Using a least squares regression model of binary outcomes can lead to...
inaccurate predictions and biased estimates. This is because least squares regression assumes a continuous outcome variable and uses a linear regression model to estimate the coefficients. However, when applied to binary outcomes, this can lead to problems as the linear regression model may not account for the binary nature of the outcome.
Additionally, using least squares regression for binary outcomes can result in predictions that fall outside the valid range of a binary outcome (0 or 1). This violates the assumptions of the model and can lead to unreliable and misleading predictions.
To address these issues, alternative methods such as logistic regression or probit regression are commonly used for modeling binary outcomes. These methods properly account for the binary nature of the outcome variable and provide more accurate predictions and unbiased estimates.