Question

2. A study of the relationship between age and blood pressure yielded the following data Blood Pressure (Y 126 131 161 128 1489 140 148 Test using a significance level of 5% whether there is an increasing linear relationship Age(X) 23 27 45 3 536 37 37 a. between age and blood pressure. Parameter: A- slope of regression line for blood pressure vs.age. Hypotheses: Test Statistic: t.A-A d.f- with the same variance. Rejection Region: Calculated Test: Conclusion P-value. b. Find the 95% confidence interval for the slope. c. Correlation Sample correlation coefficientr Meaning ofr Sample coefficient of determination-r- Meaning of r

Answer 1

2)

data

x	y
23	126
27	131
45	161
31	128
51	148
36	119
37	140
37	148

A)

Hypotheses

Ho : = 0

61

Ha: > 0

61

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.7094
R Square	0.5033
Adjusted R Square	0.4205
Standard Error	10.7110
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	697.5177	697.5177	6.0798	0.0487
Residual	6	688.3573	114.7262
Total	7	1385.8750
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	98.3802	16.3604	6.0133	0.0010	58.3478
x	1.0939	0.4437	2.4657	0.0487	0.0084

TS = 2.4657

df= n-2 = 6

rejection region

critical value = =t.inv(0.95,6) = 1.9432

TS > 1.9432

since TS = 2.4657 > critical value

we reject the null hypothesis

we conclude that there is positive correlation

p-value = 0.0244

b)

95% confidence interval = (0.0084,2.1795)

c)

r = 0.7094

there is moderate positive correlation

r^2 = 0.5033

meaning

50.33 % of variation in Y is explained by this model