Question

Blood pressure: A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters, for a sample of adults. The following table presents the results.

Systolic

126

109

104

115

120

119

132

117

Diastolic

86

86

79

79

68

89

76

70

The least-squares regression line y=bo+b1x=90.1741-0.0938x and E(x-x)^2=551.5000 are known for this data. Use the P -value method to test Ho:B1=0 versus H1:B1<0 . Can you conclude that systolic blood pressure is useful in predicting diastolic blood pressure? Use the a=.01 level of significance and the TI-has 84 calculator.

Compute the test statistic. Always round t-score values to three decimals places.

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression. Put systolic in x input range and Diastolic in y input range.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.109
R Square	0.012
Adjusted R Square	-0.153
Standard Error	8.206
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	4.856	4.856	0.072	0.797
Residual	6	404.019	67.337
Total	7	408.875
	Coefficients	Standard Error	t Stat	P-value
Intercept	90.174	41.247	2.186	0.071
Systolic blood pressure	-0.094	0.349	-0.269	0.797

H_o:B₁ = 0 versus H₁:B₁<0

p-value = 0.797

Since p-value is more than 0.01, we do not reject the null hypothesis and conlcude that B₁ = 0.

So, systolic blood pressure is not useful in predicting diastolic blood pressure.