A car's power output is influenced by several factors. A sample of 90 different car models of three makes from the European market is stored in the file Cars .

Develop a multiple linear regression model to predict power output \((\mathrm{kW})\), based on engine size (displacement, in cubic centimeters) and maximum speed \((\mathrm{km} / \mathrm{h})\).

a. State the multiple regression equation.

b. Interpret the meaning of the slopes, \(b_{1}\) and \(b_{2}\), in this problem.

c. Explain why the regression coefficient, \(b_{0}\), has no practical meaning in the context of this problem.

d. Predict the mean power output of cars that have a displacement of \(1800 \mathrm{~cm}^{3}\) and maximum speed of \(200 \mathrm{~km} / \mathrm{h}\).

e. Construct a \(95 \%\) confidence interval estimate for the mean power output for cars that have a displacement of \(1,800 \mathrm{~cm}^{3}\) and maximum speed of \(200 \mathrm{~km} / \mathrm{h}\).

f. Construct a 95\% confidence interval estimate for the power output for a car that has a displacement of \(1,800 \mathrm{~cm}^{3}\) displacement and maximum speed of \(200 \mathrm{~km} / \mathrm{h}\).

g. What conclusion can you reach concerning this regression model?