Regression analysis
can be used to determine the dependence of one variable (called
the endogenous or dependent variable) on other variables
(called the exogenous or independent or explanatory variables)
Linear regression models are linear in parameters,
assume the dependent variable is continuous, and the errors
are identically and normally distributed
Our Interest:
Situations in which the dependent variable is not
continuous (e.g., 0-1)
A 0-1 Example
The Data
A 0-1 Example (cont.)
Using Linear Regression
Implications of the 0-1 Example for Linear Regression
Improper Probabilities:
The predicted probabilities can be outside of
\([0, 1]\)
Heteroscedasticity:
The variance of the dependent variable is different for
different values of the independent variable
\(e^{\beta}\) is the effect of the independent
variable on the odds ratio (i.e., the probability of the
event divided by the probability of the non-event)
The 0-1 Example Revisited
Using Logistic Regression (i.e., A Binary Logit Model)