Homework Sourse3 Use the data in problem in 422 and develop a regression mo
3
Use the data in problem in 4-22 and develop a regression model to predict selling price based on 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.
State the linear equation.
Explain the overall statistical significance of the model.
Explain the statistical significance for each independent variable in the model
Interpret the Adjusted R2.
Is this a good predictive equation(s)? Which variables should be excluded (if any) and why? Explain.
| Selling Price($) | Data from problem 4-22 Square Footage | Bedrooms | Age (Years) |
| 84,000 | 1,670 | 2 | 30 |
| 79,000 | 1,339 | 2 | 25 |
| 91,500 | 1,712 | 3 | 30 |
| 120,000 | 1,840 | 3 | 40 |
| 127,500 | 2,300 | 3 | 18 |
| 132,500 | 2,234 | 3 | 30 |
| 145,000 | 2,311 | 3 | 19 |
| 164,000 | 2,377 | 3 | 7 |
| 155,000 | 2,736 | 4 | 10 |
| 168,000 | 2,500 | 3 | 1 |
| 172,500 | 2,500 | 4 | 3 |
| 174,000 | 2,479 | 3 | 3 |
| 175,000 | 2,400 | 3 | 1 |
| 177,500 | 3,124 | 4 | 0 |
| 184,000 | 2,500 | 3 | 2 |
| 195,500 | 4,062 | 4 | 10 |
| 195,000 | 2,854 | 3 | 3 |
| Use the data in problem in 4-22 and develop a regression model to predict selling price based on 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. State the linear equation. Explain the overall statistical significance of the model. Explain the statistical significance for each independent variable in the model Interpret the Adjusted R2. Is this a good predictive equation(s)? Which variables should be excluded (if any) and why? Explain. |
Solution
The regression equation is
Selling Price = 91446 + 29.9 Sqaure foot + 2117 Bedroom - 1505 AGe
R-Sq(adj) = 0.837
Hence of total variation in the model 83.7% of the variation are explained by this regression equation.
If
Age= 10 year, number of rooms=3,Square footage is 2000 the predicted Selling price is $142547
This is a good regression model.
Predictor Coef SE Coef T P
Constant 91446 26077 3.51 0.004
Sqaure foot 29.86 10.86 2.75 0.017
Bedroom 2117 10003 0.21 0.836
AGe -1504.8 370.8 -4.06 0.001
P value suggests that Bedroom is indpendent . It can be excluded
