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

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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”

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

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

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

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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