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Multiple Regression

Multiple Regression. Similar to simple regression, but with more than one independent variable R 2 has same interpretation Residual analysis is similar Confidence & Prediction Interval are similar. Multiple Regression.

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Multiple Regression

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  1. Multiple Regression • Similar to simple regression, but with more than one independent variable • R2 has same interpretation • Residual analysis is similar • Confidence & Prediction Interval are similar

  2. Multiple Regression • A multiple regression model includes a coefficient for each independent variable • Simple case is a quadratic model on a single variable • Independent variable can be indicator (dummy) variable • i.e. gender = 0 for female and gender =1 for male • Coefficients are called “partial slopes”

  3. Multiple Regression • A multiple regression model includes a coefficient for each independent variable • Collinearity occurs when two or more independent variables are correlated, thus explain the same information • Model can include interaction terms if independent variables are interact

  4. Variable Selection • Several procedures have been developed for selecting the best model for predicting Y from several independent variables (X’s) • Compare all possible regressions • Backward elimination • Forward Selection • Stepwise Elimination

  5. Logistic Regression • A regression model with a qualitative (typically dichotomous) dependent variable • Dependent variable can be thought of as a binomial response • i.e. Y=1 if patient is cured, and Y=0 otherwise • Model is constructed to predict P(Y=1) using a logistic function

  6. Logistic Regression • Linear relationship between the natural log of the odds ratio and the independent variables. • Odds ratio is the ratio of probabilities of success to failure • Each coefficient describes the size of the contribution of that “risk factor”

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