Ordinary linear regression

Question

Suppose we have data from a health survey conducted in year 2000. Data were obtained from a random sample of 1200 persons aged 25-64.

An OLS linear regression analysis was carried out in the following way:

Dependent Variable: Systolic blood pressure (SBP, in mmHg)

Independent Variables: Age (in years), BMI – body math index (kg/m2), fasting blood glucose (mg/dL)

A part of the results is shown below. The column labeled “Beta” show estimated values of partial regression coefficients. (R2 =

Variables

Beta

p-value

(Constant)

81.00

<0.0001

Age (in years)

0.48

<0.0001

BMI(kg/m2)

0.46

<0.0001

fasting blood glucose (mg/dL)

0.06

0.0028

1. Suppose the sample includes a 50-year old man whose BMI is 30 kg/m2 and whose fasting blood glucose level is 100 mg/dL. What is the value of systolic blood pressure () of this man predicted using this regression equation? (Compute up to the first decimal place, like 132.5)

2. According to the results of this regression analysis, how much expected difference (difference on average) in systolic blood pressure (in mmHg) is estimated between two groups that have 20 years of age difference (e.g., the 30-years old and 50-years old), controlling for BMI and fasting blood glucose (i.e., if comparison is made for those who have the same levels of BMI and fasting blood glucose)?

Answer 1

For problem 1) The model you have fit is: Systolic BP=beta0+beta1(age)+beta2(BMI)+beta3(fasting blood glucose) .

Note: I've typed out beta because I couldn't get the greek letter to work in this platform, I hope that's not confusing for you.

Your analysis results give you the values for the beta’s, so just plug them into the equation, along with the values given for a 50yrs. old subject: Systolic BP = 81+10.48(50) +0.46(30) +0.06(100)

Now solve for Systolic BP: Systolic BP=81+24+13.8+6 =124.8

For problem 2) Using the same model solve for age=20 and age=30, using the same value for BMI & fasting and blood glucose. Find the difference of the two to answer the question.