Chapter 4.2, Problem 4.37E

(a)

To determine

To construct the scatterplot of BAC versus beers using the data given in the table and identify which variable we can choose to be the y -variable and which we choose to be the x -variable, explain.

Answer to Problem 4.37E

The y -variable isthe blood alcohol content.

The x -variable is the beers.

Explanation of Solution

A response variable is a variable that measures an outcome or result of a study, while an explanatory variable that we think explains or causes changes in the response variables.

The y -variable is the response variable, which we expect to be the blood alcohol content because we expect the number of beers to cause the change in the blood alcohol content.

The x -variable is the explanatory variable, which we expect to be the beers because we expect the number of beers to cause the change in the blood alcohol content.

The scatterplot of the data is as follows:

The number of beers is on the horizontal axis and the residuals are on the vertical axis.

  

(b)

To determine

To find the correlation between BAC and beers using calculator and explain is the correlation an appropriate measure of the strength of the association between BAC and the beers.

Answer to Problem 4.37E

  $r=0.8943$ .

Explanation of Solution

Calculator commands used:

Assuming that you entered the x -values in list L₁ of your calculator and the y -values in list L₂ .

Use the commands STAT, CALC and 8:LinReg( $ax+b$ )

Next we determine the least square regression line by using LinReg( $a+bx$ ) L₁ ,L₂ , Y₁ .

The result should then contain r and r² .

The result will be $r=0.8943$ .

The correlation is an appropriate measure of strength because the scatterplot in part(a) does not show strong curvature.

(c)

To determine

To find the least square regression line for BAC on beers and interpret the slope and y -intercept of the regression line.

Answer to Problem 4.37E

  $a=-0.013$

  $b=0.018$

  $\begin{array}{l}\widehat{y}=a+bx\\ =-0.013+0.018x\end{array}$

Explanation of Solution

Calculator commands used:

Assuming that you entered the x -values in list L₁ of your calculator and the y -values in list L₂ .

Use the commands STAT, CALC and 8:LinReg( $ax+b$ )

Next we determine the least square regression line by using LinReg( $a+bx$ ) L₁ ,L₂ , Y₁ .

Result:

  $\begin{array}{l}\begin{array}{l}y=a+bx\hfill \\ a=-0.013\hfill \end{array}\\ b=0.018\end{array}$

Thus the least square regression line is then:

  $\begin{array}{l}\widehat{y}=a+bx\\ =-0.013+0.018x\end{array}$

a is the y -intercept which is the predicted y -value when $x=0$ .The predicted blood alcohol content is $-0.013$ ,when a student drinks zero beers.

b is the slope which is the average increase in the y -value per unit of $x$ .The blood alcohol content increases on average by $0.018$ per beer.