Chapter 3.2, Problem 70E

(a)

To determine

To make a scatterplot with rushing yards as the explanatory variable and describe what you see.

Explanation of Solution

The scatterplot with rushing yards as the explanatory variable is as:

  

From the scatterplot we can say that, the scatterplot confirms a positive linear relationship, because the scatterplot slopes upwards. The scatterplot confirms a weak relationship, because the points seem to lie far apart.

(b)

To determine

To explain what effect do you think this game has on the correlation and on the equation of the least squares regression line and calculate the correlation and equation of the least squares regression line with and without this game to confirm your answer.

Answer to Problem 70E

The game $16$ makes the correlation increase.

Explanation of Solution

For the case with outlier:

Using calculator, press on STAT and then select $1$ : Edit . and then enter the data of sugar in the list $L_1$ and enter the data of calories in the list $L_2$ .

Next, press on STAT select CALC and then select $\text{Linreg}(a+bx)$ . Next we need to finish the command by entering $L_1{L}_2$ .

  $\text{Linreg}(a+bx)L_1{L}_2$

Finally, pressing on ENTER then gives us the following result:

  $\begin{array}{l}y=a+bx\\ a=11.3891\\ b=0.0308\\ r=0.1\end{array}$

This then implies the regression line as:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=11.3891+0.0308x\end{array}$

For the case without outlier:

Using calculator, press on STAT and then select $1$ : Edit . and then enter the data of sugar in the list $L_1$ and enter the data of calories in the list $L_2$ .

Next, press on STAT select CALC and then select $\text{Linreg}(a+bx)$ . Next we need to finish the command by entering $L_1{L}_2$ .

  $\text{Linreg}(a+bx)L_1{L}_2$

Finally, pressing on ENTER then gives us the following result:

  $\begin{array}{l}y=a+bx\\ a=14.0336\\ b=0.0076\\ r=0.0180\end{array}$

This then implies the regression line as:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=14.0336+0.0076x\end{array}$

  

Thus, we note that the correlation coefficient with the outlier is more than the correlation coefficient without outlier. We then note that the outlier increases the correlation due to the fact that game $16$ as the correlation is much higher. When the outlier is removed the regression line becomes much more horizontal and thus the game $16$ makes the regression line less horizontal.

(c)

To determine

To explain what effect do you think this game has on the correlation and on the equation of the least squares regression line and calculate the correlation and equation of the least squares regression line with and without this game to confirm your answer.

Answer to Problem 70E

The game $13$ makes the correlation decrease.

Explanation of Solution

For the case with outlier:

Using calculator, press on STAT and then select $1$ : Edit . and then enter the data of sugar in the list $L_1$ and enter the data of calories in the list $L_2$ .

Next, press on STAT select CALC and then select $\text{Linreg}(a+bx)$ . Next we need to finish the command by entering $L_1{L}_2$ .

  $\text{Linreg}(a+bx)L_1{L}_2$

Finally, pressing on ENTER then gives us the following result:

  $\begin{array}{l}y=a+bx\\ a=11.3891\\ b=0.0308\\ r=0.1\end{array}$

This then implies the regression line as:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=11.3891+0.0308x\end{array}$

For the case without outlier:

Using calculator, press on STAT and then select $1$ : Edit . and then enter the data of sugar in the list $L_1$ and enter the data of calories in the list $L_2$ .

Next, press on STAT select CALC and then select $\text{Linreg}(a+bx)$ . Next we need to finish the command by entering $L_1{L}_2$ .

  $\text{Linreg}(a+bx)L_1{L}_2$

Finally, pressing on ENTER then gives us the following result:

  $\begin{array}{l}y=a+bx\\ a=7.2776\\ b=0.0505\\ r=0.3182\end{array}$

This then implies the regression line as:

  $\begin{array}{l}\widehat{y}=a+bx\\ \Rightarrow \widehat{y}=7.2776+0.0505x\end{array}$

  

Thus, we note that the correlation coefficient with the outlier is more than the correlation coefficient without outlier. Then the game $13$ makes the correlation decrease as the correlation coefficient is much lower. When the outlier is removed the regression line becomes much steeper and thus the game $13$ makes the regression line steep.