Question

1. The data below show the consumption of alcohol (X, liters per year per person, 14 years or older) and the death rate from cirrhosis, a liver disease (Y, death per 100,000 population) in 15 countries (each country is an observation unit).

   Country	Alcohol Consumption (x)	Death Rate from Cirrhosis (y)
   France	24.7	46.1
   Italy	15.2	23.6
   Germany	12.3	23.7
   Australia	10.9	7.0
   Belgium	10.8	12.3
   USA	9.9	14.2
   Canada	8.3	7.4
   England	7.2	3.0
   Sweden	6.6	7.2
   Japan	5.8	10.6
   Netherland	5.7	3.7
   Ireland	5.6	3.4
   Norway	4.2	4.3
   Finland	3.9	3.6
   Israel	3.1	5.4

a. Does the scatter plot show evidence of a linear correlation? If yes, what type?

c. Given:

E x= 134.2, E y=175.5, E x^2=1630.12, E y^2=3959.61, E xy=2419.61

Find= Sx=, Sy=, Sxy=,

d. Given slope = 1.98, find the regression line of  on  Write the answer in context of this problem.  

b= equation=

e. Interpret the slope (m) in context of this problem.

answer=

f.Given r = 0.938, find r squared. Round off to the nearest whole number.

r-squared=

g. Interpret r squared in context of his problem.

answer=

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.938829774
R Square	0.881401345
Adjusted R Square	0.872278372
Standard Error	4.170222942
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1680.180128	1680.180128	96.61338479	2.19651E-07
Residual	13	226.079872	17.39075938
Total	14	1906.26
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-5.995753288	2.097747961	-2.85818573	0.013444303	-10.52766223	-1.46384434
Alcohol Consumption	1.977915792	0.201228342	9.829210792	2.19651E-07	1.543188389	2.412643195

a) Yes, there is evidence of linera correlation and it is positive.

c) Sx (SS Regression) = 1680.18

Sy (SS Total) = 1806.26

Sxy (SS Residual) = 226.08

d) y = -5.996 + 1.98x

e) With one unit increase in alcohol consumption, death rate increases by 1.98 units.

f) R-squared = 0.938^2 = 0.881

g) 88.1% of variation in death rate from Cirrhosis is explained by alcohol consumption.