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 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

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 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.

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
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()

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
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