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

1)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.7584

2)

R2=(r2*100) =57.51 %

Diastolic = 0.48*(Systolic) +20.75

p value = 0.43 %

We have 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)