Linear regression is a population model that relates a target variable to one or multiple regressors , which can be linear or non-linear function(s) of independent variables, through an equation that is linear in parameters and the error : + + . The target and independent variables, and hence the parameters , all belong to the population and not a specific sample (hence the name population model). The subscripts and refer to different observations and independent variables, respectively, and the error (not to be confused with residual) represents the variations (from one observation to the other) in that are not explainable with variations in the s. The actual value of the population parameters will be known only if we measure the entire population, which is almost never possible. Therefore, we have no choice but to estimate these parameters somehow and use the estimated values in our population model.

Covers: theory of Linear regression
Estimated time needed to finish: 10 minutes
Questions this item addresses:
  • What is linear regression?
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Linear regression

Collaborators
Total time needed: ~37 minutes
Objectives
you learn the assumptions behind linear regression and, more importantly, what will occur if those assumptions are violated.
Potential Use Cases
refreshing knowledge on linear regression, preparing for job interview questions
Who is this for ?
BEGINNERpeople entering the field of data science and data scientists who think stat is their weak point
Click on each of the following annotated items to see details.
WRITEUP 1. What is linear regression
  • What is linear regression?
10 minutes
WRITEUP 2. Ordinary Least Squares
  • What is Ordinary Least Squares?
10 minutes
WRITEUP 3. Homoscedasticity and error normality
  • Why do we need homoscedasticity and error normality assumptions?
9 minutes
ARTICLE 4. Potential business consequences of violation in GM assumptinos
  • What are some of the consequences of violation in GM assumptinos?
8 minutes

Concepts Covered

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