Chapter 9, Problem 19E

(a)

To determine

To interpret the slope of the line in this context.

Explanation of Solution

It is given in the question that after keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature using the model . And the residual plot for his data is given in the question. The slope of the line interprets that cost decreases by $\$2.13$ per degree of average daily temperature. So, warmer temperature indicates lower costs.

(b)

To determine

To interpret the y -intercept of the line in this context.

Answer to Problem 19E

For an average monthly temperature of zero degree Fahrenheit, the cost is predicted to be $\$133$ .

Explanation of Solution

It is given in the question that after keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature using the model . And the residual plot for his data is given in the question. The y -intercept of the line interprets that for an average monthly temperature of zero degree Fahrenheit, the cost is predicted to be $\$133$ .

(c)

To determine

To explain would you except cost predictions based on this model to be accurate, too low or too high.

Answer to Problem 19E

It is too high.

Explanation of Solution

It is given in the question that after keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature using the model . And the residual plot for his data is given in the question. We except cost predictions based on this model to be too high because the residual, that is, observed minus predicted, around ${32}^0\text{F}$ are negative showing that the model overestimates the costs.

(d)

To determine

To explain what heating cost does the model predict for a month that averages ${10}^0$ .

Answer to Problem 19E

The heating cost does the model predict for a month that averages ${10}^0$ is $\$111.70$ .

Explanation of Solution

It is given in the question that after keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature using the model . And the residual plot for his data is given in the question. The heating cost does the model predict for a month that averages ${10}^0$ is measured as:

  

That concludes that the heating cost does the model predict for a month that averages ${10}^0$ is $\$111.70$ .

(e)

To determine

To explain what were the actual heating costs for that month.

Answer to Problem 19E

The actual heating cost for that month will be $\$105.70$ .

Explanation of Solution

It is given in the question that after keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature using the model . And the residual plot for his data is given in the question. The residual for that month can be assumed by the residual plot when the temperature is ${10}^0$ . The residual came out to be $-\$6$ approximately. And we know that the residual is observed minus predicted value. Thus, the actual heating cost for that month will be as :

  $\begin{array}{l}\text{Actual}=\$111.70-\$6\\ =\$105.70\end{array}$

Therefore, the actual heating cost for that month will be $\$105.70$ .

(f)

To determine

To explain should the homeowner use this model.

Answer to Problem 19E

No, they should not use.

Explanation of Solution

It is given in the question that after keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature using the model . And the residual plot for his data is given in the question. The homeowner should not use this model as the residual show a definite curve pattern and the data are probably not linear.

(g)

To determine

To explain would this model be more successful if the temperature is expressed in degrees Celsius.

Answer to Problem 19E

No, it would not be more successful.

Explanation of Solution

It is given in the question that after keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature using the model . And the residual plot for his data is given in the question. This model would not be more successful if the temperature is expressed in degrees Celsius because there would be no difference and the relationship does not depends on the units.