Statistics 101: What is Binary Logistic Regression?

I Give the Basics of This Method

Introduction to logistic regression
In this article I covered simple linear regression, and in this one I covered multiple linear regression.

Both these types of regression are for dependent variables (see this article http://www.associatedcontent.com/article/2178237/statistics_101_dependent_and_independent.html?cat=4) that are continuous. But what if the dependent variable is not continuous?

There are several ways in which a variable might not be continuous: It might be a dichotomy (dead/alive) or it might have several categories which might be ordered (e.g. liberal, moderate, conservative) or unordered (e.g. Black, White, Asian, Other). When the dependent variable is a dichotomy, we can use binary logistic regression, often simply called logistic regression.

The need for logistic regression
First, we might ask why we need logistic regression at all. Why can't we simply use linear regression? In fact, if our dependent variable is coded 0 and 1 (or with any other two numbers) then the program will run correctly, and give no errors. But analyzing a dichotomous dependent variable this way has several problems. First, it violates the assumptions of the linear regression model about the nature of the residuals. We needn't get into the details here, just trust me that it isn't a good thing to do. Second, one purpose of regression is often to make predictions, and linear regression makes predictions that make no sense for dichotomous dependent variables. E.g., if you code dead as 1 and alive as 0, then linear regression might predict 0.5 .... Half dead? Or, worse, -.2 or 1.5 .... LESS than dead? More than alive? It makes no sense.

To get around this, we do two things. First, instead of trying to model the dichotomy itself (dead/alive) we transform it into the ODDS of being alive. Here 'odds' are just like in sports. We might say that a 210 pound, 5'9" White male 52 year old has odds of 100-1 of dying in the next year (I just made that up). But the odds, while better than a dichotomy, still aren't perfect.