Acid rain Refer to Exercise $39$. Would it be appropriate to use the regression line to predict pH after$1000$ months? Justify your answer.

It is given in the question $39$that, the regression line $\stackrel{\wedge }{pH}=5.43-0.0053$(weeks) fit the data well.

Would it be appropriate to use the regression line to predict pH after $1000$months?

It is often not possible to make exact predictions when using an extrapolation line, which is used far outside the interval of values of the explanatory variable $X$. In this case, the regression line should be:

$p^H=5.43-0.0053\text{(weeks)}$

The data for our analysis show that the researcher measured acid rain for $150$consecutive weeks, so the $X$variable (weeks) for $1000$months is significantly out of the set.

At such extreme values, it is impossible to say whether increases of this magnitude ever occur.

Calculating $pH$ after $1,000$ months is an extrapolation beyond what the data indicate.