Logistic Regression

# Logistic Regression - SEMATECH 1997 Statistical Methods...

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Regression Models for a Binary Response Using EXCEL and JMP David C. Trindade, Ph.D. S TAT- T ECH Consulting and Training in Applied Statistics San Jose, CA SEMATECH 1997 Statistical Methods Symposium Austin

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Topics • Practical Examples • Properties of a Binary Response • Linear Regression Models for Binary Responses – Simple Straight Line – Weighted Least Squares • Regression in EXCEL and JMP • Logistic Response Function • Logistic Regression – Repeated Observations (Grouped Data) – Individual Observations • Logit Analysis in EXCEL and JMP • Conclusion
Practical Examples: Binary Responses Consider the following situations: • A weatherman would like to understand if the probability of a rainy day occurring depends on atmospheric pressure, temperature, or relative humidity • A doctor wants to estimate the chance of a stroke incident as a function of blood pressure or weight • An engineer is interested in the likelihood of a device failing functionality based on specific parametric readings

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More Practical Examples • The corrections department is trying to learn if the number of inmate training hours affects the probability of released prisoners returning to jail (recidivism) • The military is interested in the probability of a missile destroying an incoming target as a function of the speed of the target • A real estate agency is concerned with measuring the likelihood of selling property given the income of various clients • An equipment manufacturer is investigating reliability after six months of operation using different spin rates or temperature settings
Binary Responses • In all these examples, the dependent variable is a binary indicator response, taking on the values of either 0 or 1, depending on which of of two categories the response falls into: success-failure, yes-no, rainy- dry, target hit-target missed, etc. • We are interested in determining the role of explanatory or regressor variables X 1 , X 2 , … on the binary response for purposes of prediction.

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Simple Linear Regression Consider the simple linear regression model for a binary response: where the indicator variable Y i = 0, 1. Since , the mean response is YX ii i =+ + β ε 01 () EY X ββ E i ε= 0
Interpretation of Binary Response • Since Y i can take on only the values 0 and 1, we choose the Bernoulli distribution for the probability model. • Thus, the probability that Y i = 1 is the mean p i and the probability that Y i = 0 is 1- p i . • The mean response is thus interpreted as the probability that Y i = 1 when the regressor variable is X i . EY p p p ii i i () ( ) + × = 10 1

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Model Considerations Consider the variance of Y i for a given X i : We see the variance is not constant since it depends on the value of X i . This is a violation of basic regression assumptions.
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## This document was uploaded on 10/26/2011 for the course ENGL 250 at Iowa State.

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Logistic Regression - SEMATECH 1997 Statistical Methods...

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