Chapter 3.2, Problem 39E

(a)

To determine

To identify: the slope of the line

Answer to Problem 39E

The slope is: $b=-0.0053$

Explanation of Solution

Given:

  $\widehat{p^H}=5.43-0.0053(weeks)$

Calculation:

On comparing our equation to general equation of regression we get, the slope is:

  $b=-0.0053$

This tells us that $p^H$ is predicated to go down by -0.0053 for each added week.

Therefore, the slope is: $b=-0.0053$

(b)

To determine

To identify: the intercept of the line

Answer to Problem 39E

The intercept is: $a=5.43$

Explanation of Solution

Given:

  $\widehat{p^H}=5.43-0.0053(weeks)$

Calculation:

On comparing our equation to general equation of regression we get, the intercept is: $a=5.43$

The value of the y intercept is shows $p^H$ value when researcher started to measure the acidity.

Therefore, the intercept is: $a=5.43$

(c)

To determine

To find: the value of $p^H$

Answer to Problem 39E

The value of $p^H$ will be 4.635

Explanation of Solution

Calculation:

The regression line is:

  $\begin{array}{l}\widehat{p^H}=5.43-0.0053(weeks)\\ \widehat{p^H}=5.43-0.0053\times 150\\ =4.635\end{array}$

Since researcher measured acid rain for 150 consecutive weeks. At the end of the study

When weeks = 150 then

The $p^H$ value at the end of the study will be 4.635

Therefore, the $p^H$ value at the end of the study will be 4.635