The Surfer error "The system of regression equations is singular" could be caused by a number of factors:
- The data you are trying to grid is collinear (that is, data all in a line). Add some additional data points off the existing line of points, or choose a different method.
- If you don't have enough data points, you may not be able to go as high as third order (cubic). Try a quadratic polynomial.
- There is a high discrepancy between the X and Y data ranges and the Z data range. For example, your X data and Y data could have a very large range, which is common when the values are in hundred thousands or millions (ie. UTM or State Plane values), compared to Z data that could have a magnitude smaller range (e.g. in the tens or hundreds range). This causes the polynomial equation coefficients to be extremely small, which introduces instabilities into the fit equation and illustrates the limitations of computer precision.
If the issue is caused by the above, you can work around the problem by subtracting a base value from the X and Y values and then creating the polynomial grid. For example, create new data columns in your data file. If your X and Y data are on the order of 500,000 and 6,000,000 respectively, subtract 500,000 from the X data and 6,000,000 from the Y (to reduce the size of the XY values) and put the new data into these columns. Then grid the data using these XY columns with Polynomial Regression. After the grid is created, add the subtracted values back into the XY positions using the Grids | Calculate | Transform command with an the Offset operation.
Updated October 2021