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The maintenance manager at a trucking company wants to build a regression model

ID: 3314629 • Letter: T

Question

The maintenance manager at a trucking company wants to build a regression model to forecast time until the first engine overhaul based on four explanatory variables: (1) annual miles driven, (2) average load weight, (3) average driving speed, and (4) oil change interval. Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks.

a. Estimate the time until the first engine overhaul as a function of all four explanatory variables. (Round your answers to 4 decimal places.)

b-1. At the 10% significance level, are the explanatory variables jointly significant? First, specify the competing hypotheses.

b-2. Find the p-value.

b-3. What is the conclusion to the test?

(Click to select)RejectDo not reject H0, we (Click to select)cancannot conclude the explanatory variables are jointly significant in explaining the time until the first engine overhaul.

c-1. Are the explanatory variables individually significant at the 10% significance level? First, specify the competing hypotheses.

c-2. Show the relevant steps of the test. What is the conclusion? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.)

Time Until First Engine Overhaul (Yrs) Annual Miles Driven (000) Average Load Weight (tons) Average Driving Speed (mph) Oil Change Interval (000 miles) 7.9 42.8 19 46 15 0.9 98.5 25 46 29 8.5 43.4 21 64 14 1.3 110.7 27 60 26 1.4 102.3 28 51 17 2.1 97.1 24 63 20 2.5 92.8 23 55 15 7.4 53.9 20 65 13 8.2 51.4 22 52 17 4.1 84.9 25 56 28 0.5 120.4 29 52 23 5.1 77.5 25 48 27 5.2 68.6 21 48 25 5.3 54.9 24 58 23 5.7 66.7 20 58 26 8.5 39.4 20 50 16 5.8 52.7 21 56 25 5.9 54.2 19 48 17 4.4 74.8 22 65 25 6.3 58.7 20 54 16 6.7 52.3 22 53 19 7.0 68.6 18 51 19 3.9 94.6 23 54 23 7.2 45.7 17 58 15 6.1 61.2 24 58 19

Explanation / Answer

for above below is regression output:

a-1) time =13.4343-0.0896*miles-0.0732*load+0.0048*spped-0.0297*oil

b-1)

H0: 1 = 2 = 3 = 4 = 0; HA: At least one j 0

b-2) p-value < 0.01

b-3)

Reject H0, we can  conclude the explanatory variables are jointly significant in explaining the time until the first engine overhaul.

c-1)

H0: j = 0; HA: j 0

c-2)

Regression Statistics Multiple R 0.9539 R Square 0.9099 Adjusted R Square 0.8918 Standard Error 0.8113 Observations 25 ANOVA df SS MS F Regression 4.00 132.87 33.22 50.47 Residual 20.00 13.16 0.66 Total 24.00 146.03 Coefficients Standard Error t Stat P-value Intercept 13.4343 2.1924 6.1275 0.0000 miles -0.0896 0.0121 -7.3845 0.0000 load -0.0732 0.0907 -0.8065 0.4295 spped 0.0048 0.0290 0.1640 0.8714 oil -0.0297 0.0393 -0.7550 0.4590