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 perference. 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, and the size of the cleaning crew. Complete parts a through d below.

Time   Square_Feet   Rooms   Bathrooms   Crew
131   1546   8   2   3
146   1600   7   1.5   2
131   1629   8   2   3
142   1642   7   1.5   3
143   1710   8   2.5   3
163   1718   7   1.5   3
140   1812   8   2.5   4
162   1929   10   2.5   3
139   1933   8   2.5   3
166   2012   7   2.5   2
147   2015   8   2.5   3
78   2038   10   2.5   4
148   2049   10   2   3
160   2076   8   2   3
159   2140   10   2   4
120   2148   9   2   2
120   2149   10   3   3
111   2157   9   2.5   2
149   2177   9   2   3
142   2189   12   2.5   3
162   2190   10   2.5   2
115   2191   11   2.5   4
144   2204   11   2.5   3
124   2209   8   2.5   4
146   2210   10   3.5   3
93   2212   9   3   3
172   2214   11   3   4
146   2238   12   3.5   3
132   2257   11   3.5   3
147   2257   13   3.5   3
161   2259   9   3   3
148   2270   10   3   3
143   2271   10   3.5   3
151   2306   8   3   3
151   2335   11   2.5   3
183   2348   10   2.5   2
171   2350   14   3   3
179   2364   13   3   2
179   2367   10   4   2
109   2381   11   3.5   4
174   2405   11   4   3
159   2408   11   3   3
133   2447   11   3   3
208   2457   11   3   2
192   2464   12   3.5   2
147   2485   9   3.5   3
120   2518   12   4   4
162   2550   13   4   3
114   2564   13   4.5   3
164   2571   12   3.5   3
143   2583   11   3.5   3
164   2590   14   3.5   3
121   2598   11   4.5   4
239   2602   15   4.5   2
168   2602   14   4   3
153   2681   11   3.5   3
147   2706   12   3.5   3
159   2728   11   4   3
172   2771   13   4   2
175   2784   14   4.5   4
177   2881   15   4.5   2
177   2937   14   4   2
155   3010   14   4   3
180   3038   13   4   2
158   3096   14   4.5   3
154   3174   14   4.5   2
160   3187   15   4.5   3
196   3230   15   4.5   2
161   3319   14   4.5   3
165   3518   13   4.5   3

a. Construct a regression model using all the independent variables. Let ModifyingAbove y with carety be the predicted time in​ minutes, x1 be the square​ feet, x2 be the number of​ rooms, x3 be the number of​ bathrooms, and x4 be the size of the crew.

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

b. calculate the multiple coefficient of determination

c.Test the significance using .05

4. calculate the adjusted multiple coefficient of determination

Answer 1

Using Excel

data -> data analysis -> regression

Result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.619836494
R Square	0.38419728
Adjusted R Square	0.346301728
Standard Error	20.76535462
Observations	70
ANOVA
	df	SS	MS	F	Significance F
Regression	4	17486.57453	4371.643632	10.13832123	1.9353E-06
Residual	65	28027.9969	431.1999523
Total	69	45514.57143
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	164.6632982	22.17538133	7.425500188	3.05951E-10	120.3760036
Square_Feet	4.56696E-05	0.013063098	0.003496074	0.99722125	-0.026043138
Rooms	4.133837156	2.056855368	2.009785044	0.048608405	0.026013329
Bathrooms	-0.67161431	6.069046876	-0.110662238	0.912225176	-12.79233789
Crew	-19.23285449	4.157670955	-4.6258722	1.82888E-05	-27.53629676

a) y^ = 164.6633 + 0.00004567 Square_feet + 4.133837* rooms -0.6716*Bathrooms -19.2329 Crew

b) R^2 =

0.38419728

c) Significance F = 1.9353E-06 < 0.05

hence the model is overall significant

d) adjusted R^2 = 0.346301728

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