Practice Problem Ch. 15 – this is #15.14 in the book.
There is some evidence that drinking moderate amounts of wine helps prevent heart attacks (this helps
you with your direction). The table gives data on yearly wine consumption (liters of alcohol from
drinking wine, per person) and yearly deaths from heart disease (deaths per 100,000 people) in a dozen
developed nations.
Alcohol
from
wine
3.9
2.4
2.9
9.1
0.7
7.9
Country
Austria
Canada
Denmark
France
Ireland
Italy
Heart
disease
deaths
167
191
220
71
300
107
Country
Spain
Sweden
Switzerland
United Kingdom
United States
West Germany
Alcohol
from
wine
6.5
1.6
5.8
1.3
1.2
2.7
Heart
disease
deaths
86
207
115
285
199
172
1. Make a scatterplot that shows how wine consumption affects heart disease. increments of 25.
Heart Disease Vs. Alcohol Consumption
Heart Disease deaths
350
300
250
200
150
100
50
0
0
2
4
6
8
10
Alcohol
2. Use your calculator to obtain the LSRL equation and correlation.
Heart disease deaths = 266-23.4(Alcohol); r=.9032; strong, negative, linear correlation.
3. Formulate null and alternative hypotheses about the slope of the true regression line.
H a :   0 (There is no linear association between a country’s annual per person wine consumption
and yearly deaths from heart disease)
H a :   0 (There is a negative linear association between a country’s annual per person wine
consumption and yearly deaths from heart disease)
4. Report the sum of the 12 residuals and the sum of the squares of the residuals. What is the value of s
(the standard error about the line)?
L3: L2-Y1(L1) to get residuals; then do 1 var stats on L3 to get the following:
Sum of 12 residuals =  x  1e 11  0 ; Sum of squares of the residuals:  x 2  10,803.3597
Chapter 15
S (approximates  ) =
 (residuals)
n2
2

10803.3597
 32.868
10
5. The model for regression inference has 3 parameters: , , and . Estimate these parameters from
the data. approximates
a approximates a

b approximates b = -23.3567
s approximates s = 32.868
6. Computer output reports that the standard error of the slope is SEb = 3.511. Use this to construct a
95% confidence interval for the slope  of the true regression line.
Degrees of freedom = 12-2 = 10
b  t *SEb = -23.3567  (2.228)(3.511) = (-31.18, -15.53)
With 95% confidence, we estimate that the number of deaths from heart disease (per 100,000
people) decreased on average between 15.46 and 30.47 for each additional liter of wine consumed
per person.