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

750      35.00

533      28.50

391      18.25

497      27.50

724      38.00

765      40.50

770      38.25

491      24.25

544      30.25

674      33.25

787      37.50

849      43.75

317      15.50

279      16.00

685      33.75

407      18.25

288      15.75

784      35.75

727      33.75

384      19.25

show your working

Answer 1

Solution-

B. After running the regression analysis, we obtain the following regression output-

SUMMARY OUTPUT Regression Statistics MultipleR R Square Adjusted R Square Standard Error Observations 0.979139137 0.95871345 0.956419753 1.923200832 20 ANOVA MS Significance F Regression Residual Total 18 19 1545.973374 1545.973 417.9773 6.58836E-14 66.57662593 3.698701 1612.55 Intercept X Variable 1 Coefficients Standard Error tstat P-value Lower 95% U er95% 1.498219793 1.419250147 1.055642 0.305096 -1.483514121 4.479953706 0.0474871720.002322736 20.44449 6.59E-14 0.042607284 0.05236706

Regression equation is-

Labor hours = 1.49822 + 0.04749 * Cubic feet

C. Meaning of slope is- For each increase of one cubic foot moved, the moving time is expected to increase by b1 hours.

Thus correct option is D.

D. When cubic feet = 300, the labor hours = 1.49822 + 0.04749 * 300

= 15.744

Answers

TY!