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Chapter 11--Regression and Correlation Methods

# In this section we will see how to incorporate

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Unformatted text preview: ether the combination of the the predictor values is reasonable. Same issue arises with measure of inﬂuence diagnostics. 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 Introduction So far we considered only quantitative predictor (explanatory) variables except for the Diabetes example. In this section, we will see how to incorporate qualitative predictor variables, and what interpretation do the parameters have. The case of a qualitative dependent variable will be considered in the next section (Logistic Regression). Qualitative predictor variables are included in the model by means of Dummy Variables which are variables taking only 0’s and 1’s. 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 One Qualitative Variables With Two Categories For the Diabetes example, y is glucose and x is exercise. The independent variable x indicates whether a person does exercise or not. The question whether exercise is associated with reduction of glucose can be answered using a two sample t test. As we saw before this problem can also be treated as a regression problem. Speciﬁcally, µglucose|exercise = β0 + β1 exercise. 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 One Qualitative Variables with Two Categories For the those participants who do NOT exercise µglucose|No Eexercise = β0 . For those who do exercise, µglucose|Does Exercise = β0 + β1 . Thus, the parameter β1 (if negative) is expected REDUCTION o...
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