Chapter 4, Problem 4.1AYK

a.

To determine

To explain: The slope of the provided equation line in words and the reason of considering zero.

Explanation of Solution

Given:

The equation of the regression line is:

  $\text{BAC}=0.023\times \text{number of drinks}$

he general equation of the least squares line is:

  $\widehat{y}=a+bx$

Here, a represents the y-intercept and b represents the slope of the line.

By comparing the general equation of the least-squares line with the provided equation of a least squares line, it can be said that the slope of the $\text{BAC}=0.023\times \text{number of drinks}$ is 0.023

A positive slope indicates that an average increase (or decrease) in the value of y for each unit increase (or decrease) in the value of x . A negative slope indicates that an average increase (or decrease) in the value of y for each unit decrease (or increase) in the value of x .

The provided least squares line has a slope of 0.023. So, the value of BAC increases by 0.023 for a unit increase in number of drinks.

Here, the provided least square line does not contain the intercept term. Thus, it could be said that the intercept term is $\text{BAC}=0.023\times \text{number of drinks}$ .

b.

To determine

To find: The equation of the regression line that could be used to predict BAC from number of drinks for a 120-pound woman.

Explanation of Solution

Using the provided information, the equation of the regression line that could be used to predict BAC from number of drinks for a 120-pound woman could be written as:

  $BAC=0.038\times \text{}\text{ number of drinks}$

c.

To determine

To find: The predicted BAC for a 160-pound male who consumed 4 drinks and for 120-pound women that consumed 2 drinks.

Explanation of Solution

The predicted BAC for a 160-pound male who consumed 4 drinks can be calculated as:

  $\begin{array}{c}BAC=0.023\times \text{}\text{ number of drinks}\\ \text{=0}\text{.023}\times \text{4}\\ \text{=0}\text{.092}\end{array}$

Now, the predicted BAC for 120-pound women who consumed 2 drinks can be calculated as:

  $\begin{array}{c}BAC=0.038\times \text{}\text{ number of drinks}\\ \text{=0}\text{.038}\left(2\right)\\ =0.076\end{array}$

The obtained values of BAC for male and female do not depict the actual blood alcohol content because there would be other factors that would affect the alcohol content in the body