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<section id="linear-regression">
<span id="regression"></span><h1>Linear Regression<a class="headerlink" href="#linear-regression" title="Link to this heading">#</a></h1>
<p>Linear models with independently and identically distributed errors, and for
errors with heteroscedasticity or autocorrelation. This module allows
estimation by ordinary least squares (OLS), weighted least squares (WLS),
generalized least squares (GLS), and feasible generalized least squares with
autocorrelated AR(p) errors.</p>
<p>See <a class="reference internal" href="#module-reference">Module Reference</a> for commands and arguments.</p>
<section id="examples">
<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading">#</a></h2>
<div class="highlight-ipython notranslate"><div class="highlight"><pre><span></span><span class="go"># Load modules and data</span>
<span class="gp">In [1]: </span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="gp">In [2]: </span><span class="kn">import</span><span class="w"> </span><span class="nn">statsmodels.api</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">sm</span>
<span class="gp">In [3]: </span><span class="n">spector_data</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">datasets</span><span class="o">.</span><span class="n">spector</span><span class="o">.</span><span class="n">load</span><span class="p">()</span>
<span class="gp">In [4]: </span><span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">add_constant</span><span class="p">(</span><span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span><span class="p">,</span> <span class="n">prepend</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="go"># Fit and summarize OLS model</span>
<span class="gp">In [5]: </span><span class="n">mod</span> <span class="o">=</span> <span class="n">sm</span><span class="o">.</span><span class="n">OLS</span><span class="p">(</span><span class="n">spector_data</span><span class="o">.</span><span class="n">endog</span><span class="p">,</span> <span class="n">spector_data</span><span class="o">.</span><span class="n">exog</span><span class="p">)</span>
<span class="gp">In [6]: </span><span class="n">res</span> <span class="o">=</span> <span class="n">mod</span><span class="o">.</span><span class="n">fit</span><span class="p">()</span>
<span class="gp">In [7]: </span><span class="nb">print</span><span class="p">(</span><span class="n">res</span><span class="o">.</span><span class="n">summary</span><span class="p">())</span>
<span class="go"> OLS Regression Results </span>
<span class="go">==============================================================================</span>
<span class="go">Dep. Variable: GRADE R-squared: 0.416</span>
<span class="go">Model: OLS Adj. R-squared: 0.353</span>
<span class="go">Method: Least Squares F-statistic: 6.646</span>
<span class="go">Date: Mon, 31 Aug 2026 Prob (F-statistic): 0.00157</span>
<span class="go">Time: 17:36:53 Log-Likelihood: -12.978</span>
<span class="go">No. Observations: 32 AIC: 33.96</span>
<span class="go">Df Residuals: 28 BIC: 39.82</span>
<span class="go">Df Model: 3 </span>
<span class="go">Covariance Type: nonrobust </span>
<span class="go">==============================================================================</span>
<span class="go"> coef std err t P>|t| [0.025 0.975]</span>
<span class="gt">------------------------------------------------------------------------------</span>
<span class="n">GPA</span> <span class="mf">0.4639</span> <span class="mf">0.162</span> <span class="mf">2.864</span> <span class="mf">0.008</span> <span class="mf">0.132</span> <span class="mf">0.796</span>
<span class="n">TUCE</span> <span class="mf">0.0105</span> <span class="mf">0.019</span> <span class="mf">0.539</span> <span class="mf">0.594</span> <span class="o">-</span><span class="mf">0.029</span> <span class="mf">0.050</span>
<span class="n">PSI</span> <span class="mf">0.3786</span> <span class="mf">0.139</span> <span class="mf">2.720</span> <span class="mf">0.011</span> <span class="mf">0.093</span> <span class="mf">0.664</span>
<span class="n">const</span> <span class="o">-</span><span class="mf">1.4980</span> <span class="mf">0.524</span> <span class="o">-</span><span class="mf">2.859</span> <span class="mf">0.008</span> <span class="o">-</span><span class="mf">2.571</span> <span class="o">-</span><span class="mf">0.425</span>
<span class="o">==============================================================================</span>
<span class="ne">Omnibus</span>: 0.176 Durbin-Watson: 2.346
<span class="n">Prob</span><span class="p">(</span><span class="n">Omnibus</span><span class="p">):</span> <span class="mf">0.916</span> <span class="n">Jarque</span><span class="o">-</span><span class="n">Bera</span> <span class="p">(</span><span class="n">JB</span><span class="p">):</span> <span class="mf">0.167</span>
<span class="ne">Skew</span>: 0.141 Prob(JB): 0.920
<span class="ne">Kurtosis</span>: 2.786 Cond. No. 176.
