Chapter 3.2, Problem 37E

(a)

To determine

To predict the number of wins for a team that spends $\$200$ million on payroll.

Answer to Problem 37E

The number of wins is $88.5$ .

Explanation of Solution

It is given in the question the regression line that,

  $\widehat{y}=60.7+0.139x$

Thus, the number of wins for a team that spends $\$200$ million on payroll is calculated as:

  $\begin{array}{l}\widehat{y}=60.7+0.139x\\ =60.7+0.139(200)\\ =88.5\end{array}$

Thus, this then implies that the predicted number of wins for a team that spends $\$200$ million on payroll is $88.5$ .

(b)

To determine

To predict the number of wins for a team that spends $\$400$ million on payroll

Answer to Problem 37E

The number of wins is $116.3$ .

Explanation of Solution

It is given in the question the regression line that,

  $\widehat{y}=60.7+0.139x$

Thus, the number of wins for a team that spends $\$400$ million on payroll is calculated as:

  $\begin{array}{l}\widehat{y}=60.7+0.139x\\ =60.7+0.139(400)\\ =116.3\end{array}$

Thus, this then implies that the predicted number of wins for a team that spends $\$400$ million on payroll is $116.3$ .

(c)

To determine

To explain how confident are you in each of these predictions.

Explanation of Solution

It is given in the question the regression line that,

  $\widehat{y}=60.7+0.139x$

Thus, we need to check that how confident are we in the results of part (a) and (b). in the scatterplot given, we note that the payroll I the data set appear to range from $75$ million dollars to $275$ dollars. Since $200$ million dollars is I range of payrolls of the data set we are confident in the prediction of part (a). since $400$ million dollars is not in the range of payrolls of the data set we are not confident in the prediction of part (b) because we are using extrapolation.