Chapter 8, Problem 41E

(a)

To determine

To make a scatterplot for these data.

Explanation of Solution

In the question it shows the relationship between the age and the price of the cars of used Corolla. Thus, the scatterplot of the data is as follows:

  

In the scatterplot, the age is on the horizontal axis and the price is on the vertical axis.

(b)

To determine

To describe the association between age and price of a used Corolla.

Explanation of Solution

In the question it shows the relationship between the age and the price of the cars of used Corolla. In the above scatterplot we can see that the points are in the downward direction. Thus, we can say that the relationship between the age and the price is negative. The points in the scatterplot are less scattered and in a straight line. Thus the relationship between the age and the price of the Corolla is negative, strong and linear.

(c)

To determine

To explain do you think a linear model is appropriate.

Answer to Problem 41E

Yes, the linear model is appropriate.

Explanation of Solution

In the question it shows the relationship between the age and the price of the cars of used Corolla. We can say that a linear model is appropriate for this data because we can see that the points are in the downward direction. Therefore the relationship between the age and the price is negative. And the points in the scatterplot are less scattered and in a straight line. Thus the relationship between the age and the price of the Corolla is negative, strong and linear.

(d)

To determine

To find out what is the correlation between age and price.

Answer to Problem 41E

  $r=-0.972$ .

Explanation of Solution

In the question it shows the relationship between the age and the price of the cars of used Corolla. It is given using the computer software that:

  $R^2=94.4\%$

As, we know that the points in the scatterplot are moving in a downward direction. So, the correlation would be negative. Thus, to find the correlation between the age and the price, we have following:

  $\begin{array}{l}{r}^2=R^2\\ \Rightarrow r=-\sqrt{0.944}\\ =-0.972\end{array}$

(e)

To determine

To explain the meaning of $R^2$ in this context.

Explanation of Solution

In the question it shows the relationship between the age and the price of the cars of used Corolla. And we know that, $R^2=94.4\%$ . Thus, $R^2$ is the coefficient of determination that shows the amount of variation in the variables used. Thus, in this context it represents that the age accounts for $94.4\%$ of the variation in advertised price.

(f)

To determine

To explain why doesn’t this model explain $100\%$ of the variability in the price of a used Corolla.

Explanation of Solution

In the question it shows the relationship between the age and the price of the cars of used Corolla. Thus, this model does not explain $100\%$ of the variability in the price of a used Corolla because of the other factors that contributes to the used car Corolla and these other factors are options, condition of the car, the mileage of the car, etc.