Chapter 18, Problem 43CE

a:

To determine

Regression equation.

Explanation of Solution

The general regression line can be derived as follows:

The intercept is denoted by IC and the coefficient is denoted by CE.

${\text{Variable}}_{\text{Dependent}}=\text{IC}+{\text{CE}}_{\text{X1}}\times {\text{X1+CE}}_{\text{X2}}\times \text{X2}+\mathrm{...}+{\text{CE}}_{\text{Xn}}\times \text{Xn}+\text{Error}$        (1)

Mileage is determined by the speed. Substitute the respective value in Equation (1) to derive the regression equation.

$\widehat{\text{Mileage}}={\text{β}}_0+{\text{β}}_1\times \text{speed}+{\text{β}}_2\times {\text{Speed}}^2+\text{ε}$

b:

To determine

Regression process.

Explanation of Solution

The regression output is obtained using the statistical software. The result is as given below:

c:

To determine

Fitness of the model.

Explanation of Solution

The standard error is 3.86 and ${\text{R}}^2$ is 0.7102. Thus, the model fits well.