Question

The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four explanatory variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table. ime until First Annual Miles Average Load Average Driving 011 Change Engine Overhaul 91 7.9 0.9 6.1 Driven 42.8 98.5 Weight 25 24 Speed 46 46 Interva 15 29 61.2 58 19 a. For each explanatory variable, discuss whether it is likely to have a positive or negative causal effect on time until the first engine overhaul. Explanatory variable Annual Miles Driven Average Load Weight Average Driving Speed Oil Change Interval Effect on time ative ative ative tive ime =1134343] es 00732 Load+ 000475 Speed +0029 c. Based on part (a), are the signs of the regression coefficients logical? Regression coefficients Annual Miles Driven Average Load Weight Average Driving Speed Oil Change Interval Signs logical ogical not logical not logical d. What is the predicted time before the first engine overhaul for a particular truck driven 60,000 miles per year with an average load of 22 tons, an average driving speed of 57 mph, and 18,000 miles between oil changes. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) ime First me Untu 1 Engine Overhaul Driven eight SpeedInterval Anhual Miles Average Load Average Driing oil Change 42.8 98.5 43.4 110.7 102.3 97.1 92.8 53.9 51.4 84.9 120.4 77.5 68.6 54.9 66.7 39.4 52.7 54.2 74.8 58.7 52.3 68.6 94.6 45.7 61.2 46 46 64 15 29 14 26 17 20 15 13 17 28 23 27 25 19 25 21 27 28 2 7.9 3 |0.9 4 8.5 5 1.3 6 1.4 7 2.1 8 2.5 9 7.4 10 8.2 11 4.1 12 0.5 13 5.1 14 5.2 15 5.3 16 5.7 17 8.5 18 5.8 19 5.9 20 4.4 21 6.3 22 6.7 23 7.0 24 3.9 25 7.2 26 6.1 63 23 20 52 56 52 48 48 58 58 50 56 48 65 29 25 21 20 20 21 19 26 16 25 17 25 16 19 19 23 15 19 20 53 18 23 17 24 54 58 58

Answer 1

a)

Annual miles driven Negative  ( As miles increase time will also increase)

Average load weight Negative

Average driving speed Positive

Oil change interval Negative

c)

Annual Miles Driven logical.
Average Load Weight logical
Average Driving Speed logical
Oil Change Interval logical

d)

SUMMARY OUTPUT Regression Statistics Multiple FR R Square Adjusted R Square Standard Error Observations 0.953200081 0.908590394 0.890308473 0.816972269 25 ANOVA MS Significance F Regression Residual Total 4 132.6847262 33.17118156 20 13.34887377 0.667443689 24 49.69884669 4.10803E-10 146.0336 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95 .0% 13.24658523 2.262935422 5.853717743 0.09107437 0.012548851 7.257607413 0.05776245 0.095734689 -0.603359666 0.004304191 0.029171483 0.147547902 0.030822327 0.039581342-0.77870848 8.526184672 17.96698579 8.526184672 17.96698579 5.07277E-07-0.117251082 -0.064898192 0.117251082-0.064898192 0.141936611 0.065154838 0.445267717 0.113387559 0.051742906 -0.113387559 0.051742906 9.9989E-06 Intercept Miles Load Speed Oil change 0.553051319 -0.25746151 0.1419366110.25746151 0.056546456 0.065154838 0.056546456 0

You can see the coefficients of miles,load,speed and oil change

Given

Truck driven distance = 60 (in 1000's)

Load = 22 tonnes

Speed = 57 mph

Distance between oil change = 18 (in 1000's)

Now we can find expected time

Time = 13.2455 - 0.0941 * 60 - 0.0578 * 22 + 0.0043 * 57 - 0.0308 * 18 = 6.019 ~ 6.02 (2 decimal places)