statsmodels.regression.linear_model.RegressionResults

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]

詳細的註釋回頭再寫~

This class summarizes the fit of a linear regression model
It handles the output of contrasts, estimates of covariance, etc.

Returns:

• aic – Akaike’s information criteria. For a model with a constant −2llf+2(df_model+1)−2llf+2(df_model+1). For a model without a constant −2llf+2(df_model)−2llf+2(df_model).
• bic – Bayes’ information criteria. For a model with a constant −2llf+log(n)(df_model+1)−2llf+log⁡(n)(df_model+1). For a model without a constant −2llf+log(n)(df_model)−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