Chapter 13, Problem 13.25SE

a.

To determine

To find: The equation of the fitted least-squares line

Explanation of Solution

Given:

The Minitab output is:

  

Plot is:

  

From the provided output, the equation of the regression line is:

  $y=8.585+3.88208x-0.21663x^2$

a.

To determine

To interpret: The value of $R^2$ and comment on the fit of the model.

Explanation of Solution

From the provided output, the coefficient of determination is 0.944. It means that 99.8% of the variation in the model is explained. Since, the value is large enough it means that the provided model is fit enough.

c.

To determine

To find: Whether the model is significant at 5% level of significance.

Explanation of Solution

From the provided excel output; the p -value is equal to 0.000 which implies that the regression model is highly significant.

c.

To determine

To find: Whether there is sufficient evidence to show that the quadratic model provides a better fir to the data than a simple linear model.

Explanation of Solution

The prediction equation relating $\widehat{y}$ and $x_1$ when $x_2=4$ can be calculated as:

  $\begin{array}{c}Y=-28.4+1.46x_1+3.84\left(4\right)\\ =-28.4+1.46x_1\end{array}$

d.

To determine

To find: The number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.

Explanation of Solution

Since, the p -value is less than the level of significance. Thus, it could be said that the quadratic model provided a better fit than a simple linear model

e.

To determine

To explain: Whether normality assumptions have been violated using the residual plot.

Explanation of Solution

From the provided residual plot, it could be said that there is no violation of normality assumptions. It means that model is well fitted.