1. The average cost for rushed jobs is less than the average cost for those not rushed ($40.43 versus $38.59). Usually, having to do things in a hurry increases costs. Add the dummy variable D(Rush) to the stepwise model. Does the sign of the slope seem right now? How would you explain what’s happening? (Hint: look at Table 2.)
2. The stepwise model (Table 6) includes the explanatory variable Sq. Temp Deviation, the square of the difference between room temperature and 75 degrees. Why 75? Add Room Temp itself to the regression, and then use the resulting estimates to find the optimal center for this quadratic effect.
3. Suppose you initialize backward stepwise regression from the saturated model. Use Plant rather than Manager in this model. Must the backward search eventually reach the model chosen by the forward search? Try it and see.
4. If you were asked about the costs produced by the number of machine hours, what would you say? The stepwise model omits the explanatory variable Machine Hours, in effect assigning a slope of 0 to this variable. To get a better answer, add this variable to the stepwise model and interpret the estimate and its confidence interval. How do those results compare to the estimate from the saturated model as ft in Question 3?
5. Fit the saturated regression of the number of projects per 1,000 on the variables defined in the next 33 columns of the data table (Pct Added Housing Sq Ft through Income [per cap] 2000).
(a) Why is this model difficult to interpret?
(b) How accurately will this model predict new locations?
6. Apply forward stepwise regression to build a more parsimonious model from this collection of potential explanatory variables. Be sure to avoid over-fitting. Interpret, if you can, the model obtained by stepwise. Is collinearity a problem?
7. What happens in the stepwise selection process if dummy variables for the 11 states are added to the stepwise search and the search is restarted?
8. Does the model obtained by stepwise meet the conditions of the MRM? What are the implications of your evaluation?
A building contractor operating throughout the southeastern United States tracks the number of building projects originating in communities. The contractor would like to better understand which types of communities generate the most projects (per 1,000 in population). These data give the number of projects (per 1,000) in 293 communities, along with demographic and economic characteristics of the communities.