# 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:

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

For example, for a 3D data set,

## 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.