Question

The owner of a moving company usually has her most experienced manager predict the total number of labor hours required to complete a move. While useful, the owner is interested in a more accurate method of predicting the number of labor hours required. As a preliminary effort, data was collected on the number of work hours required to complete a move, number of cubic feet moved, the number of large pieces, and if an elevator was present.

How much correlation is there between the variables?

How much of the variability in strength is explained by the predictors?

Which of the predictor variables are significant at the 0.05 level?

At the 0.05 level of significance, what is the conclusion about the overall model hypothesis test?

What is the 90% confidence interval around the variable Elevator?

How are the degrees of freedom residuals computed?

At α = 0.001, is the overall model significant?

Estimate the number of hours required when 325 cubic feet are moved with 3 large pieces of furniture and no elevator is present.

Estimate the number of hours required when 425 cubic feet are moved with 7 large pieces of furniture and an elevator is present.

Estimate the number of hours required when 375 cubic feet are moved with 2 large pieces of furniture and no elevator is present.

Hours	Feet	Large	Elevator
24.00	545	3	Yes
13.50	400	2	Yes
26.25	562	2	No
25.00	540	2	No
9.00	220	1	Yes
20.00	344	3	Yes
22.00	569	2	Yes
11.25	340	1	Yes
50.00	900	6	Yes
12.00	285	1	Yes
38.75	865	4	Yes
40.00	831	4	Yes
19.50	344	3	Yes
18.00	360	2	Yes
28.00	750	3	Yes
27.00	650	2	Yes
21.00	415	2	No
15.00	275	2	Yes
25.00	557	2	Yes
45.00	1028	5	Yes
29.00	793	4	Yes
21.00	523	3	Yes
22.00	564	3	Yes
16.50	312	2	Yes
37.00	757	3	No
32.00	600	3	No
34.00	796	3	Yes
25.00	577	3	Yes
31.00	500	4	Yes
24.00	695	3	Yes
40.00	1054	4	Yes
27.00	486	3	Yes
18.00	442	2	Yes
62.50	1249	5	No
53.75	995	6	Yes
79.50	1397	7	No

Answer 1

using excel>data analysis>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.9806
R Square	0.9616
Adjusted R Square	0.9579
Standard Error	3.0557
Observations	36
ANOVA
	df	SS	MS	F	Significance F
Regression	3	7472.6419	2490.8806	266.7649	0.0000
Residual	32	298.7956	9.3374
Total	35	7771.4375
	Coefficients	Standard Error	t Stat	P-value	Lower 90%	Upper 90%
Intercept	2.9904	1.9078	1.5674	0.1268	-0.2412	6.2221
Feet	0.0256	0.0038	6.8015	0.0000	0.0192	0.0320
Large	5.0424	0.7216	6.9882	0.0000	3.8201	6.2646
Elevator	-6.7683	1.3821	-4.8972	0.0000	-9.1093	-4.4272

09806 , strong correlation is there between the variables.

95.79 % variability in strength is explained by the predictors.

All the predictor variables are significant at the 0.05 level because p-value is less than 0.05.

At the 0.05 level of significance, the conclusion about the overall model hypothesis test is statistically significant because the p-value of the overall model is less than 0.05.

the 90% confidence interval around the variable Elevator is (-9.1093, -4.4272)

the degrees of freedom residuals computed is 32

At α = 0.001, yes the overall model significant because the p-value is less than 0.001.

the number of hours required when 325 cubic feet are moved with 3 large pieces of furniture and no elevator is present is

Hours = 2.9904 +0.0256 feet +5.0424 Large -6.7683 elevator

= 2.9904 +0.0256*325 +5.0424 *3 -6.7683 *0

= 26.4376 hours

the number of hours required when 425 cubic feet are moved with 7 large pieces of furniture and an elevator is present is

hours =2.9904 +0.0256*425 +5.0424 *7-6.7683 *1

= 42.3989 hours

the number of hours required when 375 cubic feet are moved with 2 large pieces of furniture and no elevator is present is

hours =2.9904+0.0256*375 +5.0424 *2-6.7683 *0

= 22.6752 hours