Ordinary Least Squares

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

Contents

  1. Ordinary Least Squares
    1. Univariate
    2. Linear Model

Univariate

The regression line passes through two points:

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and

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These points, with the generic equation for a line, can prove that the slope of the regression line is equal to:

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The generic formula for the regression line is:

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Linear Model

The linear model can be expressed as:

model1.svg

If these assumptions can be made:

  1. Linearity

  2. Exogeneity

  3. Random sampling
  4. No perfect multicolinearity

  5. Homoskedasticity

Then OLS is the best linear unbiased estimator (BLUE) for these coefficients.

Using the computation above, the coefficients are estimated to produce:

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The variance for each coefficient is estimated as:

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Where R2 is calculated as:

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Note also that the standard deviation of the population's parameter is unknown, so it's estimated like:

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