Question

5. A group of investigators is working on setting up a screening program for hypertension. In order to see if and how age might be considered in the screening process, investigators performed a regression analysis on 118 individuals looking at the association between age and systolic blood pressure (SBP). Scatterplot of the data (with fit line and R2) and regression-analysis output are presented below. R2 Linear 0.346 225 O 200 75- 150 O 100- 20 30 60 80 40 Age (years) Table1: Linear regression output 95% Confidence Parameter Std. Error Interval Intercept 90.31 5.80 15.57 78.83 101.80 slope (age) 8.06 0.66 0.87 0.11 1.09 Dependent Variable:Systolic blood pressure a. "(1 point) Write out the equation of the regression line which relates age to SBP? b. *(1 point) Using this regression output compute an estimate for the average SBP of people 30 years of age. Also compute an estimate for 40 year-olds. What is estimated difference in average SBP associated with one year of difference in age? c. d. (1 point) What is the estimate difference in average SBP associated with a 10year difference in age? e. *(1point Do these data indicate good evidence at the a-5% significance level of an association between age and SBP? f How good of a predictor is age of SBP (i.e. what percent of the variation of SBP is explained by SBP in this dataset)? Systolic E aunssaud poojg

Answer 1

a. The regression equation is   .

SBP 90.31 + (0.87 x age

b. For age 30

SBP 90.31 (0.87 x 30) 116.41

For age 40

SBP 90.31 (0.87 x 40) 125.11

c. The estimated difference in SBP with a one year of difference in age is .

0.87

d. The estimated difference in average SBP associated with a 10 year difference in age is   .

8.7 0.87 x 10

e. Since the value of t-stistic for the slope is ,   the data do not good evidence of an association between age and SBP at 5% significance level.

8.06 (0.66, 1.09)

f. It is given that   .

R20.346

Hence 34.6% of the variation of SBP is explained by age in this dataset, which is very low.

So we can say that age is not at all a good predictor of SBP.