Linear Regression¶

Introduction¶

Linear regressions, as a class of results, can be calculated directly, and do not need an iterative process like nonlinear regressions do. See Linear Regression in the appendices for a more in-depth explanation. A linear regression can be constructed from any model that is a linear combination of functions; the coefficients in the linear combination are the parameters to be found.

There are two types of linear regressions supported in CurveExpert: linear and polynomial. All other regressions, even if they could be calculated as a linear-type regression through a variable transformation, are computed with the nonlinear regression engine.

Linear Fit¶

In CurveExpert Professional, you can choose to calculate a straight line regression:

$y = ax + b$

by choosing Calculate->Linear Fit. For multivariate datasets (more than one independent variable), a straight line regression is computed as

$y = \sum_j^{NVAR} a_j x_j + b$

For example, for a 3D data set,

$y = ax_1 + bx_2 + c$

nth Order Polynomial Fit¶

To calculate a polynomial via linear regression, choose Calculate->nth Order Polynomial Fit. A prompt will appear to ask for the degree of polynomial desired. Also, in the same prompt, you can choose to force the polynomial through the origin, which forces the intercept to zero. Also, you may choose the desired weighting for each point in the dataset (see Weighting for further information) After entering the degree (and origin forcing or weighting as appropriate), the polynomial will be computed and added to the result list.

Note

Polynomial fits computed via linear regression are supported only for 2D datasets. To compute a similar polynomial for multivariate datasets, use the nonlinear regression capability, selecting or defining a model as necessary.