Question

A cleaning service sends crews to residential homes on either a once-a-month or twice-a-month schedule, depending on the customer's preference. The owner would like to predict the amount of time (in minutes) required to clean a house based on the square footage of the house, the total number of rooms in the house, the number of bathrooms it has, the size of the cleaning crew, and whether or not the household has children. Data from randomly selected homes are given in the accompanying table. Complete parts a through d below.

Time   Square_Feet   Rooms   Bathrooms   Crew   Children
132   1548   8   2   3   0
146   1599   7   1.5   2   0
131   1630   7   2   3   0
141   1640   8   1.5   3   0
144   1711   8   2.5   3   1
162   1719   7   1.5   3   1
140   1814   8   2.5   4   1
162   1927   9   2.5   3   1
138   1932   8   2.5   3   0
165   2010   7   2.5   2   1
146   2015   9   2.5   3   1
77   2036   9   2.5   4   0
147   2050   9   2   3   0
159   2077   8   2   3   1
160   2138   9   2   4   1
119   2146   10   2   2   0
119   2147   9   3   3   0
112   2159   10   2.5   2   0
150   2176   10   2   3   0
143   2187   11   2.5   3   0
163   2188   8   2.5   2   1
115   2192   11   2.5   4   0
145   2205   11   2.5   3   0
125   2208   9   2.5   4   0
146   2209   10   3.5   3   1
92   2211   9   3   3   0
172   2214   10   3   4   1
147   2238   11   3.5   3   0
132   2255   11   3.5   3   0
148   2256   12   3.5   3   0
160   2259   10   3   3   1
149   2270   10   3   3   1
143   2271   11   3.5   3   1
151   2305   10   3   3   0
152   2334   10   2.5   3   1
183   2349   10   2.5   2   1
170   2351   13   3   3   0
179   2365   13   3   2   1
180   2365   12   4   2   1
110   2381   12   3.5   4   0
173   2407   11   4   3   1
160   2407   11   3   3   0
134   2446   10   3   3   0
209   2458   13   3   2   1
191   2462   11   3.5   2   1
148   2485   10   3.5   3   1
119   2515   11   4   4   0
162   2550   12   4   3   1
115   2562   14   4.5   3   0
163   2571   13   3.5   3   0
144   2580   11   3.5   3   0
164   2592   13   3.5   3   1
122   2597   12   4.5   4   0
241   2599   15   4.5   2   1
167   2601   13   4   3   1
154   2679   13   3.5   3   1
147   2706   11   3.5   3   1
159   2727   12   4   3   0
173   2773   13   4   2   0
175   2783   15   4.5   4   0
177   2878   15   4.5   2   0
178   2936   13   4   2   1
154   3007   13   4   3   0
179   3035   12   4   2   1
158   3097   13   4.5   3   0
153   3177   15   4.5   2   0
160   3188   14   4.5   3   1
197   3230   15   4.5   2   1
160   3319   14   4.5   3   0
165   3517   13   4.5   3   1

a. Check for the presence of multicollinearity.

Find the variance inflation factor (VIF) for each independent variable. Let x5=1 if there are children and let x5=0 otherwise.

Independent Variable		VIF
Square Feet	(x1 )
Rooms	(x2 )
Bathrooms	(x3 )
Crew	(x4 )
Children	(x5 )

There __ a presence of multicollinearity in the model, because _______ of the VIFs is(are) greater than 5.0.

b. If multicollinearity is present, take the necessary steps to eliminate it. What independent variables need to be eliminated from the model? Select all that apply.

A. x1 (Square Feet)

B. x2 (Rooms)

C. x3 (Bathrooms)

D. x4 (Crew)

E. x5 (Children)

F. No variables need to be eliminated because there is no significant source of multicollinearity.

c. Perform a best subsets regression and choose the most appropriate model for these data.

Which independent variables should be included in the model? Select all that apply.

x1 (square feet)

x2 (rooms)

x3 (bathrooms)

x4 (crew)

x5 (children)

d. Identify the regression equation for the model in part c. Let ModifyingAbove y be the predicted Time left parenthesis min right parenthesisTime (min).Select the correct choice below and fill in the answer boxes to complete your choice.

y=_+(_)x1+(_)x2+(_)x4+(_)x5

y=_+(_)x4

y=(_)+(_)x1+(_)x2+(_)x3+(_)x4+(_)x5

y=(_)+(_)x2

Answer 1