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More Multiple Linear Regression
John McGready
Johns Hopkins University
Lecture Topics
Examples of linear regression from the public health/
medical literature
Multiple linear regression—where is the line?
Collinearity
Assumptions of MLR
Correlation in MLR
3
Section A
Examples from the Literature
Smoking and Cognition
Cigarette Smoking and Cognitive Decline in Midlife:
Evidence From a Perspective Birth Cohort Study
(Richards, M., Jarvis, M., et al. American Journal of Public
Health. Vol 93. No. 96. 2003)
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Smoking and Cognition
Abstract
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Smoking and Cognition
Outcome
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Smoking and Cognition
Potential confounders
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Smoking and Cognition
Results from MLR
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Smoking and Cognition
Results from MLR
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Smoking and Cognition
Regression model detailed in 2nd column
  Change in memory score = intercept*+ smoking
(three categories) + sex (binary) + education level
(four categories) + social class (five categories)
* Intercept not shown in table
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Smoking and Cognition
Information in footnotes
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Smoking and Cognition
Results from MLR
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Smoking and Cognition
Results from MLR
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Smoking and Cognition
Smoking more than 20 cigarettes at age 43 was
associated with a greater decline in memory scores
between 43 and 53 years (by 1.10 units on average, 95%
CI .30 to 1.89 units) relative to subjects who did not
smoke at age 43
No statistical differences in change in memory scores
between ages 43 and 53 were found between smokers
who smoked 1-20 cigarettes per day at age 43, and
subjects who did not smoke at age 43
15
Blood Pressure and Snoring
Blood Pressure, Snoring, Obesity, and Nocturnal
Hypoxaemia (Hoffstein, V. Lancet. No. 244. 1994)
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Blood Pressure and Snoring
Author’s summary
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Blood Pressure and Snoring
Regression results
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Blood Pressure and Snoring
Regression results
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Blood Pressure and Snoring
SI = “snoring index” defined by authors as “number of
snores per hour”
Unadjusted analysis
  A one-unit increase in the snoring index is
associated with a .004 mmHg increase in blood
pressure (95% CI .002 mmHg - .006 mmHg)
  Doesn’t seem like “much” but snoring index of
subjects in this article ranges from less than
100 – greater than 400
Continued
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Blood Pressure and Snoring
SI = “snoring index” defined by authors as “number of
snores per hour”
Adjusted analysis
  A one-unit increase in the snoring index is
associated with no increase in blood pressure
(95% CI -.002 mmHg - +.002 mmHg)
  After adjustment, relationship between BP and
snoring “disappears”: confounding?
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Blood Pressure and Snoring
Regression results
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Blood Pressure and Snoring
Footnote
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