Using a least squares regression model of binary outcomes can lead to
some issues and inaccuracies in the predicted probabilities and classification of the outcomes. This is because a least squares regression model assumes that the dependent variable is a continuous variable, not a binary variable.
In a binary outcome model, the dependent variable can only take two values, typically represented as 0 and 1. However, the least squares regression model can predict values outside of this range, leading to probabilities that are greater than 1 or less than 0. This violates the assumptions of the binary outcome model and can lead to unreliable predictions.
Additionally, the least squares regression model does not account for the non-linear relationship between the predictor variables and the binary outcome. This can result in an inaccurate estimation of the probabilities and misclassification of the outcomes.
To overcome these issues, it is better to use a specific binary outcome model such as logistic regression, which is designed to handle binary outcomes and can provide more accurate predictions and classifications.