<span class="o">==============================================================================</span>
<span class="ne">Notes</span>:
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="n">Standard</span> <span class="n">Errors</span> <span class="n">assume</span> <span class="n">that</span> <span class="n">the</span> <span class="n">covariance</span> <span class="n">matrix</span> <span class="n">of</span> <span class="n">the</span> <span class="n">errors</span> <span class="ow">is</span> <span class="n">correctly</span> <span class="n">specified</span><span class="o">.</span>
</pre></div>
</div>
<p>Detailed examples can be found here:</p>
<ul class="simple">
<li><p><a class="reference internal" href="examples/notebooks/generated/ols.html"><span class="doc">OLS</span></a></p></li>
<li><p><a class="reference internal" href="examples/notebooks/generated/wls.html"><span class="doc">WLS</span></a></p></li>
<li><p><a class="reference internal" href="examples/notebooks/generated/gls.html"><span class="doc">GLS</span></a></p></li>
<li><p><a class="reference internal" href="examples/notebooks/generated/recursive_ls.html"><span class="doc">Recursive LS</span></a></p></li>
<li><p><a class="reference internal" href="examples/notebooks/generated/rolling_ls.html"><span class="doc">Rolling LS</span></a></p></li>
</ul>
</section>
<section id="technical-documentation">
<h2>Technical Documentation<a class="headerlink" href="#technical-documentation" title="Link to this heading">#</a></h2>
<p>The statistical model is assumed to be</p>
<blockquote>
<div><p><span class="math notranslate nohighlight">\(Y = X\beta + \epsilon\)</span>, where <span class="math notranslate nohighlight">\(\epsilon\sim N\left(0,\Sigma\right).\)</span></p>
</div></blockquote>
<p>Depending on the properties of <span class="math notranslate nohighlight">\(\Sigma\)</span>, we have currently four classes available:</p>
<ul class="simple">
<li><p>GLS : generalized least squares for arbitrary covariance <span class="math notranslate nohighlight">\(\Sigma\)</span></p></li>
<li><p>OLS : ordinary least squares for i.i.d. errors <span class="math notranslate nohighlight">\(\Sigma=\textbf{I}\)</span></p></li>
<li><p>WLS : weighted least squares for heteroskedastic errors <span class="math notranslate nohighlight">\(\text{diag}\left (\Sigma\right)\)</span></p></li>
<li><p>GLSAR : feasible generalized least squares with autocorrelated AR(p) errors
<span class="math notranslate nohighlight">\(\Sigma=\Sigma\left(\rho\right)\)</span></p></li>
</ul>
<p>All regression models define the same methods and follow the same structure,
and can be used in a similar fashion. Some of them contain additional model
specific methods and attributes.</p>
<p>GLS is the superclass of the other regression classes except for RecursiveLS,
RollingWLS and RollingOLS.</p>
<section id="references">
<h3>References<a class="headerlink" href="#references" title="Link to this heading">#</a></h3>
<p>General reference for regression models:</p>
<ul class="simple">
<li><p>D.C. Montgomery and E.A. Peck. “Introduction to Linear Regression Analysis.” 2nd. Ed., Wiley, 1992.</p></li>
</ul>
<p>Econometrics references for regression models:</p>
<ul class="simple">
<li><p>R.Davidson and J.G. MacKinnon. “Econometric Theory and Methods,” Oxford, 2004.</p></li>
<li><p>W.Green. “Econometric Analysis,” 5th ed., Pearson, 2003.</p></li>
</ul>
<div class="toctree-wrapper compound">
</div>
</section>
<section id="attributes">
<h3>Attributes<a class="headerlink" href="#attributes" title="Link to this heading">#</a></h3>
<p>The following is more verbose description of the attributes which is mostly
common to all regression classes</p>
<dl class="simple">
<dt>pinv_wexog<span class="classifier">array</span></dt><dd><p>The <cite>p</cite> x <cite>n</cite> Moore-Penrose pseudoinverse of the whitened design matrix.
