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In: Statistics and Probability

The following data give the selling price, square footage, number of bedrooms, and age of houses...

The following data give the selling price, square footage, number of bedrooms, and age of houses that have sold in a neighborhood in the past 6 months. Develop three regression models to predict the selling price based upon each of the other factors individually. Which of these is best?

Selling Price Square Footage Bedrooms Age (Years)
84000 1670 2 30
79000 1339 2 25
91500 1712 3 30
120000 1840 3 40
127500 2300 3 18
132500 2234 3 30
145000 2311 3 19
164000 2377 3 7
155000 2736 4 10
168000 2500 3 1
172500 2500 4 3
174000 2479 3 3
175000 2400 3 1
177500 3124 4 0
184000 2500 3 2
195500 4062 4 10
195000 2854 3 3

Solutions

Expert Solution

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Model-1:

SUMMARY OUTPUT- 1 : S.Price and Square Footage
Regression Statistics
Multiple R 0.83664028
R Square 0.699966957
Adjusted R Square 0.679964754
Standard Error 21360.30433
Observations 17
ANOVA
df SS MS F Significance F
Regression 1 1.6E+10 1.6E+10 34.99449 2.8346E-05
Residual 15 6.84E+09 4.56E+08
Total 16 2.28E+10
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 26532.23614 21408.36 1.23934 0.234261 -19098.59279
Square Footage 51.02721153 8.625852 5.915614 2.83E-05 32.64164423

Model-2:

SUMMARY OUTPUT- 2: S.Price and Bedroom
Regression Statistics
Multiple R 0.658191861
R Square 0.433216526
Adjusted R Square 0.395430961
Standard Error 29358.3391
Observations 17
ANOVA
df SS MS F Significance F
Regression 1 9881936525 9.88E+09 11.46513 0.004072954
Residual 15 12928681122 8.62E+08
Total 16 22810617647
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 20331.63265 38780.77643 0.524271 0.607751 -62327.63526
Bedrooms 41403.06122 12227.64736 3.38602 0.004073 15340.44794

Model-3:

SUMMARY OUTPUT 3: S.Price and Age
Regression Statistics
Multiple R 0.838265
R Square 0.702688
Adjusted R Square 0.682867
Standard Error 21263.22
Observations 17
ANOVA
df SS MS F Significance F
Regression 1 1.6E+10 1.6E+10 35.45208 2.64302E-05
Residual 15 6.78E+09 4.52E+08
Total 16 2.28E+10
Coefficients Standard Error t Stat P-value Lower 95%
Intercept 182504.7 7581.975 24.07087 2.12E-13 166344.107
Age -2424.91 407.2635 -5.95416 2.64E-05 -3292.975195

From the above output of the regression models

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orchestra answered 1 year ago
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