# Linear model

**linear modelslinearlinear processlinear model of communicationlinear relationshipscaling-and-summing modelstatistical linear model**

In statistics, the term linear model is used in different ways according to the context.wikipedia

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### Linear regression

**regression coefficientmultiple linear regressionregression**

The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model.

Such models are called linear models.

### Dependent and independent variables

**dependent variableindependent variableexplanatory variable**

Given a (random) sample the relation between the observations Y i and the independent variables X ij is formulated as

In the simple stochastic linear model the term y_i is the i th value of the dependent variable and x_i is the i th value of the independent variable.

### Statistics

**statisticalstatistical analysisstatistician**

In statistics, the term linear model is used in different ways according to the context.

Early statistical models were almost always from the class of linear models, but powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (such as neural networks) as well as the creation of new types, such as generalized linear models and multilevel models.

### General linear model

**multivariate linear regressionmultivariate regressionGLM**

The general linear model or multivariate regression model is a statistical linear model.

### Time series

**time series analysistime-seriestime-series analysis**

However, the term is also used in time series analysis with a different meaning.

### Statistical theory

**statisticalstatistical theoriesmathematical statistics**

In each case, the designation "linear" is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible.

### Statistical model

**modelprobabilistic modelstatistical modeling**

For the regression case, the statistical model is as follows.

### Least squares

**least-squaresmethod of least squaresleast squares method**

### Autoregressive–moving-average model

**ARMAautoregressive moving average modelautoregressive moving average**

An example of a linear time series model is an autoregressive moving average model.

### Innovation (signal processing)

**InnovationinnovationsInnovations vector**

where again the quantities ε t are random variables representing innovations which are new random effects that appear at a certain time but also affect values of X at later times.

### Covariance

**covariantcovariationcovary**

This particular aspect of the structure means that it is relatively simple to derive relations for the mean and covariance properties of the time series.

### Nonlinear dimensionality reduction

**manifold learninglocally linear embeddingnon-linear dimensionality reduction**

One example of this is nonlinear dimensionality reduction.

### Generalized linear model

**generalized linear modelslink functiongeneralised linear model**

### Linear system

**linearlinear systemslinear theory**

### Cochrane–Orcutt estimation

**Cochrane–Orcutt procedure**

Cochrane–Orcutt estimation is a procedure in econometrics, which adjusts a linear model for serial correlation in the error term.

### Multilevel model

**Hierarchical linear modelingMultilevel modelshierarchical linear model**

These models can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to non-linear models.

### Degrees of freedom (statistics)

**degrees of freedomdegree of freedomEffective degrees of freedom**

The term is most often used in the context of linear models (linear regression, analysis of variance), where certain random vectors are constrained to lie in linear subspaces, and the number of degrees of freedom is the dimension of the subspace.

### Multivariate adaptive regression spline

**Multivariate adaptive regression splinesHinge functionsMARS**

It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables.

### John Nelder

**John Ashworth NelderNelderNelder, John**

While leading research at Rothamsted Experimental Station, Nelder developed and supervised the updating of the statistical software packages GLIM and GenStat: Both packages are flexible high-level programming languages that allow statisticians to formulate linear models concisely.

### Prais–Winsten estimation

**Prais–Winsten transformationPrais and WinstenPrais–Winsten estimate**

In econometrics, Prais–Winsten estimation is a procedure meant to take care of the serial correlation of type AR(1) in a linear model.

### Total sum of squares

**sum of squaressum of the squared deviations of the values of the dependent variable**

In statistical linear models, (particularly in standard regression models), the TSS is the sum of the squares of the differences between the dependent variable and its mean:

### Mathematical model

**mathematical modelingmodelmathematical models**

### Logistic regression

**logit modellogisticlogistic model**

We assume a linear relationship between the predictor variables, and the log-odds of the event that Y=1.

### Shayle R. Searle

**Searle, Shayle R.Shayle Robert SearleShayle Searle**

He was a leader in the field of linear and mixed models in statistics, and published widely on the topics of linear models, mixed models, and variance component estimation.