Questions in bold: What is the average number of labor hours required for a move
ID: 3053769 • Letter: Q
Question
Questions in bold:
What is the average number of labor hours required for a move? (2 point
Write the theoretical linear model in equation form (3 points).
Write the estimated linear regression model in equation form (3 points).
Predict the labor hours for moving 500 cubic feet with 2 large pieces of furniture (4 points)
Is the model statistically useful to explain and predict labor hours? Use a formal test and describe all the necessary steps (8 poi
Interpret the R2 (3 points)
What explanatory variables are statistically significant at the 5% level? (4 points)
Interpret the coefficient related to “feet” (cubic feet moved) (3 point)
Interpret the intercept (3 points).
Do cubic feet moved (feet) has a positive effect on sales? Use a formal test and describe all the necessary steps (8 points)
Calculate and interpret a 90% confidence interval for the effect of cubic feet moved (feet) on labor hours (8 points).
Is there a multicollinearity problem related to the variable “feet”? Calculate and interpret the VIF value (6 points)
Data:
The owner of a moving company typically has her most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proven useful in the past but the manager has the business objective of developing a more accurate method of predicting moving labor hours (y= hours) using regression analysis. The owner has decided to use the number of cubic feet moved (x1=feet) and the number of pieces of large furniture (x2=large) as explanatory variables.
Summary Statistics
Hours
Feet
Large
min
9.00
220.00
1.00
max
79.50
1397.00
7.00
mean
28.96
625.56
3.06
std. dev.
14.901
280.58
1.413
SUMMARY OUTPUT of regression of labor hours (dependent variable) on cubic feet moved and (feet) and number of pieces of large furniture moved (large)
Regression Statistics
Multiple R
0.966
R Square
0.933
Adjusted R Square
0.929
Standard Error
3.980
Observations
36.000
ANOVA
df
SS
MS
F
Significance F
Regression
2.000
7248.706
3624.353
228.805
0.000
Residual
33.000
522.732
15.840
Total
35.000
7771.438
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-3.915
1.674
-2.339
0.026
-7.321
-0.510
Feet
0.032
0.005
6.934
0.000
0.023
0.041
Large
4.223
0.914
4.619
0.000
2.363
6.083
SUMMARY OUTPUT of regression of cubic feet moved (feet)(dependent variable) on number of pieces of large furniture moved (large)
Regression Statistics
Multiple R
0.85
R Square
0.73
Adjusted R Square
0.72
Standard Error
148.25
Observations
36.00
ANOVA
df
SS
MS
F
Significance F
Regression
1.00
2008170.09
2008170.09
91.37
0.00
Residual
34.00
747262.80
21978.32
Total
35.00
2755432.89
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
107.61
59.55
1.81
0.08
-13.42
228.63
Large
169.51
17.73
9.56
0.00
133.47
205.55
Hours
Feet
Large
min
9.00
220.00
1.00
max
79.50
1397.00
7.00
mean
28.96
625.56
3.06
std. dev.
14.901
280.58
1.413
Explanation / Answer
1. What is the average number of labor hours required for a move? (2 point)
Average number of labor hours needs are 28.96
2. Write the theoretical linear model in equation form (3 points).
labour hours = Intercept + beta1 * (cubic Feet moved) + beta2 * (number of pieces of large furniture moved)
3. Write the estimated linear regression model in equation form (3 points).
labours hours = -3.915 + 0.032*(cubic Feet moved)+4.223(number of pieces of large furniture moved)
4. Predict the labor hours for moving 500 cubic feet with 2 large pieces of furniture (4 points)
labours hours = -3.915 + 0.032*(cubic Feet moved)+4.223(number of pieces of large furniture moved)
Given
cubic Feet moved = 500
number of pieces of large furniture moved = 2
Required equation
labours hours = -3.915 + 0.032*(500)+4.223(2) = 20.531 hours
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