Part (a) (3 points) Use the “Trucks.xls” data set and run a multiple regression

Question

Part (a)             (3 points)

Use the “Trucks.xls” data set and run a multiple regression with “Maintenance cost per month” as dependent variable on the following independent variables: “Age,” “Miles per month,” and “Diesel dummy.”

You must submit your actual Excel file with the output as part of the assignment.

Part (b)            (2 points)

Interpret the estimated value of the intercept, i.e., explain what the number means in this regression.

Part (c)            (2 points)

Interpret the estimated value of the coefficient on the “Age” variable, i.e., explain what the number means in this regression.

Part (d)            (2 points)

Interpret the estimated value of the coefficient on the “Miles per month” variable, i.e., explain what the number means in this regression.

Part (e)            (2 points)

Interpret the estimated value of the coefficient on the “Diesel dummy” variable, i.e., explain what the number means in this regression.

Part (f)             (2 points)

Are there any coefficient estimates that are statistically significant? If so, name one and explain how you can tell that it is statistically significant.

Part (g)            (2 points)

Are there any coefficient estimates that are not statistically significant? If so, name one and explain how you can tell that it is not statistically significant.

Part (h)            (3 points)

What is the predicted maintenance cost for a truck that is seven years old, gets driven 800 miles per month, and has a Diesel engine?

Part (i)             (3 points)

Consider a new “Gasoline dummy” variable that is “1” when a truck has a gasoline engine and “0” when it has a Diesel engine. Suppose that we then run a new multiple regression with “Maintenance cost per month” as dependent variable on the following independent variables: “Age,” “Miles per month,” and “Gasoline dummy.” (That is, it is the same regression as in Part (a), but with the “Gasoline dummy” variable instead of the “Diesel dummy.”) What would the estimated value of the coefficient on the “Gasoline dummy” be?

Part (j)             (2 points)

What percentage of the variation in the dependent variable can be explained by variation in the independent variables?

Part (k)            (2 points)

What percentage of the variation in the dependent variable cannot be explained by variation in the independent variables?

Speedy Delivery's Truck Maintenance Maintenance cost per month (in Dollars) Age (in years) Miles per month Diesel dummy (1 = Diesel; 0 = gasoline) 382 3 818 0 469 8 812 1 503 8 857 1 432 6 819 1 478 6 821 1 493 10 1008 1 461 6 849 1 503 10 883 1 546 8 870 1 380 9 803 1 471 9 815 1 444 2 757 1 452 9 831 1 546 8 870 1 380 9 803 1 471 9 815 1 444 2 757 1 452 9 831 1 561 12 838 1 496 8 839 1 466 10 865 0 422 8 869 0 474 10 845 0 558 10 885 0 497 10 859 0 355 3 806 0 436 2 785 0 514 11 980 0 497 10 859 0 355 3 806 0 436 2 785 0 514 11 980 0 466 10 865 0 422 8 869 0 474 10 845 0 329 7 853 1 505 10 822 1 433 9 848 1 357 8 760 1 329 3 741 1 478 6 821 1 493 10 1008 1 558 10 885 0 359 7 751 0 427 5 780 0 474 9 857 0 382 3 818 0 459 8 826 0 406 3 798 0 459 8 826 0 359 7 751 0 427 5 780 0 329 7 853 1 505 10 822 1 433 9 848 1 357 8 760 1 329 3 741 1 478 6 821 1 474 9 857 0 382 3 818 0 406 3 798 0 452 9 831 1 546 8 870 1 380 9 803 1 471 9 815 1 444 2 757 1 452 9 831 1 561 12 838 1 496 8 839 1 466 10 865 0 422 8 869 0 474 10 845 0 558 10 885 0 406 3 798 0 452 9 831 1 546 8 870 1 380 9 803 1 471 9 815 1 329 7 853 1 505 10 822 1 359 7 751 0 427 5 780 0 474 9 857 0 382 3 818 0 459 8 826 0 406 3 798 0 459 8 826 0 359 7 751 0 427 5 780 0 329 7 853 1 505 10 822 1 433 9 848 1 357 8 760 1

Explanation / Answer

Interpretation:

Intercept : Keeping other variable as zero, minimum maintance cost is 22.41

Age: Keeping others constant, for every 1 year change maintainance cost increase by 7.77 dollars

Miles per month: Keeping others constant, for every change in one mail, maintainance cost increase by 0.438

37.7% percentage of the variation in the dependent variable can be explained by variation in the independent

variables

62.3% of the variation in the dependent variable cannot be explained by variation in the independent variables

SUMMARY OUTPUT Regression Statistics Multiple R 0.614059 R Square 0.377068 Adjusted R Square 0.356071 Standard Error 50.08156 Observations 93 ANOVA df SS MS F Significance F Regression 3 135121.8 45040.6 17.95761 3.38E-09 Residual 89 223226.5 2508.163 Total 92 358348.3 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 22.40844 95.92265 0.23361 0.815825 -168.188 213.0047 -168.188 213.0047 Age (in years) 7.773931 2.448827 3.174553 0.002062 2.908164 12.6397 2.908164 12.6397 Miles per month 0.438067 0.125793 3.482449 0.000772 0.18812 0.688015 0.18812 0.688015 Diesel dummy (1 = Diesel; 0 = gasoline) 1.897994 10.74104 0.176705 0.860142 -19.4442 23.24021 -19.4442 23.24021

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