﻿ Key concepts: Fitting lines

# Key concepts: Fitting lines

## Choosing nonlinear regression, rather than linear regression to fit a line

Prism offers separate analyses for linear regression and nonlinear regression. But the nonlinear regression analysis can fit a straight-line model. This is useful when you want to take advantage of features in Prism's nonlinear regression analysis that Prism does not offer in its linear regression analysis, such as the ability to compare two models, apply weighting, or automatically exclude outliers. See a longer discussion of the advantages of using the nonlinear regression analysis to fit a straight line.

## Fitting straight lines on graphs with nonlinear axes

The nonlinear regression analysis fits the data, not the graph. Since Prism lets you choose logarithmic or probability axes, some graphs with data points that form a straight line follow nonlinear relationships. Prism's collection of "Lines" equations includes those that let you fit nonlinear models to graphs that appear linear when the X axis is logarithmic, the Y axis is logarithmic, both axes are logarithmic, or when the Y axis uses a probability scale. In these cases, linear regression will fit a straight line to the data but the graph will appear curved since an axis (or both axes) are not linear. In contrast, nonlinear regression to an appropriate nonlinear model will create a curve that appears straight on these axes.

## Segmental linear regression

Segmental regression fits one line to all data points with X less than some value X0, and another line to all points with X greater than X0, ensuring that the two lines intersect at X0.

Segmental linear regression is helpful when X is time, and you did something at time=X0 to change the slope of the line. Perhaps you injected a drug, or rapidly changed the temperature. In these cases, your model really does have two slopes with a sharp transition point.