Question

Recorded in the table below are the blood pressure measurements (in millimeters) for a sample of 12 adults. Does there appear to be a linear relationship between the diastolic and systolic blood pressures? At the 5% significance level, test the claim that systolic blood pressure and diastolic blood pressure have a linear relationship.

Systolic	Diastolic
107	71
157	103
134	87
119	69
108	69
118	88
113	77
116	70
112	75
105	66
123	77
130	76

Data Table: Blood Pressure 8

Hypotheses:
H₀: Slope and Correlation are both zero
H₁: Slope and Correlation are both not zero

Results:
What is the correlation coefficient? Use 4 decimal places in answer.
r = _____

What percent of the variation of absences are explained by the model? Round to nearest hundredth percent (i.e. 65.31%).
R²=_____

What is the equation for the regression line? Use 2 decimal places in answers.
Diastolic = (Systolic) + ______

State the p-value. Round answer to nearest hundredth percent (i.e. 2.55%).
p-value = _____

Conclusion:
We_____ sufficient evidence to support the claim that the correlation coefficient and slope of the regression line are both statistically different than zero (p__ 0.05).
(Use “have” or “lack” for the first blank and “<” or “>” for the second blank.)

Answer 1

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.858112
R Square	0.736356
Adjusted R Square	0.709992
Standard Error	5.705367
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	909.1545	909.1545	27.92997	0.000355
Residual	10	325.5122	32.55122
Total	11	1234.667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.5216	14.25129	0.176938	0.863089	-29.2323	34.27546
Systolic	0.622566	0.117801	5.284881	0.000355	0.360089	0.885044

Hypotheses:
H0: Slope and Correlation are both zero
H1: Slope and Correlation are both not zero

Results:
the correlation coefficient
r =0.8581

the variation of absences are explained by the model
R2=73.64

What is the equation for the regression line? Use 2 decimal places in answers.
Diastolic = 0.62(Systolic) +2.52

State the p-value. Round answer to nearest hundredth percent (i.e. 2.55%).
p-value =0.00

Conclusion:
We have sufficient evidence to support the claim that the correlation coefficient and slope of the regression line are both statistically different than zero