Linear Regression
Linear models with independently and identically distributed errors, and for errors with heteroscedasticity or autocorrelation. This module allows estimation by ordinary least squares (OLS), weighted least squares (WLS), generalized least squares (GLS), and feasible generalized least squares with autocorrelated AR(p) errors.
See Module Reference for commands and arguments.
Examples
# Load modules and data import numpy as np import statsmodels.api as sm spector_data = sm.datasets.spector.load() spector_data.exog = sm.add_constant(spector_data.exog, prepend=False) # Fit and summarize OLS model mod = sm.OLS(spector_data.endog, spector_data.exog) res = mod.fit() print res.summary()
Detailed examples can be found here:
Technical Documentation
The statistical model is assumed to be
, where
depending on the assumption on , we have currently four classes available
- GLS : generalized least squares for arbitrary covariance
- OLS : ordinary least squares for i.i.d. errors
- WLS : weighted least squares for heteroskedastic errors
- GLSAR : feasible generalized least squares with autocorrelated AR(p) errors
All regression models define the same methods and follow the same structure, and can be used in a similar fashion. Some of them contain additional model specific methods and attributes.
GLS is the superclass of the other regression classes.
References
General reference for regression models:
- D.C. Montgomery and E.A. Peck. ?Introduction to Linear Regression Analysis.? 2nd. Ed., Wiley, 1992.
Econometrics references for regression models:
- R.Davidson and J.G. MacKinnon. ?Econometric Theory and Methods,? Oxford, 2004.
- W.Green. ?Econometric Analysis,? 5th ed., Pearson, 2003.
Attributes
The following is more verbose description of the attributes which is mostly common to all regression classes
-
pinv_wexog : array
-
cholsimgainv : array
-
df_model : float
- The model degrees of freedom is equal to
p
- 1, wherep
is the number of regressors. Note that the intercept is not counted as using a degree of freedom here. -
df_resid : float
- The residual degrees of freedom is equal to the number of observations
n
less the number of parametersp
. Note that the intercept is counted as using a degree of freedom here. -
llf : float
- The value of the likelihood function of the fitted model.
-
nobs : float
- The number of observations
n
-
normalized_cov_params : array
-
sigma : array
-
wexog : array
-
wendog : array
Module Reference
Model Classes
OLS (endog[, exog, missing, hasconst]) | A simple ordinary least squares model. |
GLS (endog, exog[, sigma, missing, hasconst]) | Generalized least squares model with a general covariance structure. |
WLS (endog, exog[, weights, missing, hasconst]) | A regression model with diagonal but non-identity covariance structure. |
GLSAR (endog[, exog, rho, missing]) | A regression model with an AR(p) covariance structure. |
yule_walker (X[, order, method, df, inv, demean]) | Estimate AR(p) parameters from a sequence X using Yule-Walker equation. |
QuantReg (endog, exog, **kwargs) | Quantile Regression |
Results Classes
Fitting a linear regression model returns a results class. OLS has a specific results class with some additional methods compared to the results class of the other linear models.
RegressionResults (model, params[, ...]) | This class summarizes the fit of a linear regression model. |
OLSResults (model, params[, ...]) | Results class for for an OLS model. |
QuantRegResults (model, params[, ...]) | Results instance for the QuantReg model |
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