# statsmodels.regression.linear_model.OLS¶

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

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

Examples

>>> 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>


Notes

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

Methods

 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.

Attributes

 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