# Second Blog

2018-07-08

During the second month of GSoC, I focused more on LsqFit.jl. LsqFit.jl is a simple (for now) package to perform non-linear regression. One example of non-linear model is the exponential model, which takes a one-element predictor variable $t$. The model function is:

Given that the function $m$ is non-linear, there’s no analytical solution for the best $\boldsymbol{\gamma}$. We have to use computational tools to find the least squares solution. Besides LsqFit.jl in Julia, there’re other packages to perform non-linear least squares, such as Scipy.optimize in Python and nls in R.

LsqFit.jl is still at its early stage, during the last month my work included:

1. documentation and tutorial
2. weight parameter
3. output and tools

I build the documentation based on the Github README.md and added more details on non-linear regression, which could help beginners to understand the code and workflow behind. The documentation is held here.

There was a issue regarding weight parameter, which was caused by sending wrong residual function. The fix could be a simple fix or a better fix but involves more changes. I took a look at what other packages do, nls in R doesn’t support weights and Scipy.optimize in Python took the error standard deviation or eatimated covariance as the parameter, which may not make sense at the first look but has computational advantage. The discussion could be seen here.

The last thing is fitting result output and tools, including functions computing R-squared and adjusted R-squared to help users see results more straightforward.

Other than what I mentioned, some work unfinished includes an early but usable version of NLSolve.jl documentation, considering the existing documentation of NLSolve.jl covers most topics needed, and preparing LsqFit.jl for Julia v0.7 changes. There’re lots of changes in v0.7 and the algorithm behaves very strange in v0.7, showing different results form v0.6, I’ll come back to this issue when I finished other functionalities.

For the next month, my focus will still be on LsqFit.jl, including more algorithms for least squares and bootstrap method for assessing goodness of fit.