class statsmodels.regression.linear_model.OLS(endog, exog=None, missing='none', hasconst=None, **kwargs) [source]

A simple ordinary least squares model.

  • endog (array-like) – 1-d endogenous response variable. The dependent variable.
  • exog (array-like) – A nobs x k array where nobs is the number of observations and k is the number of regressors. An intercept is not included by default and should be added by the user. See statsmodels.tools.add_constant.
  • missing (str) – Available options are ‘none’, ‘drop’, and ‘raise’. If ‘none’, no nan checking is done. If ‘drop’, any observations with nans are dropped. If ‘raise’, an error is raised. Default is ‘none.’
  • hasconst (None or bool) – Indicates whether the RHS includes a user-supplied constant. If True, a constant is not checked for and k_constant is set to 1 and all result statistics are calculated as if a constant is present. If False, a constant is not checked for and k_constant is set to 0.

scalar – Has an attribute weights = array(1.0) due to inheritance from WLS.

See also



>>> import numpy as np
>>> import statsmodels.api as sm
>>> Y = [1,3,4,5,2,3,4]
>>> X = range(1,8)
>>> X = sm.add_constant(X)
>>> model = sm.OLS(Y,X)
>>> results = model.fit()
>>> results.params
array([ 2.14285714,  0.25      ])
>>> results.tvalues
array([ 1.87867287,  0.98019606])
>>> print(results.t_test([1, 0]))
<T test: effect=array([ 2.14285714]), sd=array([[ 1.14062282]]), t=array([[ 1.87867287]]), p=array([[ 0.05953974]]), df_denom=5>
>>> print(results.f_test(np.identity(2)))
<F test: F=array([[ 19.46078431]]), p=[[ 0.00437251]], df_denom=5, df_num=2>


No constant is added by the model unless you are using formulas.


fit([method, cov_type, cov_kwds, use_t]) Full fit of the model.
fit_regularized([method, alpha, L1_wt, …]) Return a regularized fit to a linear regression model.
from_formula(formula, data[, subset, drop_cols]) Create a Model from a formula and dataframe.
get_distribution(params, scale[, exog, …]) Returns a random number generator for the predictive distribution.
hessian(params[, scale]) Evaluate the Hessian function at a given point.
hessian_factor(params[, scale, observed]) Weights for calculating Hessian
information(params) Fisher information matrix of model
initialize() Initialize (possibly re-initialize) a Model instance.
loglike(params[, scale]) The likelihood function for the OLS model.
predict(params[, exog]) Return linear predicted values from a design matrix.
score(params[, scale]) Evaluate the score function at a given point.
whiten(Y) OLS model whitener does nothing: returns Y.


df_model The model degree of freedom, defined as the rank of the regressor matrix minus 1 if a constant is included.
df_resid The residual degree of freedom, defined as the number of observations minus the rank of the regressor matrix.
endog_names Names of endogenous variables
exog_names Names of exogenous variables

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.