Your model looses precision. We’ll explain why. — In the previous article, we saw how leaving out important variables causes the regression model’s coefficients to become biased. In this article, we’ll look at the converse of this situation namely, the damage caused to your regression model from stuffing it with variables that are entirely superfluous. What are irrelevant and superfluous variables?

We’ll understand what is Omitted Variable Bias and illustrate its calculation using a real-world data set — We‘ll study the consequences of failing to include important variables in a linear regression model. For illustration, we’ll base our discussion on a real world data set of automobile characteristics. …

And a tutorial on how to calculate them using a real-world data set — Conditional Variance and Conditional Covariance are concepts that are central to statistical modeling. In this article, we’ll learn what they are, and we’ll illustrate how to calculate them using a real-world data set. First, a quick refresher on what is variance and covariance. Variance of a random variable measures its…

A tutorial on how the variance-covariance matrices are constructed and when to be skeptical about the data they report — I am basing this article on a topic that I hope will be a joy to read for those of you who are mathematically inclined, and also for those of us who have wondered what standard errors are or where they come from. As a quick refresher of concepts: the…

An illustration of how an artifact that is fundamental to regression modeling is constructed, using a real-world data set — The variance-covariance matrix forms the keystone artifact of regression models. The variance-covariance matrix of the regression model’s errors is used to determine whether the model’s error terms are homoskedastic (constant variance) and uncorrelated. The variance-covariance matrix of the fitted regression model’s coefficients is used to derive the standard errors and…

And a Python tutorial to get you up and running with the RE model on a real world data set — The Random Effects regression model is used to estimate the effect of individual-specific characteristics such as grit or acumen that are inherently unmeasurable. Such individual-specific effects are often encountered in panel data studies. …

And a Python tutorial on how to build and train a Fixed Effects model on a real-world panel data set — The Fixed Effects regression model is used to estimate the effect of intrinsic characteristics of individuals in a panel data set. Examples of such intrinsic characteristics are genetics, acumen and cultural factors. Such factors are not directly observable or measurable but one needs to find a way to estimate their…

And a detailed analysis of its goodness-of-fit using Python and statsmodels — In this article, we’ll get to know about panel data datasets, and we’ll learn how to build and train a Pooled OLS regression model for a real world panel data set using statsmodels and Python. After training the Pooled OLSR model, we’ll learn how to analyze the goodness-of-fit of the…

A step-by-step tutorial to get up and running with the Poisson HMM — A Poisson Hidden Markov Model is a mixture of two regression models: A Poisson regression model which is visible and a Markov model which is ‘hidden’. In a Poisson HMM, the mean value predicted by the Poisson model depends on not only the regression variables of the Poisson model, but…