Returns : | **Attributes** :
aic :
Aikake’s information criteria
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bic :
Bayes’ information criteria
System Message: WARNING/2 (-2llf + \log(n)(df_model+1))
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(./math.tex
LaTeX2e <2005/12/01>
Babel <v3.8l> and hyphenation patterns for english, usenglishmax, dumylang, noh
yphenation, loaded.
(/usr/share/texmf-texlive/tex/latex/base/article.cls
Document Class: article 2005/09/16 v1.4f Standard LaTeX document class
(/usr/share/texmf-texlive/tex/latex/base/size12.clo))
(/usr/share/texmf-texlive/tex/latex/base/inputenc.sty
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pinv_wexog :
See specific model class docstring
centered_tss :
The total sum of squares centered about the mean
cov_HC0 :
See HC0_se below. Only available after calling HC0_se.
cov_HC1 :
See HC1_se below. Only available after calling HC1_se.
cov_HC2 :
See HC2_se below. Only available after calling HC2_se.
cov_HC3 :
See HC3_se below. Only available after calling HC3_se.
df_model : :
Model degress of freedom. The number of regressors p - 1 for the
constant Note that df_model does not include the constant even though
the design does. The design is always assumed to have a constant
in calculating results for now.
df_resid :
Residual degrees of freedom. n - p. Note that the constant is
included in calculating the residual degrees of freedom.
ess :
Explained sum of squares. The centered total sum of squares minus
the sum of squared residuals.
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 :
Only available if HC#_se 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 property. It is not evaluated until it is called.
When it is called the RegressionResults instance will then have
another attribute cov_HC0, which is the full heteroskedasticity
consistent covariance matrix and also het_scale, which is in
this case just resid**2. HCCM matrices are only appropriate for OLS.
HC1_se :
MacKinnon and White’s (1985) alternative heteroskedasticity robust
standard errors.
Defined as sqrt(diag(n/(n-p)*HC_0)
HC1_se is a property. It is not evaluated until it is called.
When it is called the RegressionResults instance will then have
another attribute cov_HC1, which is the full HCCM and also het_scale,
which is in this case n/(n-p)*resid**2. HCCM matrices are only
appropriate for OLS.
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_se is a property. It is not evaluated until it is called.
When it is called the RegressionResults instance will then have
another attribute cov_HC2, which is the full HCCM and also het_scale,
which is in this case is resid^(2)/(1-h_ii). HCCM matrices are only
appropriate for OLS.
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_se is a property. It is not evaluated until it is called.
When it is called the RegressionResults instance will then have
another attribute cov_HC3, which is the full HCCM and also het_scale,
which is in this case is resid^(2)/(1-h_ii)^(2). HCCM matrices are
only appropriate for OLS.
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.
rsquared :
R-squared of a model with an intercept. This is defined here as
1 - ssr/centered_tss
rsquared_adj :
Adjusted R-squared. This is defined here as
1 - (n-1)/(n-p)*(1-rsquared)
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.
stand_errors :
The standard errors of the parameter estimates.
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)
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