Question

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? use 1 for yes and 0 for no

develop a regression model to predict selling price based on the square footage and number of bedrooms. Use this to predict the selling price of a 2,000-square-foot house with three bedrooms. Should the number of bedrooms be included in the model? Why or why not?

develop a regression model to predict selling price based on the square footage, number of bedrooms, and age. Use this to predict the selling price of a 10-year-old, 2,000-square-foot house with three bedrooms.

Selling Price	Square Feet	Bedrooms	Age (yrs)	Renovated?
84000	1670	2	30	Yes
79000	1339	2	25	Yes
91000	1712	3	30	No
120000	1840	3	40	Yes
127500	2300	4	18	No
155000	2736	4	10	Yes
168000	2500	3	1	No
132000	2234	4	30	No
177000	3124	5	0	No
195000	2854	4	20	Yes

Answer 1

using minitab >stat>Regression

we have

Regression Analysis: Selling Price versus Square Feet, Bedrooms

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 13460923932 6730461966 35.99 0.000
Square Feet 1 4840113218 4840113218 25.88 0.001
Bedrooms 1 269141274 269141274 1.44 0.269
Error 7 1309101068 187014438
Total 9 14770025000

Model Summary

S R-sq R-sq(adj) R-sq(pred)
13675.3 91.14% 88.60% 81.14%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -12054 18058 -0.67 0.526
Square Feet 82.9 16.3 5.09 0.001 4.33
Bedrooms -11781 9821 -1.20 0.269 4.33

Regression Equation

Selling Price = -12054 + 82.9 Square Feet - 11781 Bedrooms

the selling price of a 2,000-square-foot house with three bedrooms.

Predicted Selling Price = -12054 + 82.9*2000- 11781*3 =118403

No , the number of bedrooms should not be included in the model because it is a significant variable.

using minitab>stat>Regression

we have

Regression Analysis: Selling Price versus Square Feet, Bedrooms, Age (yrs)

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 3 13667964178 4555988059 24.80 0.001
Square Feet 1 3556336871 3556336871 19.36 0.005
Bedrooms 1 439188244 439188244 2.39 0.173
Age (yrs) 1 207040246 207040246 1.13 0.329
Error 6 1102060822 183676804
Total 9 14770025000

Model Summary

S R-sq R-sq(adj) R-sq(pred)
13552.7 92.54% 88.81% 74.48%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -45356 36114 -1.26 0.256
Square Feet 99.8 22.7 4.40 0.005 8.55
Bedrooms -16615 10745 -1.55 0.173 5.28
Age (yrs) 588 554 1.06 0.329 2.66

Regression Equation

Selling Price = -45356 + 99.8 Square Feet - 16615 Bedrooms + 588 Age (yrs)

the selling price of a 10-year-old, 2,000-square-foot house with three bedrooms is

Selling Price = -45356+ 99.8*2000-16615*3+588*10 = 110279