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Question
NARRBEGIN: SA_79_81The information below represents the relationship between the selling price (Y, in $1,000) of a home, the square footage of the home (
), and the number of rooms in the home (
). The data represents 60 homes sold in a particular area of East Lansing, Michigan and was analyzed using multiple linear regression and simple regression for each independent variable. The first two tables relate to the multiple regression analysis.| Summary measures | |
| Multiple R | 0.941 |
| R-Square | 0.885 |
| Adj R-Square | 0.866 |
| StErr of Estimate | 20.84 |
| Regression coefficients | |
| Coefficient | |
| Constant | -13.9705 |
| Size | 7.4336 |
| Number of Rooms | 5.3055 |
= 0.8812)| Coefficient | Std Err | t-value | p-value | |
| Constant | 14.771 | 19.691 | 0.7502 | 0.4665 |
| Size | 7.816 | 0.796 | 9.8190 | 0.0000 |
= 0.3657)| Coefficient | Std Err | t-value | p-value | |
| Constant | -93.460 | 108.269 | -0.8632 | 0.4037 |
| Number of Rooms | 41.292 | 15.082 | 2.7379 | 0.0169 |
(A) Use the information related to the multiple regression model to determine whether each of the regression coefficients are statistically different from 0 at a 5% significance level. Summarize your findings.
(B) Test at the 5% significance level the relationship between Y and X in each of the simple linear regression models. How does this compare to your answer in (A)? Explain.
(C) Is there evidence of multicollinearity in this situation? Explain why or why not.
Answer
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