Acid rainResearchers studying acid rain measured the acidity of precipitation in a Colorado wilderness area for $150$consecutive weeks. Acidity is measured by pH. Lower pH values show higher acidity. The researchers observed a linear pattern over time. They reported that the regression line $\stackrel{\wedge }{pH}$=$5.43-0.0053$(weeks) fit the data well^$16$.

(a) Identify the slope of the line and explain what it means in this setting.

(b) Identify the y-intercept of the line and explain what it means in this setting.

(c) According to the regression line, what was the pH at the end of this study?

It is given in the question that, the regression line $\stackrel{\wedge }{pH}=5.43-0.0053$(weeks) fit the data well.

Identify the slope of the line and explain what it means in this setting.

We have$\mathrm{PH}\text{-hat}=5.43-.0053\left(\text{weeks}\right)$

Here, the slope of the line is $-.0053$.

In other words, for every week that increases, there is a decrease of$-0053PH$

Linear regression lines produce slopes based on the number multiplied by the explanatory variable, which represents the predicted decrease in localid="1649926389024" $y$when localid="1649926396257" $x$increases by one unit.

It is given in the question that, the regression line $\stackrel{\wedge }{pH}=5.43-0.0053$(weeks) fit the data well.

Identify the y-intercept of the line and explain what it means in this setting.

According to this equation, the $\mathrm{pH}$value will be $5.43$after $0$weeks when the $y-$intercept is $5.43$.

When the explanatory variable is $0$, the y-intercept represents the value of the response variable.

It is given in the question that, the regression line $\stackrel{\wedge }{pH}=5.43-0.0053$(weeks) fit the data well.

According to the regression line, what was the pH at the end of this study?

$\mathrm{PH}\text{-hat}=5.43-.0053\left(\text{weeks}\right)$

$150$weeks have passed since the experiment began.

localid="1649927050227" $$\begin{gathered} pH-\text{hat}=5.43-.0053\left(150\right) \\ pH-hat=4.635 \end{gathered}$$

Any predicted value can be found by substituting the value of the explanatory variable.