(Solved): Problem 3 [ 36 points] The brake horsepower developed by an automobile engine on a dynamometer is ...

Problem 3 [ 36 points] The brake horsepower developed by an automobile engine on a dynamometer is thought to be a function of the engine speed in revolutions per minute (RPM), the road octane number of the fuel, and the engine compression. An experiment is run in the laboratory and the following data are collected. 1. [8 points] Fit a multiple linear regression model to the data (To setup the model in Design Expert, select Custom Designs \( \rightarrow \) Blank Spreadsheet \( \rightarrow \) enter the number o factors and follow the prompts) 2. [7 points] Test for significance of regression. What conclusions can you draw? 3. [7 points] Are all 3 regressor variables useful in the model? 4. [7 points] Analyze the residuals and comment on model adequacy. 5. [7 points] Add interaction terms to the model, calculated the new regression coefficients and analyze the regression significance.