Chapter 17, Problem 58CE

a:

To determine

Derive the regression equation.

Explanation of Solution

The ANOVA table output is obtained using the statistical software. The result is given below:

The general regression line can be derived as follows:Intercept is denoted by IC and the coefficient is denoted by CE

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

Substitute the respective value in Equation (1) to derive the regression equation.

$\widehat{\text{y}}=\text{164}\text{.01}+0.14\times \text{X1+0}\text{.0313}\times \text{X2}$

b:

To determine

Testing the hypothesis.

Explanation of Solution

The null hypothesis (H₀) ${\text{β}}_{\text{1}}=0$ and the alternative hypothesis (H₁) is ${\text{β}}_{\text{1}}\ne 0$.

The calculated t value is 1.72 and the p value is 0.0974. Since the p value is significantly different from 0, the alternate hypothesis is not accepted.

c:

To determine

Testing the new hypothesis.

Explanation of Solution

The null hypothesis (H₀) ${\text{β}}_{\text{2}}=0$ and the alternative hypothesis (H₁) is ${\text{β}}_{\text{2}}\ne 0$.

The calculated t value is 4.64 and the p value is 0.0001. Since the p value is nearly equal to 0, the alternate hypothesis is accepted.

d:

To determine

Standard error.

Explanation of Solution

The standard error is 63.08 and the R square value is 0.4572. This indicates the good fit of the model.

e

To determine

Normality requirement.

Explanation of Solution

The distribution of the variable is obtained using the statistical software. The result is given below:

The required condition is that the variable should be distributed normally. Since the histogram is bell shaped, the error variable is distributed normally. Thus, the required condition is satisfied.

The variance of the error is obtained using the statistical software. The result is given below:

From Figure 2, it is known that the error variable is not constant.

f:

To determine

Calculate the upper limit and the lower limit.

Explanation of Solution

The upper limit and the lower limit areobtained using the statistical software. The result is given below:

The lower limit is 69.2 and the upper limit is 349.3.