Question: An automotive engineer would like to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower \(\left(X_{1}\right)\) and the number of cylinders of a car \(\left(X_{2}\right) . X_{2}\) equals to 1 if the car has 6 cylinders and zero if the car has 4 cylinders. She obtained the following output using Excel.

1. Is the interaction term significant in Model 3? Use \(5 \%\) significance level.
2. Is there a difference between the regression models for cars with 4 \(\begin{array}{llllll}\text { cylinders and } & 6 & \text { cylinders? } & \text { Use } & 5 \% & \text { significance } & \text { level. }\end{array}\) \(\left(F=\frac{\left(S S E_{R}-S S E_{F}\right) /(K-L)}{S S E_{F} /(N-K-1)}\right.\),
   the critical value of the corresponding partial \(\mathrm{F}\) test is 3.2145 ).
3. If Model 3 is adopted, estimate the automobile mileages for a car with 10 horsepower and 6 cylinders.

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