Suppose researchers are interested in the relationship betwe

Suppose researchers are interested in the relationship between systolic blood pressure and periodontal disease in a population of low-income families. In order to address the relationship most efficiently, the researchers have decided to model age as a potential confounding variable. During the analysis phase of their investigation, the researchers found it most appropriate to model age as a dummy variable. The variable was quantified in quartiles, and grouped in the following manner.

Category1) Age<25

Category2) Age (25, 35)

Category3) Age (36, 45)

Category4) Age >46

A) Organize these age categories into a set of dummy variables. Describe what a 1 and 0 indicate for each dummy variable.

B) Suppose a multiple linear regression model generated the following results for the dummy variable representing age. Describe the relationship presented.

Parameter Estimates

Variable

DF

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

Intercept

B

0.10811

0.02370

4.56

<.0001

agedummy1

B

0.07642

0.03436

2.22

0.0265

agedummy2

B

-0.02932

0.03452

-0.85

0.3960

agedummy3

B

-0.00421

0.03517

-0.12

0.9047

agedummy4

0

REF

.

.

.

Solution

a) dummy1 = 1 if age<25
   = 0 otherwise
dummy2 = 1 if 25 < age <35
   = 0 otherwise

dummy3 = 1 if 36 < age <45
   = 0 otherwise

dummy4 = 1 if age > 45
   = 0 otherwise

b) y = 0.10811 + 0.07642*(agedummy1) -0.02932*( agedummy2) - 0.00421*(agedummy4)

There is a positive relation between y and agedummy1...and there are negative relation between age and agedummy 2 and between y and age dummy 3 and age dummy 4 does not contribute to y and has no effect to determine y....