statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, a proper linear model is a

linear regression In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...

model in which the weights given to the predictor

variables Variable may refer to: Computer science * Variable (computer science), a symbolic name associated with a value and whose associated value may be changed Mathematics * Variable (mathematics), a symbol that represents a quantity in a mathemat ...

are chosen in such a way as to optimize the relationship between the prediction and the criterion. Simple regression analysis is the most common example of a proper linear model.

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

is the most common example of an improper linear model.

Bibliography

* Regression models {{Statistics-stub