Equation: Fitting a straight line on a semi-log or log-log graph

Fitting straight lines on graphs with nonlinear axes

The nonlinear regression analysis fits the data, not the graph. Since Prism lets you choose logarithmic, 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, or both axes are logarithmic. 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.

Entering and fitting data

1.	Create an XY table, and enter your X and Y values.

2.	Go to the graph, double click on an axis to bring up the Format Axis dialog. Change one or both axes to a logarithmic scale.

3.	Click Analyze, choose Nonlinear regression (not Linear regression) and then choose one of the semi-log or log-log equations from the "Lines" section of equations.

Equations

Semilog line -- X axis is logarithmic, Y axis is linear

Y=Yintercept + Slope*log(X)

On semilog axis	On linear axes

Semilog line -- X axis is linear, Y axis is logarithmic

Y=10^(Slope*X + Yintercept)

On semilog axis	On linear axes

Log-log line -- Both X and Y axes are logarithmic

Y = 10^(slope*log(X) + Yintercept)

On log-log axes	On linear axes

Since both axes are transformed the same way, the graph is linear on both sets of axes. But when you fit the data, the two fits will not be quite identical.

Parameters

In all three equations, Y intercept is in units of the Y values, and Slope is in units of the Y values divided by units of the X values.