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Chapter20

# Chapter20 - Introduction Logistic Regression Model Chapter...

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Introduction Logistic Regression Model Inferential Tools Chapter 20: Logistic Regression for Binary Response Variables STAT 3022 Fall 2011 University of Minnesota December 5, 2011

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Introduction Logistic Regression Model Inferential Tools Introduction The general setup for data analysis can be split into four main categories, according to explanatory & response variables: Response Quantitative Binary Explanatory Quantitative Linear Regression Logistic Regression (Ch 7–12) (Ch 20–21) Categorical ANOVA χ 2 test for independence (Ch 2–6) (Ch 18–19) Here two-sample t -procedures fall under “ANOVA” classification.
Introduction Logistic Regression Model Inferential Tools Introduction How to work with a regression model where the response is binary : y = 1 , if yes 0 , if no For example, y = 1 for subjects who developed lung cancer y = 0 for subjects who did not Mean of y is a probability of developing lung cancer. Standard linear regression inadequate because it permits probabilities less than 0 and greater than 1. Most important solution is logistic regression .

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Introduction Logistic Regression Model Inferential Tools Survival in the Donner Party Example In 1846, Donner Party left Springfield, IL for California by covered wagon. Group became stranded in Sierra Nevada mountains. 40 of the 87 members died from famine and exposure to cold. Response : Survival (1 for yes, 0 for no) Explanatory : Sex and Age For given age, were the odds of survival greater for women than for men?
Introduction Logistic Regression Model Inferential Tools Survival in the Donner Party Example > donner\$surv <- vector() > for(i in 1:45){ + if(donner\$STATUS[i]=="SURVIVED") + donner\$surv[i] <- 1 + else(donner\$surv[i] <- 0) + } > attach(donner) > head(donner) AGE SEX STATUS surv 1 23 MALE DIED 0 2 40 FEMALE SURVIVED 1 3 40 MALE SURVIVED 1 4 30 MALE DIED 0 5 28 MALE DIED 0 6 40 MALE DIED 0 > plot(surv~AGE,col=as.numeric(SEX),pch=as.numeric(SEX)) > legend(50,1.0,col=c(1,2),pch=c(1,2),legend=c("FEMALE","MALE"))

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Introduction Logistic Regression Model Inferential Tools Survival in the Donner Party ● ● 20 30 40 50 60 0.0 0.2 0.4 0.6 0.8 1.0 AGE surv FEMALE MALE
Introduction Logistic Regression Model Inferential Tools Survival in the Donner Party Example Consider the separate-lines model: > msat <- lm(surv~AGE*SEX) > summary(msat) Call: lm(formula = surv ~ AGE * SEX) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.62607 0.34114 4.767 2.37e-05 *** AGE -0.03088 0.01034 -2.985 0.00476 ** SEXMALE -1.09064 0.40402 -2.699 0.01004 * AGE:SEXMALE 0.02460 0.01208 2.036 0.04824 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.4431 on 41 degrees of freedom Multiple R-squared: 0.2754, Adjusted R-squared: 0.2224 F-statistic: 5.194 on 3 and 41 DF, p-value: 0.003914

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Introduction Logistic Regression Model Inferential Tools Survival in the Donner Party ● ● 20 30 40 50 60 0.0 0.2 0.4 0.6 0.8 1.0 AGE surv FEMALE MALE
Introduction Logistic Regression Model Inferential Tools Survival in the Donner Party Example Problems with using linear regression: Linearity assumption violated – obvious from scatterplot Small R 2 because the relationship is not linear

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Chapter20 - Introduction Logistic Regression Model Chapter...

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