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When it comes to statistical modeling few things are as tried and tested as linear regression.

In this post I'll give a fairly informal definition of linear regression, overview the goals of linear regression, and talk about a few things you can use it for.

In statistics, linear regression is an approach for modeling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X.

Galton called this phenomenon regression, as in 'A father's son's height tends to regress (or drift towards) the mean (average) height.'

By doing this, we could take multiple men and their son's heights and do things like tell a man how tall we expect his son to be...before he even has a son!

To roughly estimate a regression line, it's pretty simple: Just draw a line that is as close as possible to every point on your graph.

Without getting in too deep into the math, if we refer back to earlier in the post, we mentioned that our goal with linear regression is to minimize the vertical distance between all the data points and our line.

There are lots of different ways to minimize this, (sum of squared errors, sum of absolute errors, etc), but all these methods have a general goal of minimizing this distance.

In our example, we can see that if we were to take the total vertical distance between the points the the red line DR, and the total vertical distance between the points and the green DG or blue line DB, the total distance between the points and the red line is smaller.

From just this example you could estimate how tall a man's son will be before he has one, determine which of your friends is freakishly tall with respect to their dad, or even compare different groups of men and their sons over time to analyze trends.

While this post intentionally breezes over the math aspects of linear regression, its undeniable that to use linear regression in practice, you need to have a thorough understanding of both the qualitative and quantitative characteristics of the regression.

That said, linear regression is a great place to start learning statistical modeling techniques, and the links below should help you get going!

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