Ordinary least squares

Okun's law in macroeconomics states that in an economy the GDP growth should depend linearly on the changes in the unemployment rate. Here the ordinary least squares method is used to construct the regression line describing this law. The observed values are shown in blue, the expected ones are shown in black.

Ordinary least squares or linear least squares is a method for estimating unknown parameters in statistics. It is a method used in linear regression. The goal of the method is to minimize the difference between the observed responses and the responses predicted by the linear approximation of the data. A smaller difference means that model fits the data better. Ordinary least squares is a special case of a method commonly called least squares. The resulting estimator can be expressed by a simple formula.

Ordinary Least Squares Media

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  OLS estimation can be viewed as a projection onto the linear space spanned by the regressors. (Here each of X_1 and X_2 refers to a column of the data matrix.)

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  Scatterplot of the data, the relationship is slightly curved but close to linear

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  Example of OLS: regression of weight against height of american women; this picture shows dataset and fitted regression line

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  Example of OLS regression, avg weight regressed on height in population of american women; this graph shows the residuals of the regression.

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  Residuals to a quadratic fit for correctly and incorrectly converted data.