Statsmodels Examples Python Wls Py At Main Github

Leo Migdal

-Dec 4, 2025, 11:39 AM

statsmodels examples python wls py at main github

There was an error while loading. Please reload this page. Misspecification: true model is quadratic, estimate only linear Two groups for error variance, low and high variance groups In this example, w is the standard deviation of the error. WLS requires that the weights are proportional to the inverse of the error variance.

Compare the WLS standard errors to heteroscedasticity corrected OLS standard errors: Draw a plot to compare predicted values in WLS and OLS: When performing linear regression, Ordinary Least Squares (OLS) is often the go-to method. However, OLS relies on several key assumptions, one of the most critical being that the variance of the errors is constant across all observations (homoscedasticity). What happens when this assumption is violated, a phenomenon known as heteroscedasticity? Enter Weighted Least Squares (WLS).

This powerful technique adjusts the regression model to account for varying error variances, leading to more efficient and reliable parameter estimates. In this tutorial, we”ll dive into implementing WLS in Python using the robust Statsmodels library, guiding you through the process step-by-step. Weighted Least Squares is a generalization of OLS that allows for observations to have different weights in the regression. In essence, WLS gives more “weight” to observations that are more precise (i.e., have smaller error variance) and less weight to observations that are less precise (have larger error variance). This approach addresses the problem of heteroscedasticity, where the spread of residuals changes across the range of predicted values. If left unaddressed, heteroscedasticity can lead to unbiased but inefficient OLS estimates, meaning your standard errors will be incorrect, and hypothesis tests might be misleading.

WLS is particularly useful in situations where the reliability or precision of your data points varies. Here are some common scenarios: There was an error while loading. Please reload this page. This page provides a series of examples, tutorials and recipes to help you get started with statsmodels. Each of the examples shown here is made available as an IPython Notebook and as a plain python script on the statsmodels github repository.

We also encourage users to submit their own examples, tutorials or cool statsmodels trick to the Examples wiki page SARIMAX: Frequently Asked Questions (FAQ) State space modeling: Local Linear Trends Fixed / constrained parameters in state space models State space modeling: Local Linear Trends State space models: concentrating out the scale

statsmodels is a Python package that provides a complement to scipy for statistical computations including descriptive statistics and estimation and inference for statistical models. The documentation for the latest release is at The documentation for the development version is at Recent improvements are highlighted in the release notes https://www.statsmodels.org/stable/release/ When performing linear regression, we often assume that the errors (residuals) are equally spread across all observations.

This is known as homoscedasticity. However, in many real-world datasets, this assumption doesn’t hold true. When the variance of the errors is not constant, we encounter a phenomenon called heteroscedasticity. Ignoring heteroscedasticity can lead to inefficient parameter estimates and incorrect standard errors, making your statistical inferences unreliable. This is where Weighted Least Squares (WLS) regression comes to the rescue. In this comprehensive guide, we’ll explore WLS and demonstrate how to implement it effectively using the powerful Statsmodels library in Python.

Weighted Least Squares is a variation of Ordinary Least Squares (OLS) regression. While OLS minimizes the sum of the squared residuals, WLS minimizes a weighted sum of squared residuals. Heteroscedasticity: This is the primary reason. When errors have different variances, observations with larger variances contribute more “noise” to the model. WLS assigns smaller weights to observations with larger variances and larger weights to observations with smaller variances, effectively “down-weighting” the noisier data points. Varying Precision: Some observations might be inherently more precise or reliable than others.

WLS allows you to incorporate this prior knowledge into your model by giving more precise observations higher weights. The weights are presumed to be (proportional to) the inverse of the variance of the observations. That is, if the variables are to be transformed by 1/sqrt(W) you must supply weights = 1/W. A 1-d endogenous response variable. The dependent variable. A nobs x k array where nobs is the number of observations and k is the number of regressors.

An intercept is not included by default and should be added by the user. See statsmodels.tools.add_constant. A 1d array of weights. If you supply 1/W then the variables are pre- multiplied by 1/sqrt(W). If no weights are supplied the default value is 1 and WLS results are the same as OLS. Available options are ‘none’, ‘drop’, and ‘raise’.

If ‘none’, no nan checking is done. If ‘drop’, any observations with nans are dropped. If ‘raise’, an error is raised. Default is ‘none’. This wiki page assembles a collection "official" and user-contributed examples, tutorials and recipes for statsmodels. A set of notebook examples are provided as part of the official Statsmodels documentation.

If you have an interesting example, or if you can write a quick tutorial describing one of statsmodels' features, please consider posting it here. We would be delighted! Feel free to post your example file in any of the common formats (e.g. .py, .rst, .html) and to use any hosting service you like. One very slick, free, and convenient alternative is to: www.dropbox.com/scl/fo/mylhfjbpl2zlc5z5m4prq/h?dl=0&rlkey=li52chs6rcl6lejspde6n0oqf

Statsmodels Examples Python Wls Py At Main Github

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Compare The WLS Standard Errors To Heteroscedasticity Corrected OLS Standard

This Powerful Technique Adjusts The Regression Model To Account For

WLS Is Particularly Useful In Situations Where The Reliability Or

We Also Encourage Users To Submit Their Own Examples, Tutorials