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.

Time until First Engine Overhaul	Annual Miles Driven	Average Load Weight	Average Driving Speed	Oil Change Interval
7.7	43.0	15.0	46.0	18.0
0.7	98.2	20.0	51.0	33.0
⋮	⋮	⋮	⋮	⋮
6.1	60.8	28.0	56.0	22.0

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.

b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

TimeˆTime^  =  +  Miles +    Load +    Speed +  Oil

c. Based on part (a), are the signs of the regression coefficients logical?

d. What is the predicted time before the first engine overhaul for a particular truck driven 55,000 miles per year with an average load of 22 tons, an average driving speed of 55 mph, and 15,000 miles between oil changes. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Time Until First Engine Overhaul	Annual Miles Driven	Average Load Weight	Average Driving Speed	Oil Change Interval
7.7	43	15	46	18
0.7	98.2	20	51	33
8.8	43.1	22	67	11
1.3	110.6	29	65	21
1.5	102.5	27	47	14
2	97.2	24	58	21
2.5	92.6	24	60	20
7.2	53.7	21	63	8
8.2	51.7	27	52	21
4.2	84.8	21	52	25
0.3	120.8	27	54	20
5.1	78	24	53	28
5	68.8	17	48	22
5	54.7	24	59	24
5.4	66.7	15	55	25
8.7	39	16	54	12
5.7	52.9	17	55	27
5.7	54.5	21	44	14
4.1	74.6	25	64	21
6.5	58.5	24	59	12
6.4	52.5	17	49	24
6.8	68.4	20	47	17
4.3	94.3	27	54	20
7.4	46.2	12	56	19
6.1	60.8	28	56	22

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)

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)