Zero Intercept Procedures

Zero-Intercept Procedures

TableCurve 3D’s linear equations all include a Z-intercept in the fit. This poses an interesting problem if you know the surface must pass through the origin and you wish to force it through this 0,0,0 point.

TableCurve 3D does furnish two effective methods for forcing surface-fits to pass through the origin. These methods apply to both linear and non-linear equations. Before describing these, a caution is in order.

When TableCurve 3D’s best equations indicate the presence of a non-zero Z-intercept, and you have included 0,0,0 in the data set, it is frequently the case that the data insufficiently maps the trend or profile near the origin. For example, a flowmeter may not be responsive at near-zero flow rates or near-freezing temperatures because of static frictional forces or state changes. The non-zero intercept that occurs in fitting is thus quite valid. When an equation is forced to have a zero Z-intercept, its effectiveness as an approximating function may suffer. For this reason, it is advised that you carefully compare the non-zero and zero-intercept versions.

Weight 0,0 Data Pair

Unless explicitly entered, all data points in TableCurve 3D have a default weight factor of 1.0. The weighting is a linear multiplier rather than a variance divisor. To force a surface through the origin, use the TableCurve 3D Editor option. If you do not already have a 0,0,0 data triplet, insert or add it to the table. Enter 1E8 for the weight. With this 0,0,0 point given 100 million times the weighting of the other points, the surfaces for all equations fitted will essentially pass through the origin.

Beware of precision losses outside of TableCurve 3D if you simply drop this near-zero intercept parameter. If the equation is a linear one, use the Precision option in the Review to see the fractional errors which result from zeroing the a coefficient. This is immediately below the significance table.

User-Function without Z-Intercept

The second procedure involves building a user-defined function that lacks this Z-intercept term. This procedure is limited to a specific equation of interest. It is best to create this function using starting estimates from the fit with the non-zero intercept. Since user functions must have parameters in sequence from #A to #H, you will have to rename the b in the equation as #A, the c as #B, etc..

Although this approach requires more effort than the weighting procedure and is limited to a single equation, the surface will pass perfectly through the origin and the statistics will not be impacted by the weighting.