 .215 3.648 .000 .714 .361 .158 .539 1.854
number bedrooms 1.636 4.327 .022 .378 .706 .590 .040 .016 .531 1.884
a Dependent Variable: selling price in $1000s