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! 5. Describe your scatterplot. Be sure to describe all four characteristics of a scatterplot. Based on your description, guess what r is (give an approximate value) 6. What is the overall trend of the relationship between beer consumption and BAC level? In other words, scatterplot in plain English 7. For each variable (r and y) find the mean. The standard deviation has been given to you. -280-0os82 8. For this data set, the correlation coefficient is r 0.927. Is this consistent with your guess in Question #5? Describe and interpret the correlation. 9. on your scatterplot (Question #4), guess where you would draw a line that comes close to describing the data. Draw your guess as a dashed line. You will compare your guessed line with the one you actually compute below. 10. Compute the slope and intercept of the regression line. Slope: y-intercept:- 11. Write the equation of the regression line using (replace and with your computed values from question #10. Remember that the hat on the y means that this is a predicted value for y, which isn't necessarily the same as a value for y in the data itself.) 12. Identify and interpret the regression coefficients, in context. y-intercept: Slope 13. Use the equation of the regression line to predict BAC twice, for 4 beers and 8 beers: r-4 r- 8 14. Put these two points you just computed in Question #13 on your graph and then draw a solid line through them. This is the graph of the regression line that you ust computed. Does it look pretty close to the line you guessed in question #9?

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

y = (0, 1 + 0.034 + 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).