Unit-weighted regression

In statistics, unit-weighted regression is a simplified and robust version (Wainer & Thissen, 1976) of multiple regression analysis where only the intercept term is estimated. That is, it fits a model

${\displaystyle {\hat {y}}={\hat {f}}(\mathbf {x} )={\hat {b}}+\sum _{i}x_{i}}$

where each of the ${\displaystyle x_{i}}$ are binary variables, perhaps multiplied with an arbitrary weight.

Contrast this with the more common multiple regression model, where each predictor has its own estimated coefficient:

${\displaystyle {\hat {y}}={\hat {f}}(\mathbf {x} )={\hat {b}}+\sum _{i}{\hat {w}}_{i}x_{i}}$

In the social sciences, unit-weighted regression is sometimes used for binary classification, i.e. to predict a yes-no answer where ${\displaystyle {\hat {y}}<0}$ indicates "no", ${\displaystyle {\hat {y}}\geq 0}$ "yes". It is easier to interpret than multiple linear regression (known as linear discriminant analysis in the classification case).