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Section B
More Examples
Hourly Wages

Recall the regression relating hourly wages (U.S. $) to years of
formal education for a random sample of 534 workers from 1985

Workers who differ by one year in education levels have wages that
differ by $0.75/hour on average (95% CI: $0.60 to $0.90 per hour;
higher wages associated with more years of education)
3
Hourly Wages

What is the relationship between hourly wages and worker’s sex?
(1 = female, 0 = male)
4
Hourly Wages

What is the relationship between hourly wages and worker’s sex?
(1 = female, 0 = male)

Female workers earned an average of $2.11/hour less than male
workers in 1985 (95% CI $1.26 to $2.97 less per hour)
5
Hourly Wages

What is the relationship between hourly wages and, years of formal
education and worker’s sex? (1 = female, 0 = male): MLR
6
Hourly Wages

Adjusted relationships from the MLR

Relationship between wages and sex adjusted for years of education
-  Female workers earned an average of $2.12/hour less than male
workers with the same level of education in 1985 (95% CI $1.33
to $2.92 less per hour)

Relationship between wages and years of education adjusted for sex
(sex-adjusted relationship)
-  Workers of the same sex who differ by one year in education
levels have wages that differ by $0.75/hr on average (95% CI:
$0.60 to $0.90 per hour; higher wages associated with more
years of education)
7
Recapping the Results

So far we have results from three models
Years of
education
Unadjusted
Unadjusted
Adjusted
SLR1: x = years
of education
SLR2: x = sex
MLR: x1 = years of
education, x2 = sex
0.75 (0.60-0.90)
Sex (1 = F)
R2
0.15
0.75 (0.60-0.90)
-2.11 (-2.97, -1.26)
-2.12 (-2.91, -1.33)
0.04
0.19
8
Example 2: Hemoglobin

SLR from Hb on Packed Cell Volume (PCV)

The estimated mean difference in Hemoglobin levels for two groups
of subjects who differ by 1% in PCV is 0.20 g/dL (95% CI 0.10 to 0.30
g/dL) subjects with greater PCV have greater Hb levels on average
9
Example 2: Hemoglobin

SLR from Hb on age (years)

The estimated mean difference in hemoglobin levels for two groups
of subjects who differ by one year of age is 0.13 g/dL (95% CI 0.09
to 0.17 g/dL): older subjects have greater Hb levels on average
10
Hemoglobin

What is the relationship between hemoglobin and patient PCV and
age?: MLR
11
Hemoglobin

Adjusted relationships from the MLR

Relationship between Hb and PCV adjusted for age
-  The estimated mean difference in Hemoglobin levels for two
groups of subjects of the same age who differ by 1% in PCV is
0.10 g/dL (95% CI 0.04 to 0.17 g/dL) subjects with greater PCV
have greater Hb levels on average

Relationship between Hb and age adjusted for PCV
-  The estimated mean difference in hemoglobin levels for two
groups of subjects with the same PCV who differ by one year of
age is 0.10 g/dL (95% CI 0.07 to 0.14 g/dL): older subjects have
greater Hb levels on average
12
Recapping the Results

So far we have results from three models
PCV (%)
Unadjusted
Unadjusted
Adjusted
SLR1: x = PCV
SLR2: x = age
MLR: x1 = PCV, x2 = age
0.20 (0.10-0.30)
Age
(years)
R2
0.51
0.10 (0.04-0.17)
0.13 (0.09, 0.017)
0.10 (0.07, 0.14)
0.75
0.84
13