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7 The Logistic Regression Model In this chapter we will consider regression models when the regressand is Y ,X , Y ,X , ..., Y ,X dichotomous or binary in nature. The data is of the form ( 1 1 ) ( 2 2 ) ( n n ), where the dependent variable Y, i = 1, …, n are the observed binary outputs i assumed to be independent (in the statistical sense) of each other, the vector X, i i = 1,…, n, are the covariates (independent variables in the sense of a regression problem) associated with Yi. In the previous chapter we considered the linear regression model where the regressand was assumed to be continuous along with the assumption of normality for the error distribution. Here, we will consider a Gaussian (normal) model for the binary regression model, which is more widely known as the probit model. A more generic model has emerged during the past four decades in the form of a logistic regression model. We will consider the logistic regression model for rest of the chapter. The approach in this chapter will be on the following lines: ‹ The binary regression problem ‹ The probit regression model ‹ The logistic regression model ‹ Model validation and diagnostics ‹ Receiving operator curves ‹ Logistic regression for the German credit screening dataset The Logistic Regression Model The binary regression problem Consider the problem of modeling the completion of a stat course by students based on t