Suppose we have data from a health survey conducted in year2000. Data were obtained from a random sample of 1000 persons.
An OLS linear regression analysis was carried out in thefollowing way:
Dependent Variable: Systolic blood pressure (SBP, in mmHg)
Independent Variables: Gender (1 if female, 0 if male)
Age (in years)
Education (binary variables for “Notgraduated from high school” and “Graduated from high school (butnot from college)”; the reference category is “Graduated fromcollege”)
A part of the results is shown below. The column labeled “Beta”show estimated values of partial regression coefficients. (It canbe interpreted that beta’s for the reference categories, “Male” and“Graduated from college”, are fixed to be zero.) Thep-values are for the two-sided test.
Variables | Beta | p-value |
(Constant) | 100.00 | <0.01 |
Gender (Female) | -3.00 | 0.04 |
Age (in years) | 0.50 | <0.01 |
Education | | |
Not graduated from high school | 5.00 | <0.01 |
Graduated from high school | 2.00 | 0.08 |
1. According to the results of this regression analysis, howmuch expected difference in systolic blood pressure (in mmHg) isestimated:
1-1. between the two education categories, “Not graduated fromhigh school” and “Graduated from college”, controlling for genderand age (i.e., among those who have the same gender and at the sameage)?
1-2. between males and females, controlling for age andeducation?
2. Suppose we change the reference category of education from“Graduated from college” to “Graduated from high school” and do thesame regression analysis again.
What will be the value of partial regression coefficient (beta)for “Not graduated from high school”?
(Hint: The expected SBP differences among the educationcategories do not change.)
