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)[source]¶ This class summarizes the fit of a linear regression model.
It handles the output of contrasts, estimates of covariance, etc.
Returns: Attributes
aic
Aikake’s information criteria. For a model with a constant . For a model without a constant .
bic
Bayes’ information criteria For a model with a constant . For a model without a constant
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 tstats
df_model
Model degress 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
Fstatistic 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
pvalue of the Fstatistic
fittedvalues
The predicted the 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.
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/(np)*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/(np)*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)/(1h_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)/(1h_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)/(1h_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)/(1h_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 twotailed p values for the tstats of the params.
resid
The residuals of the model.
resid_pearson
wresid normalized to have unit variance.
rsquared
Rsquared 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 Rsquared. This is defined here as 1  (nobs1)/df_resid * (1rsquared) if a constant is included and 1  nobs/df_resid * (1rsquared) if no constant is included.
scale
A scale factor for the covariance matrix. Default value is ssr/(np). 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 eigenvals
()Return eigenvalues sorted in decreasing order. ess
()f_pvalue
()fittedvalues
()fvalue
()get_robustcov_results
([cov_type, use_t])create new results instance with robust covariance as default mse_model
()mse_resid
()mse_total
()nobs
()resid
()resid_pearson
()Residuals, normalized to have unit variance. rsquared
()rsquared_adj
()scale
()ssr
()summary
([yname, xname, title, alpha])Summarize the Regression Results summary2
([yname, xname, title, alpha, ...])Experimental summary function to summarize the regression results uncentered_tss
()wresid
()Attributes
use_t