Orthogonal Polynomials

The Orthogonal Polynomials tab generates orthogonal polynomial columns from a numeric column. Using these columns as predictors in Linear Regression significantly reduces the condition number of the design matrix compared to the raw polynomial basis $x, x^2, \dots, x^d$, improving the precision of regression coefficients.

Basic Usage

Opening Orthogonal Polynomials

Select Data > Orthogonal Polynomials... from the menu bar to open a new Orthogonal Polynomials tab.

Generating Columns

1. Select the target dataset from the Dataset dropdown
2. Select the numeric column to transform in Source column
3. Set the maximum polynomial degree in Degree (1 to 30)
4. Click Preview to inspect the result
5. Enter a name for the output dataset in Output Name
6. Click Save as Dataset

The original dataset is not modified. A new derived dataset is created containing all original columns plus poly_1, poly_2, ..., poly_{degree}. Rows with null, NaN, or Infinity in the source column are skipped.

Polynomial Regression Workflow

To use orthogonal polynomials instead of the raw polynomial basis:

1. In the Orthogonal Polynomials tab, generate degree-$d$ polynomial columns from the x column and save the dataset
2. Open a Linear Regression tab and select the saved derived dataset
3. Set y as the response variable
4. Set poly_1, poly_2, ..., poly_d as explanatory variables
5. Read the coefficients, R-squared, and residual SD directly

The R-squared and fitted values from orthogonal polynomial regression are identical to those from raw polynomial regression. The coefficient values differ because the basis is different, but the model fit is the same.

Next steps

• Linear Regression - Regression analysis with orthogonal polynomial columns

See also

• Numerical Computing Fundamentals - How condition numbers affect accuracy
• Numerical Accuracy - NIST StRD benchmark accuracy verification
• Dummy Coding - Encoding categorical variables as dummy variables