Proper linear model
Encyclopedia
In statistics
, a proper linear model is a linear regression
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
is the most common example of a proper linear model. Unit-weighted regression
is the most common example of an improper linear model.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, a proper linear model is a linear regression
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
model in which the weights given to the predictor variables
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
are chosen in such a way as to optimize the relationship between the prediction and the criterion. Simple regression analysis
Regression analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...
is the most common example of a proper linear model. Unit-weighted regression
Unit-weighted regression
In statistics, unit-weighted regression is perhaps the easiest form of multiple regression analysis, a method in which two or more variables are used to predict the value of an outcome....
is the most common example of an improper linear model.