Chapter PII, Problem 15RE

(a)

To determine

To write the equation of the regression line.

Answer to Problem 15RE

   .

Explanation of Solution

It is given in the question that researchers want to study that can we predict the horsepower of the engine that manufacturers will put in a car by knowing the weight of the car. The regression analysis is as:

  $\begin{array}{l}\text{Intercept}=3.49834\\ \text{Weight}=34.3144\\ R^2=84.1\%\end{array}$

Thus, the regression line will be defined as:

  

(b)

To determine

To explain do you think the car’s weight is measured in pounds or thousands of pounds.

Answer to Problem 15RE

The car’s weight is measured in thousands of pounds.

Explanation of Solution

It is given in the question that researchers want to study that can we predict the horsepower of the engine that manufacturers will put in a car by knowing the weight of the car. The regression analysis is as:

  $\begin{array}{l}\text{Intercept}=3.49834\\ \text{Weight}=34.3144\\ R^2=84.1\%\end{array}$

Thus, the regression line will be defined as:

  

Thus, we think that the car’s weight is measured in thousands of pounds because if weight was measured pounds then the residual plot would make no sense and a car with a horsepower of over $2000$ is unheard of.

(c)

To determine

To explain do you think this linear model is appropriate.

Answer to Problem 15RE

Yes, the model is appropriate.

Explanation of Solution

It is given in the question that researchers want to study that can we predict the horsepower of the engine that manufacturers will put in a car by knowing the weight of the car. The regression analysis is as:

  $\begin{array}{l}\text{Intercept}=3.49834\\ \text{Weight}=34.3144\\ R^2=84.1\%\end{array}$

Thus, the regression line will be defined as:

  

Thus, we think that this linear model is appropriate because the residuals are well spread.

(d)

To determine

To explain how much how much horsepower does this car have.

Answer to Problem 15RE

  $115.04$ horsepower this car have.

Explanation of Solution

It is given in the question that researchers want to study that can we predict the horsepower of the engine that manufacturers will put in a car by knowing the weight of the car. The regression analysis is as:

  $\begin{array}{l}\text{Intercept}=3.49834\\ \text{Weight}=34.3144\\ R^2=84.1\%\end{array}$

Thus, the regression line will be defined as:

  

Thus, the horsepower of this car whose residual is of $22.5$ horsepower weighing $2595$ pounds is as:

  

So, we have,

  $\begin{array}{l}\text{Residual}=\text{Observed}-\text{Predicted}\\ \Rightarrow 22.5=\text{Observed}-92.54\\ \Rightarrow \text{Observed}=115.04\end{array}$