Chapter 3.2, Problem 42E

To determine

To find:whether it is suitable to predictJ’s natural-gas consumption or not

Answer to Problem 42E

we can surely predict J's natural gas-consumption in a future month with an average temperature of 65^oF.

Explanation of Solution

Extrapolation is the use of a regression line for prediction far outside the interval of values of the explanatory variable $X$ used to obtain the line. Such predictions are often not accurate. Consider the case how much gas, in this case, the equation of the least square as:

  $\widehat{Y}=1425-19.87X$

Average temperature 65^oF is not very far outside of $X-values$ for our data. Hence we can surely predict Joan's natural gas-consumption in a future month with an average temperature of 65^oF.