Chapter 4.2, Problem 4.51E

(a)

To determine

To predict the weight of the soap after $30$ days using the regression equation in the previous exercise and tell what’s wrong in this.

Answer to Problem 4.51E

  $-56.1$ days.

Explanation of Solution

To calculate, replace day in the equation given by $30$ :

Weight $\begin{array}{l}=133.2-6.31(30)\\ =-56.1\end{array}$

The weight cannot be negative and thus is impossible. The cause is that it is expected that after $30$ days there is nothing left of the bar of soap.

(b)

To determine

To explain ${\text{r}}^2=0.996$ value means.

Explanation of Solution

The square of the correlation ${\text{r}}^2$ is the fraction of the variation in the values of y that is explained by the least square regression of $y\text{ on }x$ .

Thus, in this case it means that $99.6\%$ of the variation is explained by the regression line.

(c)

To determine

To construct the residual plot for this data and explain is a linear model appropriate in this case.

Explanation of Solution

We note that for day $0\text{ to }12$ that the linear model is appropriate, however for a larger number of days the residuals deviate further from zero and thus the model is less appropriate.

The residual plot is as: