Long Notes for ANOVA & Logistic Reg with Explanation by XyL.pdf

Long Notes for ANOVA & Logistic Reg with Explanation by XyL.pdf

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1 Introduction to ANOVA, Regression, and Logistic Regression, Course Notes Predictive Modeling Using Logistic Regression 1. Introduction Cases(observations, examples) Input variables(predictors, explanatory) Target variable(outcome, response) In supervised classification , the target is a class label. A predictive model assigns, to each case, a score that measures the propensity that the case belongs to a particular class. With two classes, the target is binary and usually represents the occurrence of an event. The term supervised is used when the class label is known for each case. The prediction model is used on new cases where the input values are known but the class labels are unknown. The aim is generalization , which is predicting the outcome on novel cases. Traditional statistical analysis like hypothesis test are common inferential tools. Predictive modelers like logistic regression are used to infer how input variable affect the target. Analytical challenges: Opportunistic data, Mixed Measurement Scales, High Dimensionality, Rare Target Event, Nonlinearities and Interactions, Model selection(overfitting or using too complex a model is common, might be too sensitive to peculiarities in the sample data set and not generalize well to new data. Underfitting disregards the true features.) 2. Fitting the M odel 2.1 The Model We are always modelling the outcome log(p/(1-p), we define the function logit(p)=log(p/(1-p)) and use the name logit for convenience.
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2 Logistic regression is a special case of the generalized linear model . Each input variable affects the logit linearly. The coefficients are the slopes. The method of maximum likelihood (ML) is usually used to estimate the unknown parameters in the logistic regression model. The likelihood function is the joint probability density function of the data treated as a function of the parameters. The maximum likelihood estimates are the values of the parameters that maximize the probability of obtaining the sample data. Many SAS procedures can be used; most notable are the LOGISTIC, GENMOD, CATMOD, and DMREG procedures (SAS Enterprise Miner). Interpreting the parameters(Q60,calculate probability of default with SAS): logit(Pi)=log(odds)=Beta0+Beta1X1=log(Pi/1-Pi)=default(eg.) odds =Pi/1-Pi =exp(default) Pi=odds/(1+odds) Pi =exp(default)/1+exp(default) =1/(1+exp(-default) Introduction to the LOGISTIC Procedure The LOGISTIC procedure fits a binary logistic regression model. The seven input variables included in the model were selected arbitrarily. The DES (short for descending) option is used to reverse the sorting order for the levels of the response variable Ins. The CLASS statement names the classification variables to be used in the analysis. The CLASS statement must precede the MODEL statement(Q63, logistic model statements, CLASS statement for categorical predictors). The PARAM option in the CLASS statement specifies the parameterization method for the classification variable or variables and
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