Chapter 4.2, Problem 4.50E

(a)

To determine

To explain carefully what the slope $b=-6.31$ tell us how fast the soap lost weight.

Explanation of Solution

The slope means that if one more day passes then the weight of the bar of soap decreases by about $6.31$ grams.

(b)

To determine

To interpret the y -intercept, $133.2$ .

Explanation of Solution

The y -intercept $133.2$ means that if you did not use the bar of soap yet, it weighs about $133.2$ grams.

(c)

To determine

To use the regression equation to calculate the weight of the soap on day four.

Answer to Problem 4.50E

The weight of the bar of soap is about $107.96$ grams.

Explanation of Solution

To calculate, replace day with $4$ in the equation:

Weight $\begin{array}{l}=133.2-6.31(4)\\ =107.96\end{array}$

Thus the weight of the bar of soap is about $107.96$ grams.

(d)

To determine

To construct the regression line on the scatterplot from the previous question.

Explanation of Solution

The regression line on the scatterplot is as follows: