Singularities in a Fit matrix indicates that there is insufficient data to properly solve the posed problem. A singular matrix means that it cannot be inverted properly, which is similar to dividing by zero in scalar problems.

The most simple case of this happening occurs when there are three equations but four unknowns in algebra. This system cannot properly be solved. In a Fit, this issue is more likely to occur when the runs are not sufficiently independent, which will lead to a singular matrix.

For example, consider a data set with variables x,y and output response z:

x,y,z

1,2,3

5,2,1

6,4,4

 

Notice that run 3 is a combination of runs 1 and 2 added together. The three runs would produce two pieces of information in a linear regression, which would result in a singular matrix.

The effect is that it is not possible to determine which of the input variables is responsible for a change in the output response.

The conclusion is that the data set is incompatible with the Fit specification. The most likely solution is to choose another Fit, modify the Fit settings, or obtain more data.