Chapter 3.2, Problem 40E

(a)

To determine

To find: The slope of the line

Answer to Problem 40E

The slope is b = -19.87

Explanation of Solution

Given:

The equation of the least squares line is $\widehat{y}=1425–19.87x.$

  

Calculation:

On comparing our equation to general equation of regression we get, the slope is: b = -19.87

This tells us that the gas consumed is predicted to go down by -19.87cubic feet for each added temperature.

Conclusion:

Hence, the slope is: b = -19.87.

(b)

To determine

To identify: the y intercept of the line and explain why the y intercept is risky to use.

Answer to Problem 40E

The Y intercept is: a = 1425

Explanation of Solution

Calculation:

On comparing our equation to general equation of regression we get, the Y intercept is: $a=1425$

The Y intercept of a regression line $\widehat{y}=a+bX$ is the predicted response $\widehat{y}$ when explanatory variable X = 0. This prediction is of no statistical use unless X can actually take values near 0 that’s why it’s risky to use this value as a prediction.

Conclusion:

Hence, the Y intercept is: $a=1425$

This prediction is of no statistical use unless X can actually take values near 0 that’s why it’s risky to use this value as a prediction.

(c)

To determine

To predict: the amount of natural gas Joan will use in a month

Answer to Problem 40E

Joan uses 828.9 cubic gas.

Explanation of Solution

Calculation:

The regression line is:

  $\widehat{y}=1425–19.87X$

At temperature (X) = ${30}^{\circ }$ F then the regression equation becomes $\widehat{y}=1425–19.87\left(30\right) =828.9$

This shows that Joan uses 828.9 cubic feet gas (approx.) to maintain the temperature 30 degrees Fahrenheit.

Conclusion:

Hence, Joan uses 828.9 cubic feet gas (approx).