Chapter 3.2, Problem 41E

To determine

To predict: $p^H$ after 1000 months using the regression line

Answer to Problem 41E

  $p^H$ Value after 1000 months is an extrapolation of the relationship

Explanation of Solution

Calculation:

Extrapolation is the use of a regression line far outside the interval of values of the explanatory variable $X$ used to obtain the line. Such predications are often not accurate Consider the case acid rain, regression line is:

  $p^H=5.43-0.0053(weeks)$

Since researcher measured acid rain for 150 consecutive weeks, 1000 months is far outside the set of explanatory variable $X(weeks)$ for our data. We can't say whether increases - this large ever occur, or whether the relationship remains linear at such extreme values. Predicating $p^H$ value after 1000 months is an extrapolation of the relationship beyond what the data show.