## Ordinary Least Squares Regression: Explained Visually

From the post:

Statistical regression is basically a way to predict unknown quantities from a batch of existing data. For example, suppose we start out knowing the height and hand size of a bunch of individuals in a “sample population,” and that we want to figure out a way to predict hand size from height for individuals not in the sample. By applying OLS, we’ll get an equation that takes hand size—the ‘independent’ variable—as an input, and gives height—the ‘dependent’ variable—as an output.

Below, OLS is done behind-the-scenes to produce the regression equation. The constants in the regression—called ‘betas’—are what OLS spits out. Here, beta_1 is an intercept; it tells what height would be even for a hand size of zero. And beta_2 is the coefficient on hand size; it tells how much taller we should expect someone to be for a given increment in their hand size. Drag the sample data to see the betas change.

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At some point, you probably asked your parents, “Where do betas come from?” Let’s raise the curtain on how OLS finds its betas.

Error is the difference between prediction and reality: the vertical distance between a real data point and the regression line. OLS is concerned with the squares of the errors. It tries to find the line going through the sample data that minimizes the sum of the squared errors. Below, the squared errors are represented as squares, and your job is to choose betas (the slope and intercept of the regression line) so that the total area of all the squares (the sum of the squared errors) is as small as possible. That’s OLS!

The post includes a visual explanation of ordinary least squares regression up to 2 independent variables (3-D).

Height wasn’t the correlation I heard with hand size but Visually Explained is a family friendly blog. And to be honest, I got my information from another teenager (at the time), so my information source is suspect.