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
110	74
133	91
115	83
118	88
134	87
123	77
154	94
119	69
130	76
108	69
112	75

Data Table: Blood Pressure 7

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

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Diastolic
Independent Variable: Systolic
Diastolic = 20.752817 + 0.48186343 Systolic
Sample size: 12
R (correlation coefficient) = 0.7583533
R-sq = 0.57509972
Estimate of error standard deviation: 5.9920008

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	20.752817	16.061723	? 0	10	1.2920667	0.2254
Slope	0.48186343	0.13097726	? 0	10	3.6789855	0.0043

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	485.95927	485.95927	13.534934	0.0043
Error	10	359.04073	35.904073
Total	11	845

Hence,

r = 0.7584

R2 = 57.51%

Diastolic = 0.48*Systolic + 20.75

p - value = 0.43%

Have; <