# statsmodels.regression.linear_model.RegressionResults¶

class statsmodels.regression.linear_model.RegressionResults(model, params, normalized_cov_params=None, scale=1.0, cov_type='nonrobust', cov_kwds=None, use_t=None, **kwargs)[source]

This class summarizes the fit of a linear regression model.

It handles the output of contrasts, estimates of covariance, etc.

Parameters
modelRegressionModel

The regression model instance.

paramsndarray

The estimated parameters.

normalized_cov_paramsndarray

The normalized covariance parameters.

scalefloat

The estimated scale of the residuals.

cov_typestr

The covariance estimator used in the results.

cov_kwdsdict

Additional keywords used in the covariance specification.

use_tbool

Flag indicating to use the Student’s t in inference.

**kwargs

Additional keyword arguments used to initialize the results.

Attributes
pinv_wexog

See model class docstring for implementation details.

cov_type

Parameter covariance estimator used for standard errors and t-stats.

df_model

Model degrees of freedom. The number of regressors p. Does not include the constant if one is present.

df_resid

Residual degrees of freedom. n - p - 1, if a constant is present. n - p if a constant is not included.

het_scale

adjusted squared residuals for heteroscedasticity robust standard errors. Is only available after HC#_se or cov_HC# is called. See HC#_se for more information.

history

Estimation history for iterative estimators.

model

A pointer to the model instance that called fit() or results.

params

The linear coefficients that minimize the least squares criterion. This is usually called Beta for the classical linear model.

Methods

 compare_f_test(restricted) Use F test to test whether restricted model is correct. compare_lm_test(restricted[, demean, use_lr]) Use Lagrange Multiplier test to test a set of linear restrictions. compare_lr_test(restricted[, large_sample]) Likelihood ratio test to test whether restricted model is correct. conf_int([alpha, cols]) Compute the confidence interval of the fitted parameters. cov_params([r_matrix, column, scale, cov_p, …]) Compute the variance/covariance matrix. f_test(r_matrix[, cov_p, scale, invcov]) Compute the F-test for a joint linear hypothesis. get_prediction([exog, transform, weights, …]) Compute prediction results. get_robustcov_results([cov_type, use_t]) Create new results instance with robust covariance as default. initialize(model, params, **kwargs) Initialize (possibly re-initialize) a Results instance. load(fname) Load a pickled results instance See specific model class docstring predict([exog, transform]) Call self.model.predict with self.params as the first argument. Remove data arrays, all nobs arrays from result and model. save(fname[, remove_data]) Save a pickle of this instance. A scale factor for the covariance matrix. summary([yname, xname, title, alpha]) Summarize the Regression Results. summary2([yname, xname, title, alpha, …]) Experimental summary function to summarize the regression results. t_test(r_matrix[, cov_p, scale, use_t]) Compute a t-test for a each linear hypothesis of the form Rb = q. t_test_pairwise(term_name[, method, alpha, …]) Perform pairwise t_test with multiple testing corrected p-values. wald_test(r_matrix[, cov_p, scale, invcov, …]) Compute a Wald-test for a joint linear hypothesis. wald_test_terms([skip_single, …]) Compute a sequence of Wald tests for terms over multiple columns.

Properties

 HC0_se White’s (1980) heteroskedasticity robust standard errors. HC1_se MacKinnon and White’s (1985) heteroskedasticity robust standard errors. HC2_se MacKinnon and White’s (1985) heteroskedasticity robust standard errors. HC3_se MacKinnon and White’s (1985) heteroskedasticity robust standard errors. aic Akaike’s information criteria. bic Bayes’ information criteria. bse The standard errors of the parameter estimates. centered_tss The total (weighted) sum of squares centered about the mean. condition_number Return condition number of exogenous matrix. cov_HC0 Heteroscedasticity robust covariance matrix. cov_HC1 Heteroscedasticity robust covariance matrix. cov_HC2 Heteroscedasticity robust covariance matrix. cov_HC3 Heteroscedasticity robust covariance matrix. eigenvals Return eigenvalues sorted in decreasing order. ess The explained sum of squares. f_pvalue The p-value of the F-statistic. fittedvalues The predicted values for the original (unwhitened) design. fvalue F-statistic of the fully specified model. llf Log-likelihood of model mse_model Mean squared error the model. mse_resid Mean squared error of the residuals. mse_total Total mean squared error. nobs Number of observations n. pvalues The two-tailed p values for the t-stats of the params. resid The residuals of the model. resid_pearson Residuals, normalized to have unit variance. rsquared R-squared of the model. rsquared_adj Adjusted R-squared. ssr Sum of squared (whitened) residuals. tvalues Return the t-statistic for a given parameter estimate. uncentered_tss Uncentered sum of squares. use_t Flag indicating to use the Student’s distribution in inference. wresid The residuals of the transformed/whitened regressand and regressor(s).