Question

1. Here are 21 observations from a dataset of liver disease deaths per 100,000 people (liver) and the liters of wine consumed per capita (wine).  To gather the data the researcher calculated wine per capita by calculating total wine consumed in a country and dividing by the population; they used official records to determine the number of people with liver disease and again divided by total population.  For this question you are welcome to use Excel, but you still need show the formula where appropriate, then fill in all values, then show the final answer.

Obs.	country	liver	wine
1	Australia	15.3	2.5
2	Austria	45.6	3.9
3	Belg/Lux	20.7	2.9
4	Canada	16.4	2.4
5	Denmark	23.9	2.9
6	Finland	19	0.8
7	France	37.9	9.1
8	Iceland	11.2	0.8
9	Ireland	6.5	0.7
10	Israel	13.7	0.6
11	Italy	42.2	7.9
12	Japan	23.2	1.5
13	Netherlands	9.2	1.8
14	New Zealand	7.7	1.9
15	Norway	12.2	0.8
16	Spain	36.4	6.5
17	Sweden	11.2	1.6
18	Switzerland	20.3	5.8
19	UK	10.3	1.3
20	US	22.1	1.2
21	West Germany	36.7	2.7

1. What is the covariance between liver and wine? (3)

2. What is the correlation coefficient between liver and wine? (3)

3. Regress liver on wine using the Excel Data Analysis pack and copy/paste the output here. (3)

4. What are the estimated intercept and slope? (6)

5. Interpret in words the intercept and slope. (5)

6. For a country that consumes 5.7 liters of wine pre capita, what is the predicted number of liver deaths per 100,000? (3)

7. What is the R² for this regression?  (2)

8. In words, what does the R² indicate? (3)

1. Test the hypothesis that the slope is equal to zero at the 5% significance level. (5)

10. What is the interpretation of the 95% confidence interval on the slope? (5)

11. Create a scatterplot of the data (liver on the y-axis and wine on the x-axis).  Make the markers small, red, triangles.  Include an appropriate title.  The axis must have appropriate titles.  Include the predicted number of liver deaths based on your regression results.  Make the prediction markers small black squares. (5)

12. Please discuss what concerns you have about whether the slope coefficient is biased or not. (5)

13. To the extent that the slope is biased, what strategies could you use to reduce or eliminate bias? (5)

Answer 1