An experiment was conducted to evaluate the performances of a diesel engine run on synthetic (coal-derived) and petroleum-derived fuel oil (Journal of Energy Resources Technology, Mar. 1990). The petroleum-derived fuel used was a number 2 diesel fuel (DF-2) obtained from Phillips Chemical Company. Two synthetic fuels were used: a blended fuel (50% coal derived and 50% DF-2) and a blended fuel with advanced timing. The brake power (kilowatts) and fuel type were varied in test runs, and engine performance was measured. The following table gives the experimental results for the performance measure, mass burning rate per degree of crank angle.

The researchers fit the interaction model 

E(y) = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₁x₂ + β₅x₁x₃

where

The results are shown in the SAS printout.

a. Conduct a test to determine whether brake power and fuel type interact. Test using α = .01.

b. Refer to the model, part a. Give the estimates of the slope of the y–x₁ line for each of the three fuel types.

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SYNFUELS Mass Burning Rate, y Brake Power, X1 Fuel Type 4 DF-2 13.2 4 Blended 17.5 4 Advanced Timing 17.5 DF-2 26.1 6 Blended 32.7 6. Advanced Timing 43.5 8 DF-2 25.9 8 Blended 46.3 8 Advanced Timing 45.6 10 DF-2 30.7 10 Blended 50.8 10 Advanced Timing 68.9 12 DF-2 32.3 12 Blended 57.1