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

A simple ordinary least squares model.


1-d endogenous response variable. The dependent variable.


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


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.’

hasconstNone 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.

See also



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 =
>>> 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>

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


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


Fisher information matrix of model


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.


OLS model whitener does nothing: returns Y.