It is approximately equal to
<span class="math notranslate nohighlight">\(\left(X^{T}\Sigma^{-1}X\right)^{-1}X^{T}\Psi\)</span>, where
<span class="math notranslate nohighlight">\(\Psi\)</span> is defined such that <span class="math notranslate nohighlight">\(\Psi\Psi^{T}=\Sigma^{-1}\)</span>.</p>
</dd>
<dt>cholsimgainv<span class="classifier">array</span></dt><dd><p>The <cite>n</cite> x <cite>n</cite> upper triangular matrix <span class="math notranslate nohighlight">\(\Psi^{T}\)</span> that satisfies
<span class="math notranslate nohighlight">\(\Psi\Psi^{T}=\Sigma^{-1}\)</span>.</p>
</dd>
<dt>df_model<span class="classifier">float</span></dt><dd><p>The model degrees of freedom. This is equal to <cite>p</cite> - 1, where <cite>p</cite> is the
number of regressors. Note that the intercept is not counted as using a
degree of freedom here.</p>
</dd>
<dt>df_resid<span class="classifier">float</span></dt><dd><p>The residual degrees of freedom. This is equal <cite>n - p</cite> where <cite>n</cite> is the
number of observations and <cite>p</cite> is the number of parameters. Note that the
intercept is counted as using a degree of freedom here.</p>
</dd>
<dt>llf<span class="classifier">float</span></dt><dd><p>The value of the likelihood function of the fitted model.</p>
</dd>
<dt>nobs<span class="classifier">float</span></dt><dd><p>The number of observations <cite>n</cite></p>
</dd>
<dt>normalized_cov_params<span class="classifier">array</span></dt><dd><p>A <cite>p</cite> x <cite>p</cite> array equal to <span class="math notranslate nohighlight">\((X^{T}\Sigma^{-1}X)^{-1}\)</span>.</p>
</dd>
<dt>sigma<span class="classifier">array</span></dt><dd><p>The <cite>n</cite> x <cite>n</cite> covariance matrix of the error terms:
<span class="math notranslate nohighlight">\(\epsilon\sim N\left(0,\Sigma\right)\)</span>.</p>
</dd>
<dt>wexog<span class="classifier">array</span></dt><dd><p>The whitened design matrix <span class="math notranslate nohighlight">\(\Psi^{T}X\)</span>.</p>
</dd>
<dt>wendog<span class="classifier">array</span></dt><dd><p>The whitened response variable <span class="math notranslate nohighlight">\(\Psi^{T}Y\)</span>.</p>
</dd>
</dl>
</section>
</section>
<section id="module-statsmodels.regression.linear_model">
<span id="module-reference"></span><h2>Module Reference<a class="headerlink" href="#module-statsmodels.regression.linear_model" title="Link to this heading">#</a></h2>
<section id="model-classes">
<h3>Model Classes<a class="headerlink" href="#model-classes" title="Link to this heading">#</a></h3>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.OLS.html#statsmodels.regression.linear_model.OLS" title="statsmodels.regression.linear_model.OLS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OLS</span></code></a>(endog[, exog, missing, hasconst])</p></td>
<td><p>Ordinary Least Squares</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.GLS.html#statsmodels.regression.linear_model.GLS" title="statsmodels.regression.linear_model.GLS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GLS</span></code></a>(endog, exog[, sigma, missing, hasconst])</p></td>
<td><p>Generalized Least Squares</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.WLS.html#statsmodels.regression.linear_model.WLS" title="statsmodels.regression.linear_model.WLS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">WLS</span></code></a>(endog, exog[, weights, missing, hasconst])</p></td>
<td><p>Weighted Least Squares</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.GLSAR.html#statsmodels.regression.linear_model.GLSAR" title="statsmodels.regression.linear_model.GLSAR"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GLSAR</span></code></a>(endog[, exog, rho, missing, hasconst])</p></td>
<td><p>Generalized Least Squares with AR covariance structure</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.yule_walker.html#statsmodels.regression.linear_model.yule_walker" title="statsmodels.regression.linear_model.yule_walker"><code class="xref py py-obj docutils literal notranslate"><span class="pre">yule_walker</span></code></a>(x[, order, method, df, inv, ...])</p></td>
<td><p>Estimate AR(p) parameters from a sequence using the Yule-Walker equations.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.YuleWalkerResult.html#statsmodels.regression.linear_model.YuleWalkerResult" title="statsmodels.regression.linear_model.YuleWalkerResult"><code class="xref py py-obj docutils literal notranslate"><span class="pre">YuleWalkerResult</span></code></a>(rho, sigma, Rinv)</p></td>
