The owner of a moving company typically has his most experienced manager predict
ID: 3048109 • 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 effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved as the explanatory 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. The data are stored is below
1.. What is a 95% confidence interval of the population slope ?
2. Predict the labor hours for moving 500 cubic feet.
3. Construct a 95% confidence interval of the mean labor hours for all moves of 500 cubic feet.
4. Construct a 95% prediction interval of the labor hours of an individual move that has 500 cubic feet.
5. Why is the interval in (g) narrower than the interval in (h)?
0 vss eeeeeeee o e e e e e e e o o e e e e e e e oeo EYYNNYYYYYYYYYYYYNYYYYYYYNNYYYYYYYNYN 7 3222132161443232222543323333434325 2706705462957 1509709584499 3539288337642507553767556044293 5 0 0 51 0) 1 6 17 2 4555902502505881, I 5 5 5 9 1 2 5 724514078555 2 3. 2 2 2225174 9. 6. 33323242-2. .7 9. 1222124222 01234567 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 567Explanation / Answer
Answer:
The regression line is hours = -2.3697 +0.0501*feet
1.. What is a 95% confidence interval of the population slope ?
95% CI = (0.0439, 0.0562)
2. Predict the labor hours for moving 500 cubic feet.
Predicted hours =-2.3697 +0.0501*500 = 22.68
3. Construct a 95% confidence interval of the mean labor hours for all moves of 500 cubic feet.
99% CI = (20.799, 24.5419)
4. Construct a 95% prediction interval of the labor hours of an individual move that has 500 cubic feet.
95% PI = (12.2755, 33.0654)
5. Why is the interval in (g) narrower than the interval in (h)?
Prediction intervals must account for both the uncertainty in knowing the value of the population mean, plus data scatter. So a prediction interval is always wider than a confidence interval.
Regression Analysis
r²
0.889
n
36
r
0.943
k
1
Std. Error
5.031
Dep. Var.
hours
ANOVA table
Source
SS
df
MS
F
p-value
Regression
6,910.7189
1
6,910.7189
272.99
8.15E-18
Residual
860.7186
34
25.3153
Total
7,771.4375
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=34)
p-value
95% lower
95% upper
Intercept
-2.3697
2.0733
-1.143
.2610
-6.5830
1.8437
feet
0.0501
0.0030
16.522
8.15E-18
0.0439
0.0562
Predicted values for: hours
95% Confidence Interval
95% Prediction Interval
feet
Predicted
lower
upper
lower
upper
Leverage
500
22.67048
20.79901
24.54194
12.27553
33.06542
0.033
Regression Analysis
r²
0.889
n
36
r
0.943
k
1
Std. Error
5.031
Dep. Var.
hours
ANOVA table
Source
SS
df
MS
F
p-value
Regression
6,910.7189
1
6,910.7189
272.99
8.15E-18
Residual
860.7186
34
25.3153
Total
7,771.4375
35
Regression output
confidence interval
variables
coefficients
std. error
t (df=34)
p-value
95% lower
95% upper
Intercept
-2.3697
2.0733
-1.143
.2610
-6.5830
1.8437
feet
0.0501
0.0030
16.522
8.15E-18
0.0439
0.0562
Predicted values for: hours
95% Confidence Interval
95% Prediction Interval
feet
Predicted
lower
upper
lower
upper
Leverage
500
22.67048
20.79901
24.54194
12.27553
33.06542
0.033
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