Chapter 11--Regression and Correlation Methods

# Multiple regression allows to identify which few

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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 (low-density 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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