Question

How much alcohol can one consume before one's Blood Alcohol Content (BAC) is above the legal limit? An experiment was conducted at Gallaudet University to predict Blood Alcohol Content from the number of beers. A total of 50 volunteer college students (some men and some women) were assigned a certain number of beers to drink and then, after a half an hour, their Blood Alcohol (BAC) level was measured. To make this assignment simpler, we will only use the first 6 data points ВАС . Which variable is the explanatory (r) variable, also called the independent variable? 2. Which variable is the response (v) variable, also called the dependent variable? 3. Explain how you came to your conclusion for Questions #1 and #2. 4. Sketch a scatterplot appropriate to investigate whether how BAC depends on the number of beers consumed A grid is provided on the back of this homework assignment!

Answer 1

1. The explanatory variable x is the number of beers a person drinks  

2. The response variable y is the Blood alcohol content (BAC)

3. Since BAC depends on number of beer a person drinks , and number of beer a person drinks is not affected by BAC. That is why number of beers a person drinks is the independent (explanatory ) variable and BAC is the dependent variable (response).

4.

Scatter plot 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 10

5. The four characteristics of scatter plot are

Form : From the scatter plots it seems that the association between beer consumption and BAC is  linear .

Direction : There is a positive relationship between beer consumption and BAC. (as beer consumption increases , BAC increases)

Strength: The association appears to be strong .

Outliers : No outliers as no data point is unusually far away from the linear pattern.

As the The association appears to be strong , r should be between 0.7 and 1.0.

6.From scatter plot it seems that there is a strong positive linear relationship between beer consumption and BAC level.

7.$\dpi{100} \bar{x}=$ (5+2+.....+7) /6 = 5.67

$\dpi{100} \bar{y}=(0.1+0.03 +.....+0.095)/6 = 0.0958$

8. r=0.927 , which suggests strong positive linear relationship between the explanatory and response variable .

Thus the result is consistent with the assumption in (5).