Curve fitting without a model

The term curve fitting is more general than regression. Your approach to curve fitting depends on your goal.

In some circumstances, you just want to draw a smooth curve to make a graph look attractive, or to use as a standard curve. You don't care about models, and aren't looking for best-fit values that you can interpret.

Prism provides two approaches for fitting a curve without selecting a model. From a table or graph of XY data, click Analyze, and then choose 'Fit spline/LOWESS" from the list of XY analyses.

Spline and lowess curves

A lowess curve follows the trend of the data and tends to be a bit jagged. Lowess curves can be helpful when the data progresses monotonically, but are less helpful when there are peaks or valleys. Prism lets you choose between coarse, medium and fine lowess curves. The coarse curve (left panel below) shows only the general trend, but obscures the detail. The fine curve (middle panel below) reveals the fine structure of the data, but tends to wiggle a lot. A cubic spline curve (right panel below) goes through every data point, bending and twisting as needed.

Prism generates lowess curves using an algorithm adapted from reference 1. Details.  Don't select a lowess curve unless you have well over twenty data points. Prism generates the curve as a series of line segments. Enter the number of segments you want, and check the option box if you need to see the XY coordinates of each point, or if you want to use the resulting lowess, point-to-point, or spline curve as a standard curve. Prism always generates a lowess curve with at least four times more line segments than the number of data points, and you cannot reduce the number of segments below this value.

Creating a point-to-point 'curve'

Prism's spline/lowess analysis can also create a point-to-point "curve" -- a series of line segments connecting all your data. Don't create a point-to-point curve just so you can connect points with a line on the graph. You can do that by checking an option on the Format Graph dialog from the Graphs section of your project. Only select the point-to-point analysis if you want to use the point-to-point line as a standard curve,  or if you wish to calculate area under that curve

References                                                                         

1. John Chambers et. al., Graphical Methods for Data Analysis, Wadsworth and Brooks, 1983.