The following data set for a sample of 6 randomly middle-age to elderly patients

Question

The following data set for a sample of 6 randomly middle-age to elderly patients consists of x = age of patient, and y = measured value of systolic blood pressure of patient. We expect that as people age, their blood pressure will increase. Examine the relationship between the two variables.

(a) Determine the correlation coefficient between the age and Systolic Blood Pressure.

(b) Determine the least squares regression line of age and Systolic Blood Pressure, What is the blood pressure for someone at age 56.

Age, x Systolic Blood Pressure, y 43 128 48 120 56 135 61 143 67 141 70 152

Explanation / Answer

following information has been generated using the given data

correlation coefficient between x and y=r=0.8967

(b) here we want to fit the regression equation y=a+bx=81.047+0.9644x

for x=56, y=81.047+0.9644*56=135.0534

and b=r*sd(y)/sd(x)=0.8967*10.4043/9.6738=0.9644

and a=mean(y)-b*mean(x)=136.5-0.9644*57.5=81.047

x y 43 128 48 120 56 135 61 143 67 141 70 152 mean 57.5 136.5 sd 9.6738 10.4043 cov(x,y) 90.25 (a)r=cov(x,y)/(sd(x)*sd(y))= 90.25/(9.6738*10.4043)= 0.8967

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