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Ordinary Least Squares

Ordinary Least Squares (OLS) is a linear regression method. It minimizes root mean square errors.

Contents

Univariate

The regression line passes through two points:

and

Take the generic equation form of a line:

Insert the first point into this form.

This can be trivially rewritten to solve for a in terms of b:

Insert the second point into the original form.

Now additionally insert the solution for a in terms of b.

Expand all terms to produce:

This can now be eliminated into:

Giving a solution for b:

This solution is trivially rewritten as:

Expand the formula for correlation as:

This can now be eliminated into:

Finally, b can be eloquently written as:

Giving a generic formula for the regression line:

Statistics/OrdinaryLeastSquares (last edited 2025-01-10 14:33:38 by DominicRicottone)

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-= Linear Regression =
+= Ordinary Least Squares =
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-A linear regression expresses the linear relation of a treatment variable to an outcome variable.
+'''Ordinary Least Squares''' ('''OLS''') is a linear regression method. It minimizes root mean square errors.
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-== Regression Line ==

A regression line can be especially useful on a scatter plot.
+== Univariate ==
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== Regression Computation ==