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Ordinary Least Squares Regression

Ordinary Least Squares Regression (OLS) is used by Quantum XL for outputs which are Quantitative. OLS fits the model that minimizes the sum of squares between response values and the model.

Unweighted OLS Formula

B = (X'X)-1X'Y

Weighted OLS Formula

B = (X'WX)-1X'Wy

Where:

  • B is the resulting vector of regression coefficients.
  • X is the design matrix including the constant and any predictor variables for categorical inputs.
  • X' is the transpose of the X matrix.
  • W is the weight matrix where wii is the weight value for the ith observation and all wij=0 for all i not equal to j.
  • Y is a vector of response observations.