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).

Unit-weighted regression is a method of robust regression that proceeds in three steps. First, predictors for the outcome of interest are selected; ideally, there should be good empirical or theoretical reasons for the selection. Second, the predictors are converted to a standard form. Finally, the predictors are added together, and this sum is called the variate, which is used as the predictor of the outcome.

The Burgess method was first presented by the sociologist Ernest W. Burgess in a 1928 study to determine success or failure of inmates placed on parole. First, he selected 21 variables believed to be associated with parole success. Next, he converted each predictor to the standard form of zero or one (Burgess, 1928). When predictors had two values, the value associated with the target outcome was coded as one. Burgess selected success on parole as the target outcome, so a predictor such as a history of theft was coded as "yes" = 0 and "no" = 1. These coded values were then added to create a predictor score, so that higher scores predicted a better chance of success. The scores could possibly range from zero (no predictors of success) to 21 (all 21 predictors scored as predicting success).