## What is the problem?

The problem is that the lmfitx function cannot fit a model to the data when there is an offset in the y-direction. This is because the offset causes the problem to become singular, meaning that there is no unique solution. To fix this, you can either remove the offset from the data or use a different fitting method to handle singular problems.

## What is the cause of the problem?

A poorly conditioned input matrix causes the problem. The condition number is a measure of the sensitivity of the solution of a linear system of equations to errors in the data. A high condition number indicates that the system is poorly conditioned and that small errors in the data can cause large errors in the solution. In this case, the condition number is very high, indicating that the input matrix is nearly singular. This means that any small perturbation in the input data can cause a large change in the solution.

There are two ways to fix this problem:

1) Use regularization: Regularization is a technique that can be used to stabilize an ill-posed problem. In this case, it means adding a term to the objective function that penalizes large values of the coefficients. This technique can be effective in some cases, but it may also lead to sub-optimal solutions.

2) Use better data: If possible, use better data that is not so close to singularity. This may require collecting new data or using different sources of data.

## How can the problem be fixed?

There are a few ways to fix this problem:

- Make sure that your data is free of outliers. Outliers can cause the lmfitx y offset to be singular, so removing them can often fix the problem.
- Use a different model. If you’re using a linear model, try a nonlinear model instead. This can sometimes help if your data is not well-behaved.
- Transform your data. This can sometimes help if your data is not Normally distributed.