Question

The maintenance manager at a trucking company wants to build a regression model to forecast the time until the first engine overhaul (Time in years) based on four explanatory variables: (1) annual miles driven (Miles in 1,000s), (2) average load weight (Load in tons), (3) average driving speed (Speed in mph), and (4) oil change interval (Oil in 1,000s miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks.

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a. Estimate the time until the first engine overhaul as a function of all four explanatory variables. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

TimeˆTime^  =  +  Miles +  Load +  Speed +  Oil

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

• H₀: β₁ = β₂ = β₃ = β₄ = 0; H_A: At least one β_j > 0

• H₀: β₁ = β₂ = β₃ = β₄ = 0; H_A: At least one β_j < 0

• H₀: β₁ = β₂ = β₃ = β₄ = 0; H_A: At least one β_j ≠ 0

b-2. Find the p-value.

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

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

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

• H₀: β_j = 0; H_A: β_j > 0

• H₀: β_j = 0; H_A: β_j < 0

• H₀: β_j = 0; H_A: β_j ≠ 0

c-2. Show the relevant steps of the test. What is the conclusion?

Answer 1

Solution: