1. How much alcohol can one consume before one’s blood alcohol content (BAC) is above the legal limit? Two undergraduate statistics projects, one conducted at the Ohio State University (OSU) in Columbus, Ohio and the other at the University of Western Sydney (AUS) in Sydney, Australia, explored the relationship between BAC and other variables such as amount of alcohol consumed, weight, gender and age. (This is a real dataset, located on the last page of this document). (34 Points Total)

Description of Variables:

OSU

ID = identification number

Gender

Weight = weight of each subject in pounds.

Beer = number of 12 ounce beers consumed

BAC = blood alcohol content

1 ^st Sobriety = combined score on the four road sobriety tests before alcohol consumption

2 ^nd Sobriety = combined score on the four road sobriety tests after alcohol consumption

Australia (AUS)

ID = identification number

Gender

Weight(kg)

Height (cm)

Age

1hr-BAC = BAC after the first hour

Wine = number of glasses of wine consumed during the first hour

1. Draw a scatterplot by hand of BAC versus number of beers consumed below (Accuracy will count). Label both x and y axis including units. Describe the scatterplot IN CONTEXT (Refer to your notes for what this means). Do you think the number of beers consumed would be a good predictor of BAC? WHY? (4 Points)
2. For each of the situations below, draw a scatterplot by hand showing the relationship between BAC and the difference in sobriety scores (you will need to create this variable (1 ^st Sobriety minus 2 ^nd Sobriety)). Decide which variables should be the explanatory (independent) and response (dependent) variables in each case, and describe both plots IN CONTEXT (Accuracy counts). (8 Points)
   1. Suppose you wanted to know how much coordination deteriorates because of increased alcohol in the body.
      Solution: In the context of this case the difference in sobriety scores is the dependent variable, and BAC is the independent variable, since we want to assess how alcohol (BAC) affects the deterioration in coordination.
      The following scatterplot is obtained (both by hand and also done in Excel):
   2. It is illegal to drive with a blood alcohol content over 0.08. Suppose you wanted to know how reliable the sobriety test is at determining BAC.
3. Using the OSU data, write out an equation (IN CONTEXT) for a linear regression line that predicts BAC based on the difference between the road sobriety test scores. What value of BAC would you predict for a subject who had a difference in sobriety test scores of 2.5? Is this prediction reliable? Refer to your R ² value and explain your reasoning. (3 Points).
4. Write out an equation for a linear regression line that predicts BAC by the number of beers consumed. What value of BAC would you predict for a subject who drank 4 beers? Which of the two independent variables (i.e. number of beers consumed or difference on road sobriety test scores) is a better predictor of BAC for this data? Why? (Refer to R ² values). (3 Points).
5. Complete the table of residuals below. Write your linear regression equation obtained in Part d in the top line. Make sure to write out your linear equation for every calculation like we did in class. Draw a scatterplot by hand of residuals versus predicted values using the values calculated from your chart. Indicate whether your residual plot appears to be a good fit for your data. (16 Points).

Price: $26.56

Solution: The downloadable solution consists of 15 pages, 1156 words and 8 charts.
Deliverable: Word Document