<td><p>Result of <a class="reference internal" href="generated/statsmodels.regression.linear_model.yule_walker.html#statsmodels.regression.linear_model.yule_walker" title="statsmodels.regression.linear_model.yule_walker"><code class="xref py py-func docutils literal notranslate"><span class="pre">yule_walker</span></code></a>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.burg.html#statsmodels.regression.linear_model.burg" title="statsmodels.regression.linear_model.burg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">burg</span></code></a>(endog[, order, demean])</p></td>
<td><p>Compute Burg's AP(p) parameter estimator.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.quantile_regression.QuantReg.html#statsmodels.regression.quantile_regression.QuantReg" title="statsmodels.regression.quantile_regression.QuantReg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">QuantReg</span></code></a>(endog, exog, **kwargs)</p></td>
<td><p>Quantile Regression</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.recursive_ls.RecursiveLS.html#statsmodels.regression.recursive_ls.RecursiveLS" title="statsmodels.regression.recursive_ls.RecursiveLS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RecursiveLS</span></code></a>(endog, exog[, constraints])</p></td>
<td><p>Recursive least squares</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.rolling.RollingWLS.html#statsmodels.regression.rolling.RollingWLS" title="statsmodels.regression.rolling.RollingWLS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RollingWLS</span></code></a>(endog, exog[, window, weights, ...])</p></td>
<td><p>Rolling Weighted Least Squares</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.regression.rolling.RollingOLS.html#statsmodels.regression.rolling.RollingOLS" title="statsmodels.regression.rolling.RollingOLS"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RollingOLS</span></code></a>(endog, exog[, window, min_nobs, ...])</p></td>
<td><p>Rolling Ordinary Least Squares</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.process_regression.GaussianCovariance.html#statsmodels.regression.process_regression.GaussianCovariance" title="statsmodels.regression.process_regression.GaussianCovariance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GaussianCovariance</span></code></a>()</p></td>
<td><p>An implementation of ProcessCovariance using the Gaussian kernel</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.regression.process_regression.ProcessMLE.html#statsmodels.regression.process_regression.ProcessMLE" title="statsmodels.regression.process_regression.ProcessMLE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ProcessMLE</span></code></a>(endog, exog, exog_scale, ...[, cov])</p></td>
<td><p>Fit a Gaussian mean/variance regression model</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.dimred.SlicedInverseReg.html#statsmodels.regression.dimred.SlicedInverseReg" title="statsmodels.regression.dimred.SlicedInverseReg"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SlicedInverseReg</span></code></a>(endog, exog, **kwargs)</p></td>
<td><p>Sliced Inverse Regression (SIR)</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.regression.dimred.PrincipalHessianDirections.html#statsmodels.regression.dimred.PrincipalHessianDirections" title="statsmodels.regression.dimred.PrincipalHessianDirections"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PrincipalHessianDirections</span></code></a>(endog, exog, **kwargs)</p></td>
<td><p>Principal Hessian Directions (PHD)</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.dimred.SlicedAverageVarianceEstimation.html#statsmodels.regression.dimred.SlicedAverageVarianceEstimation" title="statsmodels.regression.dimred.SlicedAverageVarianceEstimation"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SlicedAverageVarianceEstimation</span></code></a>(endog, exog, ...)</p></td>
<td><p>Sliced Average Variance Estimation (SAVE)</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="results-classes">
<h3>Results Classes<a class="headerlink" href="#results-classes" title="Link to this heading">#</a></h3>
<p>Fitting a linear regression model returns a results class. OLS has a
specific results class with some additional methods compared to the
results class of the other linear models.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.RegressionResults.html#statsmodels.regression.linear_model.RegressionResults" title="statsmodels.regression.linear_model.RegressionResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RegressionResults</span></code></a>(model, params[, ...])</p></td>
