Chapter 9, Problem 9E

(a)

To determine

To interpret the slope and intercept of the model.

Answer to Problem 9E

The use of Oakland has been growing at about $59700$ passengers per year, starting from about $282000\text{ in 1990}$ .

Explanation of Solution

In the question, the scatterplot shows the number of passengers departing from Oakland airport month by month. The residual and regression is given in question as we have,

  $\begin{array}{l}R=71.1\%\\ s=104330\end{array}$

And the variables are as follows:

  $\begin{array}{l}\text{Constant: 282584}\\ \text{Year 1990: 59704}\text{.4}\end{array}$

Dependent variable is: Passengers.

Now, by the slope and intercept of the model we can interpret that the use of Oakland has been growing at about $59700$ passengers per year, starting from about $282000\text{ in 1990}$ .

(b)

To determine

To explain what does the value of $R^2$ say about the model.

Answer to Problem 9E

  $\text{71\%}$ of the variation in passengers is accounted for this model.

Explanation of Solution

In the question, the scatterplot shows the number of passengers departing from Oakland airport month by month. The residual and regression is given in question as we have,

  $\begin{array}{l}R=71.1\%\\ s=104330\end{array}$

And the variables are as follows:

  $\begin{array}{l}\text{Constant: 282584}\\ \text{Year 1990: 59704}\text{.4}\end{array}$

Dependent variable is: Passengers.

Now, as the $R^2$ value explains the variations of the variables then the value of $R^2$ say about the model is that $\text{71\%}$ of the variation in passengers is accounted for this model.

(c)

To determine

To interpret $s_e$ in this context.

Answer to Problem 9E

  $s_e$ interprets that errors in predictions based on this model that have a standard deviation of $104330$ passengers.

Explanation of Solution

In the question, the scatterplot shows the number of passengers departing from Oakland airport month by month. The residual and regression is given in question as we have,

  $\begin{array}{l}R=71.1\%\\ s=104330\end{array}$

And the variables are as follows:

  $\begin{array}{l}\text{Constant: 282584}\\ \text{Year 1990: 59704}\text{.4}\end{array}$

Dependent variable is: Passengers.

Then $s_e$ interprets that errors in predictions based on this model that have a standard deviation of $104330$ passengers as calculated in the question.

(d)

To determine

To explain would you use this model to predict the number of passengers in $2010$ .

Answer to Problem 9E

No.

Explanation of Solution

In the question, the scatterplot shows the number of passengers departing from Oakland airport month by month. The residual and regression is given in question as we have,

  $\begin{array}{l}R=71.1\%\\ s=104330\end{array}$

And the variables are as follows:

  $\begin{array}{l}\text{Constant: 282584}\\ \text{Year 1990: 59704}\text{.4}\end{array}$

Dependent variable is: Passengers.

Now, we would not use this model to predict the number of passengers in $2010$ because that would extrapolate too far from the years we have observed.

(e)

To determine

To explain this outlier that is near the middle of this time span with a large negative residual.

Explanation of Solution

In the question, the scatterplot shows the number of passengers departing from Oakland airport month by month. The residual and regression is given in question as we have,

  $\begin{array}{l}R=71.1\%\\ s=104330\end{array}$

And the variables are as follows:

  $\begin{array}{l}\text{Constant: 282584}\\ \text{Year 1990: 59704}\text{.4}\end{array}$

Dependent variable is: Passengers.

Now, it is shown in the scatterplot that there is an outlier that is near the middle of this time span with a large negative residual which explains that the negative residual in September $2001$ , air traffic was artificially low following the attacks on $9/11$ .