Home / DOE / Analyze / Ordinary Least Squares Regression / Math Details

Math Details

The mathematics behind the fit. What the engine is for and when Run Regression chooses it are on Ordinary Least Squares Regression, and what governs a run is on Options.

The fit

Writing \(X\) for the design matrix, which holds a column for the constant and a column for each term, \(y\) for the vector of responses, and \(b\) for the coefficients:

\[ b = (X'X)^{-1} X' y \]

With weights, where \(W\) is a diagonal matrix carrying one weight per run:

\[ b = (X'WX)^{-1} X'W y \]

Weights are used for the response model when the design carries a weights column, so a row standing for more observations counts for more. The standard deviation model is always fitted unweighted, whatever Use weighted S-Hat regression on the Regression page of DOE Options is set to. See The S-Hat Model.

See Also

• Ordinary Least Squares Regression
• Options
• Run Regression