Abstract: Although Linear Regression is arguably one of the most popular analytical techniques, I believe it isn’t understood well. Several fundamental assumptions are violated during application. The objective of this note is to provide an overview of the assumptions and possible fixes.

Linear regression is arguably one of the most widely used techniques in the data science world. But, a comprehensive understanding of this technique is not universal and it is at a level that is less than desired.

First, a little history, the term regression was first used by Sir Francis Galton, a 19th century polymath. Galton was a pioneer in application of statistical methods in many branches of science, he studied the relative sizes of parents and their offsprings in various species of plants and animals. During this study he observed that a larger than average parent tends to produce a larger than average child, but the child is likely to be less large than the parent in terms of its relative position in its own generation. Galton termed this phenomenon “a regression towards mediocrity”.

Linear regression is an approach to model a relationship between a dependent variable (y) and one or more independent variables (x). In this paper, I discuss

  1. Linearity and Additiveness of relationship between dependent and independent variables.
  2. Errors are statistically independent
  3. Constant variance of errors (Homoscedasticity)
  4. Errors are Normaly distributed

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Comment by Noor Mustafa on February 2, 2017 at 10:24am

link not work

Comment by Tracey Morland on July 5, 2016 at 9:16am

It seems like the "Read full article" link is no longer working. 

Comment by Rana S Gautam on January 10, 2015 at 10:54pm

Totally agree. Fitting a regression is easy. To determine how well the data fits the model is real challenge. Important point made.

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