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Unformatted text preview: x1 is not signiﬁcant after adjusting for another
independent variable x2 .
This usually occurs when x1 and x2 are strongly related to
each other and when x2 is also related to y .
We refer to x2 as a confounder of the relationship between y
and x1 .
Multiple regression allows to identify which few variables
among a large set have a signiﬁcant relationship with the
dependent variable after adjusting for other important
variables.
After persuasively ruling out confounders causal inference
MAY be possible.
Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction
Least Square Estimates of the Parameters
Inference about the Parameters
Prediction
Assessing Adequacy of Fit
Correlation
Multiple Regression Introduction
Inferences in Multiple Regression
Tests for Subset of Regression Coeﬃcients
Prediction (Forecasting)
Dummy Variables Exercise and Bone Mineral Density Post menopause
Those who exercise less tend to have lower BMD.
They also tend to be
Older
Frailer
Heavier Age, Frailty and Weight are also risk factors for BMD.
They are confounders of the relationship between exercise and
BMD.
Multiple regression allows to adjust for these confounders. Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction
Least Square Estimates of the Parameters
Inference about the Parameters
Prediction
Assessing Adequacy of Fit
Correlation
Multiple Regression Introduction
Inferences in Multiple Regression
Tests for Subset of Regression Coeﬃcients
Prediction (Forecasting)
Dummy Variables Other Examples
People whose diet is high on fat on average have higher LDL
(lowdensity lipoprotein) cholesterol, a risk factor for coronary
heart disease (CHD).
They are also more likely to smoke and be overweight, factors
strongly associated with CHD risk.
Higher BMI predicts higher levels of Hba1c , a marker for poor
control of glucose levels.
However, Old age and ethnic background also predict higher
Hba1c Chapter 11: Regression and Correlation Methods Stat 491: Biostatistics Introduction
Least Square Estimates of the Parameters
Inference about the Parameters
Prediction
Assessing Adequacy of Fit
Correlation
Multiple Regression Introduction
Inferences in Multiple Regression
Tests for Subset of Regression Coeﬃcients
Pred...
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 Fall '12
 SolomonHarrar
 Statistics, Biostatistics, Correlation

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