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

A simple ordinary least squares model.

Parameters :

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 interecept 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.


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


>>> 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>


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


fit([method]) Full fit of the model.
from_formula(formula, data[, subset]) Create a Model from a formula and dataframe.
hessian(params) The Hessian matrix of the model
information(params) Fisher information matrix of model
loglike(params) The likelihood function for the clasical OLS model.
predict(params[, exog]) Return linear predicted values from a design matrix.
score(params) Score vector of model.
whiten(Y) OLS model whitener does nothing: returns Y.


df_model The model degree of freedom, defined as the rank of the regressor
df_resid The residual degree of freedom, defined as the number of observations

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