This client’s research was in water-acid solutions for nuclear reactors. They had a theoretical model for the viscosity of the solution as a function of the individual concentrations that needed empirical verification. The client (or rather, the client’s graduate student) had made viscosity measurements (with replicates) at a variety of mixtures.
The client then performed an analytical technique found in a standard chemical engineering text by manually multiplying matrices together. In short, the client wished for us to verify that the approach he was taking was correct.
Upon review of the client’s code it was apparent that he had manually implemented weighted least squares regression with the weights proportional to the inverse of the measurement/replication error at each mixture. We found this to be an appropriate technique and confirmed the analysis using a validated open source weighted least squares implementation in R. We then provided assistance cleaning up the methods section of the paper in order to make the analytical process clearer.
There was a very short deadline for this project (the client’s target conference’s submission deadline was to close 2 weeks after our initial meeting) and the client would be in the field for 10 of those days but we delivered correct results on time enabling the client’s graduate student to present the results.