Chapter 15: Logistic Regression

Abstract

The linear regressions we have been exploring have some underlying assumptions. First and foremost is that response and prediction variables should have a linear relationship. Buried in that assumption is the idea that these variables are quantitative. However, what if the response variable is qualitative or discrete? If it is binary, such as measuring whether participants are satisfied or not satisfied, we could perhaps dummy-code satisfaction as 1 and no satisfaction as 0. In that case, while a linear regression may provide some guidance, it will also likely provide outputs well beyond the range of [0,1], which is clearly not right. Should we desire to predict more than two responses (e.g., not satisfied, mostly satisfied, and satisfied), the system breaks down even more.