Chapter 3.2, Problem 38E

(a)

To determine

To explain:The predict mean amount of natural gas Joan will use per day in a month with a mean temperature of 30F.

Answer to Problem 38E

The predict mean amount of natural gas Joan will use per day in a month with a mean temperature of 30F, is 828.90.

Explanation of Solution

Given:

x: mean temperature in a particular month.

y: mean amount of natural gas used per day in that month.

The given OLS regression line is:

  $\widehat{y}=1425-19.87x$

Calculation:

The predict mean amount of natural gas Joan will use per day in a month with a mean temperature of 30F, can be calculated as:

  $\begin{array}{c}\widehat{y}=1425-19.87\left(30\right)\\ =828.90\end{array}$

(b)

To determine

To explain:The predict mean amount of natural gas Joan will use per day in a month with a mean temperature of 65F.

Answer to Problem 38E

The predict mean amount of natural gas Joan will use per day in a month with a mean temperature of 65F, is 133.45.

Explanation of Solution

Given:

x: mean temperature in a particular month.

y: mean amount of natural gas used per day in that month.

The given OLS regression line is:

  $\widehat{y}=1425-19.87x$

Calculation:

The predict mean amount of natural gas Joan will use per day in a month with a mean temperature of 30F, can be calculated as:

  $\begin{array}{c}\widehat{y}=1425-19.87\left(65\right)\\ =133.45\end{array}$

(c)

To determine

To explain:Are we confident that each of these predictions are true.

Explanation of Solution

Given:

As per the given above parts,

Interpretation:

To do prediction by using regression line, that is just a mathematic calculation which may not be true.

Hence, the above predicted value may be true or not be correct or true. Therefore, there is no surety that the prediction is correct.