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, whether or not the household has children, and the frequency of the cleaning schedule. Data from randomly selected homes are given in the accompanying table. Complete parts a through d below.

Time (min)   Square_Feet   Rooms   Children   Frequency
163   3,521   13   Yes   Twice
120   2,522   11   No   Once
162   1,930   9   Yes   Once
145   1,599   7   No   Twice
154   3,184   15   No   Twice
114   2,194   11   No   Twice
178   3,043   12   Yes   Once
166   2,017   7   Yes   Twice
121   2,153   10   No   Once
147   2,485   10   Yes   Once
185   2,344   10   Yes   Twice
170   2,355   13   No   Twice
178   2,928   13   Yes   Once
150   2,327   10   Yes   Twice
147   2,716   11   Yes   Once
166   2,601   13   Yes   Twice
163   1,724   7   Yes   Once
109   2,378   12   No   Once
173   2,789   14   No   Once
152   2,998   13   No   Twice
163   2,553   13   Yes   Twice
161   3,196   14   Yes   Once
168   2,594   13   Yes   Twice
160   2,073   8   Yes   Once
132   1,637   8   No   Twice
146   2,211   10   Yes   Once
148   2,254   12   No   Once
145   2,234   11   No   Twice
149   2,183   10   No   Once
150   2,305   9   No   Once
180   2,364   11   Yes   Once
121   2,155   9   No   Twice
199   3,222   15   Yes   Once
172   2,413   12   Yes   Once
140   1,635   7   No   Twice
155   2,681   12   Yes   Once
241   2,597   15   Yes   Once
135   2,445   10   No   Once
126   2,199   9   No   Twice
164   2,571   13   No   Once
160   2,130   9   Yes   Once
173   2,208   11   Yes   Twice
164   2,192   9   Yes   Once
147   2,204   10   No   Once
158   3,095   13   No   Twice

a. Using technology, construct a regression model using all of the independent variables. (Let variable Ch be the dummy variable for the Children variable. Assign a 1 if the household has children. Also, let variable Fr be the dummy variable for the frequency. Assign a 1 to a frequency of twice-a-month.)

Complete the regression equation for the model below, where yequals=Time left parenthesis min right parenthesisTime (min),x1=Square Feet, x2=Rooms, x3=Ch and x4=Fr.

Test the significance of the overall regression model using alpha (α) equals=0.050. What are the null and alternative hypotheses for this test?

State the conclusion about the significance of the Regression Model alpha (α) equals=0.050.

Answer 1

a.

The regression equation for the model :

Null hypothesis : Overall regression is not significant

Alternative hypothesis : Overall regression is significant

Consider the Significance F value in the ANOVA table

Significance F = 0.000 = P-value

Since, P-value = 0.000 < 0.05 ( Level of significance), we reject null hypothesis and conclude that Overall regression is significant at 5% level of significance.