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
8.1	42.8	22.0	50.0	10.0
0.9	98.7	26.0	49.0	25.0
⋮	⋮	⋮	⋮	⋮
6.1	61.6	28.0	54.0	16.0

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.

The effect on time is either Positive or Negative! Fill them in below.

	Explanatory variable Effect on time Annual Miles Driven Average Load Weight Average Driving Speed Oil Change Interval

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?
The below signs will be filled with the word logical or not logical!

	Regression coefficients Signs Annual Miles Driven Average Load Weight Average Driving Speed Oil Change Interval

d. What is the predicted time before the first engine overhaul for a particular truck driven 57,000 miles per year with an average load of 18 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.)

TimeˆTime^

_______ years

Excel data:

Time Until First Engine Overhaul	Annual Miles Driven	Average Load Weight	Average Driving Speed	Oil Change Interval
8.1	42.8	22	50	10
0.9	98.7	26	49	25
8.7	43.2	18	67	19
1.4	111	27	60	24
1.4	102.2	31	46	19
2	97.3	27	67	22
2.5	93.3	19	59	17
7.6	54.1	18	70	12
8.1	51.2	24	47	20
3.9	84.9	29	51	26
0.6	120.3	30	50	20
5.3	77.6	24	49	25
5	68.2	25	49	21
5.2	55.4	28	53	21
5.3	66.4	19	62	24
8.5	39.8	15	45	16
5.8	52.4	19	58	27
6.2	54.5	24	47	14
4.2	75.1	23	60	20
6.1	58.4	19	50	13
6.7	52.2	24	49	23
6.8	68.3	21	56	24
4	94.3	19	55	21
7.6	45.2	22	56	17
6.1	61.6	28	54	16

Don't care how you solve as long as answers are correct. I will like for it being correct!

Answer 1

The effect on time is either Positive or Negative! Fill them in below.

	Explanatory variable Effect on time Annual Miles Driven Negative Average Load Weight Negative Average Driving Speed Negative Oil Change Interval Positive

Coefficientsa
Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
		B	Std. Error	Beta
1	(Constant)	13.436	1.930		6.963	.000
	Annual Miles Driven	-.094	.009	-.879	-10.390	.000
	Average Load Weight	-.063	.049	-.109	-1.274	.217
	Average Driving Speed	.002	.025	.005	.070	.945
	Oil Change Interval	-.016	.039	-.029	-.409	.687
a. Dependent Variable: Time Until First Engine Overhaul

b. TimeˆTime^  = 13.436 - 0.094  Miles - 0.063 Load + 0.002 Speed -0.016  Oil

Three variables have no significant effect!

	Regression coefficients Signs Annual Miles Driven Negative Average Load Weight Negative Average Driving Speed Positive Oil Change Interval Negative

The predicted value is:-

1	57	18	57	18	Predicted
13.436	-0.094	-0.063	0.002	-0.016
13.436	-5.358	-1.134	0.114	-0.288	6.77

Predicted time is 6.77 years