Question 2 Part (a) Use the “Assignment 3 Bus Maintenance.xls” file posted with

Question

Question 2
Part (a)   

Use the “Assignment 3 Bus Maintenance.xls” file posted with this assignment to run one multiple regression that has “maintenance cost per month” as the dependent variable and “age,” “miles per month,” the “engine type” dummy variable, and “seating capacity” as independent variables.

Part (b)

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

Part (c)

Please state whether or not the intercept estimate in the previous part makes sense and explain your answer.

Part (d)   

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

Part (e)

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

Part (f)   

Which of the four slope estimates are statistically significant? Explain how you can tell.

Part (g)   

What is the predicted maintenance cost for a four-year old bus with a gasoline engine that is driven 750 miles per month and has a seating capacity of 55?

Part (h)   

How much of the variation in the dependent variable can be explained by variation in the independent variables?

Part (i)

As you can see from the R-Squared, the four included independent variables explain about 45 percent of the variation in maintenance cost. If we ran another regression that was just like the one above, but included one additional regressor that is the number of letters in the bus driver’s last name, what would happen to R-Squared? Explain your answer and state whether that is a good thing or a bad thing.

Buena School District Bus Data Maintenance cost per month (in Dollars) Age (in years) Miles per month Engine type 0 = Diesel, 1 = gasoline Seating capacity 329 7 853 0 55 329 3 741 0 55 357 8 760 0 6 433 9 848 0 55 433 9 848 0 55 455 7 828 0 55 455 7 828 0 55 461 6 849 0 55 461 6 849 0 55 452 9 831 0 42 471 9 815 0 42 444 2 757 0 14 444 2 757 0 12 427 5 780 1 14 357 8 760 0 6 382 3 818 1 8 382 3 818 1 9 452 9 831 0 42 471 9 815 0 42 469 8 812 0 55 478 6 821 0 55 478 6 821 0 55 489 9 858 0 55 489 9 858 0 55 380 9 803 0 55 444 2 757 0 14 444 2 757 0 18 452 9 831 0 42 471 9 815 0 42 546 8 870 0 55 546 8 870 0 55 496 8 839 0 55 561 12 838 0 55 355 3 806 1 55 355 3 806 1 55 422 8 869 1 55 422 8 869 1 55 422 8 869 1 55 436 2 785 1 55 436 2 785 1 55 466 10 865 1 55 466 10 865 1 55 474 10 845 1 55 474 10 845 1 55 474 10 845 1 55 497 10 859 1 55 497 10 859 1 55 514 11 980 1 55 514 11 980 1 55 558 10 885 1 55 558 10 885 1 55 558 10 885 1 55 359 7 751 1 55 359 7 751 1 55 359 7 751 1 55 382 3 818 1 6 382 3 818 1 6 406 3 798 1 55 406 3 798 1 55 406 3 798 1 55 427 5 780 1 14 459 8 826 1 55 459 8 826 1 55 459 8 826 1 55 474 9 857 1 55 474 9 857 1 55 474 9 857 1 55 444 2 757 0 14 444 2 757 0 14 427 5 780 1 14 357 8 760 0 6 382 3 818 1 6 382 3 818 1 6

Explanation / Answer

The multiple regression model is

Y=b0+b1X1+b2X2+b3X3+b4X4

X1= Age (years)

X2=Miles per month

X3=Engine Type

X4=Seating capacity

Y=Maintenance cost per month

Using the excel we find the estimated value of the regression model

If X1,X2,X3 amd X4, all is 0, the intercept is simply the expected mean value of Y at that value. Here, intercepts can be negative even if Y can’t. This usually occurs when none of the X values are close to 0. We would expect an average Maintenance cost per month of -86.22 for all other variable is not there

Since X1 is a continuous variable, b1 represents the difference in the predicted value of Y for each one-unit difference in X1, if other variable remains constant. This means that if X1 differed by one unit, and other variable did not differ, Y will differ by b1 units, on average.

Similarly, b3 is interpreted as the difference in the predicted value in Y for each one-unit difference in X3, if other variables remains constant. However, since X3 is a categorical variable coded as 0 or 1, a one unit difference represents switching from one category to the other. b3 is then the average difference in Y between the category for which X3 = 0 (the reference group) and the category for which X3= 1 (the comparison group).

The p-value is tell the estimates are statistically significant. Here Miles per month and Engine type are statistically significant because the p-value is less than 0.05 level 0f significance.

SUMMARY OUTPUT Regression Statistics Multiple R 0.673018 R Square 0.452953 Adjusted R Square 0.420774 Standard Error 42.98239 Observations 73 ANOVA df SS MS F Significance F Regression 4 104020.6 26005.14 14.07596 2.03E-08 Residual 68 125629 1847.485 Total 72 229649.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -86.2265 111.7593 -0.77154 0.443061 -309.239 136.7858 Age (in years) 3.163457 2.44931 1.291571 0.200879 -1.72407 8.050978 Miles per month 0.621444 0.151294 4.107523 0.00011 0.319541 0.923346 Engine type -22.749 10.67362 -2.13133 0.036679 -44.0479 -1.45015 Seating capacity 0.199415 0.321527 0.620211 0.537192 -0.44218 0.841012

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