Chapter 9, Problem 20E

(a)

To determine

To interpret the slope of this line in context.

Explanation of Solution

The researcher wants to find out how does the speed at which you drive affect your fuel economy. Therefore they collected the data and created a model, $\text{<mover accent="true"><mo> F</mo> <mo>^</mo></mover> uel efficiency}=32-0.1\times \text{Speed}$

And also the residual plot for the same. Now, the slope is defined by the fuel efficiency by the speed of the car. Thus, we can interpret the slope as the speed increases by $1$ mph, there is an average decrease in fuel efficiency of $0.1$ mpg.

(b)

To determine

To explain why it is silly to attach any meaning to the y -intercept.

Explanation of Solution

The researcher wants to find out how does the speed at which you drive affect your fuel economy. Therefore they collected the data and created a model, $\text{<mover accent="true"><mo> F</mo> <mo>^</mo></mover> uel efficiency}=32-0.1\times \text{Speed}$

And also the residual plot for the same. Now, it is silly to attach any meaning to the y -intercept because he intercept is the predicted fuel efficiency at zero mph. and there should not be a value at zero mph since no fuel is being used. Therefore, it is of no importance.

(c)

To determine

To explain what can you say about those predictions when this model predicts high fuel efficiency.

Explanation of Solution

The researcher wants to find out how does the speed at which you drive affect your fuel economy. Therefore they collected the data and created a model, $\text{<mover accent="true"><mo> F</mo> <mo>^</mo></mover> uel efficiency}=32-0.1\times \text{Speed}$

And also the residual plot for the same. When this model predicts high fuel efficiency, then we can say that the model is overestimating fuel efficiency and the residuals of the data are negative. This can be estimated about the predictions.

(d)

To determine

To find out what fuel efficiency does the model predicts when the car was driven at $\text{50}$ mph.

Answer to Problem 20E

The fuel efficiency will be $27$ mpg when the car was driven at $\text{50}$ mph.

Explanation of Solution

The researcher wants to find out how does the speed at which you drive affect your fuel economy. Therefore they collected the data and created a model, $\text{<mover accent="true"><mo> F</mo> <mo>^</mo></mover> uel efficiency}=32-0.1\times \text{Speed}$

And also the residual plot for the same. Now, the fuel efficiency the model predicts when the car was driven at $\text{50}$ mph is calculated as:

  $\begin{array}{l}\text{<mover accent="true"><mo> F</mo> <mo>^</mo></mover> uel efficiency}=32-0.1\times \text{Speed}\\ =32-0.1(50)\\ =27\end{array}$

Thus, the fuel efficiency will be $27$ mpg when the car was driven at $\text{50}$ mph.

(e)

To determine

To find out what was the actual fuel efficiency when the car was driven at $\text{45}$ mph.

Answer to Problem 20E

The actual fuel efficiency is $28.5$ mpg when the car was driven at $\text{45}$ mph.

Explanation of Solution

The researcher wants to find out how does the speed at which you drive affect your fuel economy. Therefore they collected the data and created a model, $\text{<mover accent="true"><mo> F</mo> <mo>^</mo></mover> uel efficiency}=32-0.1\times \text{Speed}$

And also the residual plot for the same. Now, the actual fuel efficiency when the car was driven at $\text{45}$ mph is calculated as:

  $\begin{array}{l}\text{Fuel efficiency}=32-0.1\times \text{Speed}\\ =32-0.1(45)\\ =27.5\\ r=1\\ \Rightarrow 1=y-27.5\\ \Rightarrow y=28.5\end{array}$

Thus, the actual fuel efficiency is $28.5$ mpg when the car was driven at $\text{45}$ mph.

(f)

To determine

To explain do you think there appears to be a strong association between speed and fuel efficiency or not.

Answer to Problem 20E

No, it does not appear.

Explanation of Solution

The researcher wants to find out how does the speed at which you drive affect your fuel economy. Therefore they collected the data and created a model, $\text{<mover accent="true"><mo> F</mo> <mo>^</mo></mover> uel efficiency}=32-0.1\times \text{Speed}$

And also the residual plot for the same. We do not think there appears to be a strong association between speed and fuel efficiency because as seen from the shape of the residual plot, the relationship cannot be appropriately modelled by a linear model.

(g)

To determine

To explain do you think this is the appropriate model for the association.

Answer to Problem 20E

No, it is not.

Explanation of Solution

The researcher wants to find out how does the speed at which you drive affect your fuel economy. Therefore they collected the data and created a model, $\text{<mover accent="true"><mo> F</mo> <mo>^</mo></mover> uel efficiency}=32-0.1\times \text{Speed}$

And also the residual plot for the same. Since we do not think there appears to be a strong association between speed and fuel efficiency because as seen from the shape of the residual plot, the relationship cannot be appropriately modelled by a linear model. Therefore, we can say that it does not appears to be an appropriate model for the association.