Alpha Geek
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Housing Prices A realtor wanted to find a model that relates the asking price of a house to the square footage, number of bedrooms, and number of baths. The following data are from houses in Greenville, South Carolina.
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|
Square Footage |
Bedrooms |
Baths |
Asking Price ($ thousands) |
|
3800 |
4 |
3.5 |
498 |
|
2600 |
4 |
3 |
449 |
|
2600 |
5 |
3.5 |
435 |
|
 |
 |
 |
 |
|
2250 |
4 |
4 |
400 |
|
 |
 |
 |
 |
|
3300 |
4 |
3 |
379 |
|
2750 |
3 |
2.5 |
375 |
|
2200 |
3 |
2.5 |
356 |
|
3000 |
4 |
2.5 |
350 |
|
2300 |
3 |
2 |
340 |
|
2600 |
4 |
2.5 |
332 |
|
2300 |
4 |
2 |
298 |
|
2000 |
4 |
3 |
280 |
|
2200 |
3 |
2.5 |
260 |
(a) Construct the correlation matrix. Is there any reason to be concerned with multicollinearity?
(b) Find the least-squares regression equation y = b0 + b1x1 + β2 x2 + β3 x3, where x1 is square footage, x2 is number of bedrooms, x3 is number of baths, and y is the response variable asking price.
(c) Test H0: β1 = β2 = β3 = 0 versus H1: at least one of the βi ≠0 at the α = 0.05 level of significance.
(d) Test the hypotheses H0: β1 = 0 versus H1: β1 ≠0, H0: β2 = 0 versus H1: β2 ≠0, and H0: β3 = 0 versus H1: β3 ≠0 at the α = 0.05 level of significance.
(e) Remove the explanatory variable with the highest P-value and compute the least-squares regression equation. Are all the slope coefficients significantly different from zero? If not, remove the explanatory variable with the higher P-value and compute the least-squares regression equation.
(f) Draw residual plots, a boxplot of the residuals, and a normal probability plot of the residuals to assess the adequacy of the model found in part (e).
(g) Interpret the regression coefficients for the least-squares regression equation found in part (e).
(h) Construct 95% confidence and prediction intervals for the asking price of a 2900-square-foot house in Greenville, South Carolina, with 4 bedrooms and 3 baths. Interpret the results.
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