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

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

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 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 Model can include interaction terms if independent variables are interact

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 Compare all possible regressions Backward elimination Backward elimination Forward Selection Forward Selection Stepwise Elimination Stepwise Elimination

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

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 Odds ratio is the ratio of probabilities of success to failure Each coefficient describes the size of the contribution of that “risk factor” Each coefficient describes the size of the contribution of that “risk factor”