Question

13.18 In problem 13.6 on page 501, an owner of a moving company wanted to predict the labor hours, based on cubic feet moved (stored in Moving). Using the results of that problem,

A) Determine the coefficient of determination, r², and interpret its meaning.

B) Determine the standard error of the estimate

C) How useful do you think this regression model is for predicting labor hours?

Here is problem 13.6 on page 501.

The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved as the independent variable and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and in which the travel time was an insignificant portion of the hours worked.

	A	B	C	D
1	Hours	Feet	Large	Elevator
2	24	545	3	yes
3	13.5	400	2	yes
4	26.25	562	2	no
5	25	540	2	no
6	9	220	1	yes
7	20	344	3	yes
8	22	569	2	yes
9	11.25	340	1	yes
10	50	900	6	yes
11	12	285	1	yes
12	38.75	865	4	yes
13	40	831	4	yes
14	19.5	344	3	yes
15	18	360	2	yes
16	28	750	3	yes
17	27	650	2	yes
18	21	415	2	no
19	15	275	2	yes
20	25	557	2	yes
21	45	1028	5	yes
22	29	793	4	yes
23	21	523	3	yes
24	22	564	3	yes
25	16.5	312	2	yes
26	37	757	3	no
27	32	600	3	no
28	34	796	3	yes
29	25	577	3	yes
30	31	500	4	yes
31	24	695	3	yes
32	40	1054	4	yes
33	27	486	3	yes
34	18	442	2	yes
35	62.5	1249	5	no
36	53.75	995	6	yes
37	79.5	1397	7	no

A) Construct a scatter plot.

B) Assuming a linear relationship, use the least-squares method to determine the regression coefficients b₀ and b_1.

C) Interpret the meaning of the slope, b₁, in this problem.

D) Predict the mean labor hours for moving 500 cubic feet.

E) What should you tell the owner of the moving company about the relationship between cubic feet moved and labor hours?

Answer 1

Here I attach the R code

Hours=scan()
Feet=scan()
Large=scan()
m=lm(Hours~Feet)
summary(m)
plot(Feet,Hours)
-2.36966+0.05008*500

dwtest(m)
r=residuals(m)
shapiro.test(r)

A) The R² value is 0.889. The model can explain 88.9% of the total variation.

B) The stanadard error of the estimate is 2.0733

C)This model satisfies the all regression assumption. Hence the model is adequate

The durbin watson test for autocorrelation and shappiro wilks test for normality holds.

A.

B)

The coefficients are:

b₀=-2.3697

b₁=0.0501

C) The slope indicate that for unit change in the feet the Hours increased by 0.0501 units.

D) when feet =500 cubic

Hours=-2.36966+0.05008*500=22.67034

E)There is positive linear relationship exist between the cubic feet and labor hour which clear from the scatter plot. the linear model is a perfect linear relation and the model satisfies all the regression assumption and the obtained model is adequate.