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A model with exactly one explanatory variable is a simple linear regression; a model with two or more explanatory variables is a multiple linear regression. [1] This term is distinct from multivariate linear regression , which predicts multiple correlated dependent variables rather than a single dependent variable.
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...
If both are I(0), standard regression analysis will be valid. If they are integrated of a different order, e.g. one being I(1) and the other being I(0), one has to transform the model. If they are both integrated to the same order (commonly I(1)), we can estimate an ECM model of the form
Partial regression plot; Student's t test for testing inclusion of a single explanatory variable, or the F test for testing inclusion of a group of variables, both under the assumption that model errors are homoscedastic and have a normal distribution. Change of model structure between groups of observations. Structural break test. Chow test
Regression models predict a value of the Y variable given known values of the X variables. Prediction within the range of values in the dataset used for model-fitting is known informally as interpolation. Prediction outside this range of the data is known as extrapolation. Performing extrapolation relies strongly on the regression assumptions.
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals.
The Breusch–Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these. The null hypothesis is that there is no serial correlation of any order up to p. [3]
In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model.It is used when there is a non-zero amount of correlation between the residuals in the regression model.