# 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.

Returns: **Attributes** aic – Akaike’s information criteria. For a model with a constant $$-2llf + 2(df\_model + 1)$$. For a model without a constant $$-2llf + 2(df\_model)$$. bic – Bayes’ information criteria. For a model with a constant $$-2llf + \log(n)(df\_model+1)$$. For a model without a constant $$-2llf + \log(n)(df\_model)$$ bse – The standard errors of the parameter estimates. pinv_wexog – See specific model class docstring centered_tss – The total (weighted) sum of squares centered about the mean. cov_HC0 – Heteroscedasticity robust covariance matrix. See HC0_se below. cov_HC1 – Heteroscedasticity robust covariance matrix. See HC1_se below. cov_HC2 – Heteroscedasticity robust covariance matrix. See HC2_se below. cov_HC3 – Heteroscedasticity robust covariance matrix. See HC3_se below. 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. ess – Explained sum of squares. If a constant is present, the centered total sum of squares minus the sum of squared residuals. If there is no constant, the uncentered total sum of squares is used. fvalue – F-statistic of the fully specified model. Calculated as the mean squared error of the model divided by the mean squared error of the residuals. f_pvalue – p-value of the F-statistic fittedvalues – The predicted values for the original (unwhitened) design. 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 HC0_se – White’s (1980) heteroskedasticity robust standard errors. Defined as sqrt(diag(X.T X)^(-1)X.T diag(e_i^(2)) X(X.T X)^(-1) where e_i = resid[i] HC0_se is a cached property. When HC0_se or cov_HC0 is called the RegressionResults instance will then have another attribute het_scale, which is in this case is just resid**2. HC1_se – MacKinnon and White’s (1985) alternative heteroskedasticity robust standard errors. Defined as sqrt(diag(n/(n-p)*HC_0) HC1_see is a cached property. When HC1_se or cov_HC1 is called the RegressionResults instance will then have another attribute het_scale, which is in this case is n/(n-p)*resid**2. HC2_se – MacKinnon and White’s (1985) alternative heteroskedasticity robust standard errors. Defined as (X.T X)^(-1)X.T diag(e_i^(2)/(1-h_ii)) X(X.T X)^(-1) where h_ii = x_i(X.T X)^(-1)x_i.T HC2_see is a cached property. When HC2_se or cov_HC2 is called the RegressionResults instance will then have another attribute het_scale, which is in this case is resid^(2)/(1-h_ii). HC3_se – MacKinnon and White’s (1985) alternative heteroskedasticity robust standard errors. Defined as (X.T X)^(-1)X.T diag(e_i^(2)/(1-h_ii)^(2)) X(X.T X)^(-1) where h_ii = x_i(X.T X)^(-1)x_i.T HC3_see is a cached property. When HC3_se or cov_HC3 is called the RegressionResults instance will then have another attribute het_scale, which is in this case is resid^(2)/(1-h_ii)^(2). model – A pointer to the model instance that called fit() or results. mse_model – Mean squared error the model. This is the explained sum of squares divided by the model degrees of freedom. mse_resid – Mean squared error of the residuals. The sum of squared residuals divided by the residual degrees of freedom. mse_total – Total mean squared error. Defined as the uncentered total sum of squares divided by n the number of observations. nobs – Number of observations n. normalized_cov_params – See specific model class docstring params – The linear coefficients that minimize the least squares criterion. This is usually called Beta for the classical linear model. pvalues – The two-tailed p values for the t-stats of the params. resid – The residuals of the model. resid_pearson – wresid normalized to have unit variance. rsquared – R-squared of a model with an intercept. This is defined here as 1 - ssr/centered_tss if the constant is included in the model and 1 - ssr/uncentered_tss if the constant is omitted. rsquared_adj – Adjusted R-squared. This is defined here as 1 - (nobs-1)/df_resid * (1-rsquared) if a constant is included and 1 - nobs/df_resid * (1-rsquared) if no constant is included. scale – A scale factor for the covariance matrix. Default value is ssr/(n-p). Note that the square root of scale is often called the standard error of the regression. ssr – Sum of squared (whitened) residuals. uncentered_tss – Uncentered sum of squares. Sum of the squared values of the (whitened) endogenous response variable. wresid – The residuals of the transformed/whitened regressand and regressor(s)

Methods

 HC0_se() See statsmodels.RegressionResults HC1_se() See statsmodels.RegressionResults HC2_se() See statsmodels.RegressionResults HC3_se() See statsmodels.RegressionResults aic() bic() bse() centered_tss() 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 whether restricted model is correct compare_lr_test(restricted[, large_sample]) Likelihood ratio test to test whether restricted model is correct condition_number() Return condition number of exogenous matrix. conf_int([alpha, cols]) Returns the confidence interval of the fitted parameters. cov_HC0() See statsmodels.RegressionResults cov_HC1() See statsmodels.RegressionResults cov_HC2() See statsmodels.RegressionResults cov_HC3() See statsmodels.RegressionResults cov_params([r_matrix, column, scale, cov_p, …]) Returns the variance/covariance matrix. eigenvals() Return eigenvalues sorted in decreasing order. ess() f_pvalue() f_test(r_matrix[, cov_p, scale, invcov]) Compute the F-test for a joint linear hypothesis. fittedvalues() fvalue() 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, **kwd) llf() load(fname) load a pickle, (class method) mse_model() mse_resid() mse_total() nobs() normalized_cov_params() predict([exog, transform]) Call self.model.predict with self.params as the first argument. pvalues() remove_data() remove data arrays, all nobs arrays from result and model resid() resid_pearson() Residuals, normalized to have unit variance. rsquared() rsquared_adj() save(fname[, remove_data]) save a pickle of this instance scale() ssr() 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 tvalues() Return the t-statistic for a given parameter estimate. uncentered_tss() 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 wresid()

Attributes

 use_t