The owner of a moving company typically has his most experienced manager predict

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. In a 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 20 moves in which the travel time was an insignificant portion of the hours worked. Use the data provided to complete parts (a) through (d).

B.) Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.

b0 = _____

b1 =______

C.) Interpret the meaning of the slope, b1, in this problem. Choose the correct answer below.

a.)For each increase of one hour of moving time, the number of cubic feet moved is expected to increase by b1.

b.) The approximate moving time when the number of cubic feet moved is 0 cubic feet is b1.

c.) The approximate number of cubic feet moved when the moving time is 0 hours is b1.

d.) For each increase of one cubic foot moved, the moving time is expected to increase by b1 hours.

D.) Predict the labor hours for moving 300 cubic feet. _______ Hours

Cubic_Feet_Moved Labor_Hours

713 38.75

817 44.5

711 44

403 20.5

260 15.75

682 42.25

749 45

602 32.5

722 44.5

683 40.75

387 24.5

402 23.75

318 20.75

744 42

710 38.5

742 45.5

430 21.75

310 17

316 19.5

472 29.5

Explanation / Answer

Solution:

First of all we have to develop the regression equation for the given data. For the given regression model, the dependent variable or response variable as labor hours and independent variable or predictor as cubic feet moved. The excel output for the given model is summarized as below:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.979056803

R Square

0.958552223

Adjusted R Square

0.956249569

Standard Error

2.306753165

Observations

20

ANOVA

df

SS

MS

F

Significance F

Regression

1

2215.079392

2215.07939

416.281438

6.82408E-14

Residual

18

95.77998296

5.32111016

Total

19

2310.859375

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

0.446434011

1.656443895

0.26951351

0.79059986

-3.03362547

3.926493491

Cubic Feet Moved

0.057488707

0.002817663

20.4029762

6.8241E-14

0.051569017

0.063408397

Part B

The required coefficients for the given regression model is given as below:

Intercept = b0 = 0.446434011

Slope = b1 = 0.057488707

Part C

Correct Alternative: a.) For each increase of one hour of moving time, the number of cubic feet moved is expected to increase by b1.

Part D

Here, we have to predict the labor hours for moving 300 cubic feet.

The regression equation is given as below:

Labor hours = 0.4464 + 0.0575* Cubic Feet Moved

Labor hours = 0.4464 + 0.0575*300

Labor hours = 17.6964

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.979056803

R Square

0.958552223

Adjusted R Square

0.956249569

Standard Error

2.306753165

Observations

20

ANOVA

df

SS

MS

F

Significance F

Regression

1

2215.079392

2215.07939

416.281438

6.82408E-14

Residual

18

95.77998296

5.32111016

Total

19

2310.859375

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

0.446434011

1.656443895

0.26951351

0.79059986

-3.03362547

3.926493491

Cubic Feet Moved

0.057488707

0.002817663

20.4029762

6.8241E-14

0.051569017

0.063408397

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