<td><p>This class summarizes the fit of a linear regression model.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.CompareLRTestResult.html#statsmodels.regression.linear_model.CompareLRTestResult" title="statsmodels.regression.linear_model.CompareLRTestResult"><code class="xref py py-obj docutils literal notranslate"><span class="pre">CompareLRTestResult</span></code></a>(statistic, pvalue, df_diff)</p></td>
<td><p>Result of <a class="reference internal" href="generated/statsmodels.regression.linear_model.RegressionResults.compare_lr_test.html#statsmodels.regression.linear_model.RegressionResults.compare_lr_test" title="statsmodels.regression.linear_model.RegressionResults.compare_lr_test"><code class="xref py py-meth docutils literal notranslate"><span class="pre">RegressionResults.compare_lr_test</span></code></a>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.ELTestResult.html#statsmodels.regression.linear_model.ELTestResult" title="statsmodels.regression.linear_model.ELTestResult"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ELTestResult</span></code></a>(statistic, pvalue, weights, ...)</p></td>
<td><p>Result of <code class="xref py py-meth docutils literal notranslate"><span class="pre">RegressionResults.el_test</span></code>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.OLSResults.html#statsmodels.regression.linear_model.OLSResults" title="statsmodels.regression.linear_model.OLSResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">OLSResults</span></code></a>(model, params[, ...])</p></td>
<td><p>Results class for an OLS model.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.linear_model.PredictionResults.html#statsmodels.regression.linear_model.PredictionResults" title="statsmodels.regression.linear_model.PredictionResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PredictionResults</span></code></a>(predicted_mean, ...[, df, ...])</p></td>
<td><p>Results class for predictions</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.base.elastic_net.RegularizedResults.html#statsmodels.base.elastic_net.RegularizedResults" title="statsmodels.base.elastic_net.RegularizedResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RegularizedResults</span></code></a>(model, params)</p></td>
<td><p>Results for models estimated using regularization</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.quantile_regression.QuantRegResults.html#statsmodels.regression.quantile_regression.QuantRegResults" title="statsmodels.regression.quantile_regression.QuantRegResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">QuantRegResults</span></code></a>(model, params[, ...])</p></td>
<td><p>Results instance for the QuantReg model</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.recursive_ls.RecursiveLSResults.html#statsmodels.regression.recursive_ls.RecursiveLSResults" title="statsmodels.regression.recursive_ls.RecursiveLSResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RecursiveLSResults</span></code></a>(model, params, filter_results)</p></td>
<td><p>Class to hold results from fitting a recursive least squares model</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.rolling.RollingRegressionResults.html#statsmodels.regression.rolling.RollingRegressionResults" title="statsmodels.regression.rolling.RollingRegressionResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">RollingRegressionResults</span></code></a>(model, store, ...)</p></td>
<td><p>Results from rolling regressions</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.process_regression.ProcessMLEResults.html#statsmodels.regression.process_regression.ProcessMLEResults" title="statsmodels.regression.process_regression.ProcessMLEResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ProcessMLEResults</span></code></a>(model, mlefit)</p></td>
<td><p>Results class for Gaussian process regression models</p></td>
</tr>
</tbody>
</table>
</div>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/statsmodels.regression.dimred.DimReductionResults.html#statsmodels.regression.dimred.DimReductionResults" title="statsmodels.regression.dimred.DimReductionResults"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DimReductionResults</span></code></a>(model, params, eigs)</p></td>
<td><p>Results class for a dimension reduction regression</p></td>
</tr>
</tbody>
</table>
</div>
</section>
</section>
</section>
</article>
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