Recorded in the table below are the blood pressure measurements (in millimeters)
ID: 2906586 • Letter: R
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.)
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
Explanation / Answer
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:
Analysis of variance table for regression model:
Hence,
r = 0.7584
R2 = 57.51%
Diastolic = 0.48*Systolic + 20.75
p - value = 0.43%
Have; <
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 0.0043Related Questions
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