Class 3 - Basic Regression

ARE YOU NOT ENTERTAINED?
[left: joint posterior distribution; right: sample lines from the posterior, with conventional gray regression line contour] pic.twitter.com/OBVmVOV5Wa
— Richard McElreath 🦔 (@rlmcelreath) October 29, 2021

Zoom

: 12:00pm - 2:45pm, January 31, 2022

Required Readings

Chapter 4: Geocentric models (Sections 4.1-4.4)

Lecture

Lecture 3

Slides

Link to pdf

Comprehension questions

How is a linear regression similar to a Geocentric modeling approach?

Linear regression are essentially Geocentric models. They are descriptively accurate, mechanistically wrong, and a general method of approximation.

Why are Normal (Gaussian) distributions common?

The generative argument implies that summed fluctuations tend towards normal distributions.
The statistical argument implies that estimate mean and variance (which what linear regressions are doing), the normal distribution is the least informative distribution. This is the maximum entropy argument that we’ll cover later in the course when we consider Information Theory.
The main takeaway is the variable does not have to be normally distributed for the normal model to be useful.

Why is rescaling (standardization) important for modeling?

Rescaling has multiple benefits. First, it enables comparison across different variables that have different scales (e.g., weight in pounds and height in centimeters).
Second, it enables simpler priors based on standardized distributions (e.g., Normal(0, 1) or Normal(0,5)).
Third, later in the course we’ll see where scaling makes computationally intensive (MCMC) easier; or said differently, MCMC algorithms may run slower on non-scaled data.
Rescaling also makes the intercept (alpha) means the expected dependent variable values, (e.g., in weight/height it means the expected adult weight (the DV)).