Chapter 4.1, Problem 41E

(a)

To determine

To interpret the slope of the regression line in context.

Explanation of Solution

The scatter plot shows the relationship between x =number of turnovers and y =number of points scored by the teams in the NFL.

It is given that: $\widehat{y}=460.2-4.084x$ .

The slope of the regression line is $4.084$ .

This interprets that the number of points scored by the teams in NFL decreases on average by $4.084$ number of turnovers.

(b)

To determine

To interpret the value $s=57.3$ , for the regression line.

Explanation of Solution

We have to interpret the value of $s=57.3$ , for the regression line.

As it is given that: $\widehat{y}=460.2-4.084x$ .

It is the standard deviation of the least square regression line. It means that the there is a variation between the points in the scatter plot for the number of points scored and the number of turnover in the NFL. It explain how well the regression line fits the data. Thus we have that the regression line fits around $57\%$ of the data.

(c)

To determine

To calculate and interpret the residuals for San Francisco.

Answer to Problem 41E

Residual= $-152.772$ .

Explanation of Solution

The scatter plot shows the relationship between x =number of turnovers and y =number of points scored by the teams in the NFL.

It is given that: $\widehat{y}=460.2-4.084x$ .

It is given that we have to calculate the residual who had $17$ turnover and $238$ points.

Thus, it is known that $y=238$ , to calculate $\widehat{y}$ , we have,

  $\begin{array}{l}\widehat{y}=460.2-4.084x\\ =460.2-4.084\times 17\\ =460.2-69.428\\ =390.772\end{array}$

As it is given there are $17$ turnover.

Thus, the residual is $=y-\widehat{y}$ .

Thus, we have,

Residual $\begin{array}{l}=y-\widehat{y}\\ =238-390.772\\ =-152.772\end{array}$

This means that the true value is less than the estimated value and the difference in that is $-152.772$ , this is negative therefore the estimated value is larger than the actual value.

(d)

To determine

To explain how does the point for the turnover affect the least square regression line and standard deviation of the residual.

Explanation of Solution

The scatter plot shows the relationship between x =number of turnovers and y =number of points scored by the teams in the NFL.

It is given that: $\widehat{y}=460.2-4.084x$ .

It affects the least square regression line and the standard deviation of the residual as it has a negative relationship with the number of points scored in the NFL and this affects the regression line and the standard deviation shows that the regression line fits the data very less as it is given in the question.