statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, a proper linear model is a

linear regression In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is call ...

model in which the weights given to the predictor variables are chosen in such a way as to optimize the relationship between the prediction and the criterion. Simple

regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...

is the most common example of a proper linear model.

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 :\hat = \hat(\mathbf) = \hat + \sum_i x_i wh ...

is the most common example of an improper linear model.

Bibliography

* Regression models {{Statistics-stub