The owner of a moving company typically has his most experienced manager predict
ID: 3224560 • Letter: T
Question
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 eort to provide a more accurate method, the owner has decided to use the number of cubic feet moved (x1), the number of pieces of large furniture (x2) and whether there is an elevator in the apartment building (x3 = 1 if yes, x3 = 0 if no) as the independent variables and has collected data for 36 move
Regression Analysis
r²
0.972
Adjusted r²
0.970
r
0.986
Std. Error
1.987
n
20
k
1
Dep. Var.
Time
ANOVA table
Source
SS
df
MS
F
p-value
Regression
2,443.4660
1
2,443.4660
619.20
2.15E-15
Residual
71.0315
18
3.9462
Total
2,514.4975
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=18)
p-value
95% lower
95% upper
Intercept
24.8345
1.0542
23.557
5.61E-15
22.6197
27.0494
Cases
0.1400
0.0056
24.884
2.15E-15
0.1282
0.1518
Regression Analysis
R²
0.962
Adjusted R²
0.958
n
36
R
0.981
k
3
Std. Error
3.056
Dep. Var.
Y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
7,472.6419
3
2,490.8806
266.76
1.03E-22
Residual
298.7956
32
9.3374
Total
7,771.4375
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=32)
p-value
95% lower
95% upper
Intercept
2.9904
1.9078
1.567
.1268
-0.8957
6.8766
X1
0.0256
0.0038
6.801
1.09E-07
0.0179
0.0333
X2
5.0424
0.7216
6.988
6.43E-08
3.5726
6.5122
X3
-6.7683
1.3821
-4.897
2.68E-05
-9.5835
-3.9531
Predicted values for: Y
95% Confidence Interval
95% Prediction Interval
X1
X2
X3
Predicted
lower
upper
lower
upper
Leverage
500
2
1
19.10582
#######
20.58033
12.70927
25.50236
0.056
Regression Analysis
r²
0.972
Adjusted r²
0.970
r
0.986
Std. Error
1.987
n
20
k
1
Dep. Var.
Time
ANOVA table
Source
SS
df
MS
F
p-value
Regression
2,443.4660
1
2,443.4660
619.20
2.15E-15
Residual
71.0315
18
3.9462
Total
2,514.4975
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=18)
p-value
95% lower
95% upper
Intercept
24.8345
1.0542
23.557
5.61E-15
22.6197
27.0494
Cases
0.1400
0.0056
24.884
2.15E-15
0.1282
0.1518
Regression Analysis
R²
0.962
Adjusted R²
0.958
n
36
R
0.981
k
3
Std. Error
3.056
Dep. Var.
Y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
7,472.6419
3
2,490.8806
266.76
1.03E-22
Residual
298.7956
32
9.3374
Total
7,771.4375
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=32)
p-value
95% lower
95% upper
Intercept
2.9904
1.9078
1.567
.1268
-0.8957
6.8766
X1
0.0256
0.0038
6.801
1.09E-07
0.0179
0.0333
X2
5.0424
0.7216
6.988
6.43E-08
3.5726
6.5122
X3
-6.7683
1.3821
-4.897
2.68E-05
-9.5835
-3.9531
Predicted values for: Y
95% Confidence Interval
95% Prediction Interval
X1
X2
X3
Predicted
lower
upper
lower
upper
Leverage
500
2
1
19.10582
#######
20.58033
12.70927
25.50236
0.056
Explanation / Answer
For both the models, we have R-sq>90% which is good. Also, both the models incorporate all the significant variables only.
F-stat for both the models turn out to be significant that means both the models are appropriate.
However, the second model incorporate more independent/ explanatory variables maintaining good model accuracy.
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