Homework SourseThe following data give the selling price square footage num
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 regressions models to predict the selling price based upon each of the other factors individually. Which 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 |
Solution
Model 1 is better than others because the R-squared value is higher than others.
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Model 1:
price= 91,446.493 +29.8579*Square Footage+2,116.8554*Bedrooms-1,504.7659*Age (Years)
R-squared= 0.86777
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Model 2:
Price = 26,532.2361 + 51.0272*Square Footage
R-squared= 0.69996
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Model 3:
Price=20,331.6327 + 41,403.0612*Bedrooms
R-squared=0.4332
| Regression output | confidence interval | |||||
| variables | coefficients | std. error | t (df=13) | p-value | 95% lower | 95% upper |
| Intercept | 91,446.4930 | 26,076.8905 | 3.507 | .0039 | 35,110.7962 | 147,782.1897 |
| Square Footage | 29.8579 | 10.8609 | 2.749 | .0166 | 6.3943 | 53.3214 |
| Bedrooms | 2,116.8554 | 10,003.0092 | 0.212 | .8357 | -19,493.3321 | 23,727.0430 |
| Age (Years) | -1,504.7659 | 370.8204 | -4.058 | .0014 | -2,305.8746 | -703.6572 |
