Question

E. The data below consist of seven pairs of values of X 1-1 price of alcohol relative to take-home pay. consumption of absolute alcohol in liters per head of population per year, 2cirthosis deaths per 100,000 of populations, for seven European countries. Plot Y, versus X and Y2 versus X (Y as ordinate, X as abscissa) and judge whether, in your opinion, a straight line would fit each set of data reasonably well. Country Yi France Italy West Germany 0.016 0.027 0.026 24.66 18.00 13.63 51.7 30.5 29.0 Country Y, lu Belgium United Kingdom Ireland Denmark 0.022 0.057 0.092 0.096 8.42 7.66 7.64 7.50 14.2 4.1 5.0 11.6 1. For the (X, Y2) only, evaluate the fitted least squares line and draw it on your data plot. 2. Evaluate the residuals to two decimal places. Check that e" = 0, within rounding error. 3. Obtain the analysis of variance table. 4. Find the standard errors of bo and b

Answer 1

1)

data

x	y2
0.016	51.7
0.027	30.5
0.026	29
0.022	14.2
0.057	4.1
0.092	5
0.096	11.6

result from regression in excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.709118363
R Square	0.502848853
Adjusted R Square	0.403418624
Standard Error	13.27679628
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	891.4676879	891.4676879	5.057303567	0.074384597
Residual	5	881.3665978	176.2733196
Total	6	1772.834286
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	38.06739747	9.146150138	4.162122521	0.008805953	14.55647006
x	-358.2493521	159.3037144	-2.248844941	0.074384597	-767.7525867

y2^= 38.07-358.25*x

2)

Observation	Predicted y2	Residuals
1	32.33540784	19.36459216
2	28.39466497	2.105335034
3	28.75291432	0.247085681
4	30.18591173	-15.98591173
5	17.6471844	-13.5471844
6	5.108457077	-0.108457077
7	3.675459668	7.924540332
	SUM	2.4869E-14

3)

ANOVA
	df	SS	MS	F	Significance F
Regression	1	891.4676879	891.4676879	5.057303567	0.074384597
Residual	5	881.3665978	176.2733196
Total	6	1772.834286

4)

standard error of b0 = 9.1462

standard error of b1 = 159.3037