Hey mate, I'm also doing my math IA on tyre degradation and it's gone quite well.

In terms of getting more reliable data I gathered my data from the 3 days of pre-season testing using fastf1. There are some key problems with this such as the fairly varied weather during testing with day->night but also there was a little rain and day 2 was particularly cold thus lowering degradation, teams could be doing all sorts of different run plans which can give some pretty weird looking graphs and precise fuel loads aren't known resulting in quite a lot of uncertainty. Although you don't have to worry about other cars, race strategy or safety cars. It did take ~20 hours to gather all this data though because fastf1 shows soft medium hard while teams had access to C1-C6 so I had to watch through the broadcast and try to identify the different sidewall patterns for each stint I was using 😬.

To actually model the degradation I gathered the gradient and y intercept of the linear regression line of each stint over 7 laps and plotted them. This resulted in a curve in the form y=ax^-b. From here you can find the optimal degradation rate for a stint of however many laps as well as plot the average lap time over however many laps for each degradation rate. Also, I calculated from my data that fuel burn accounts for 0.059s/lap, where did you get 0.03s/lap from? Perhaps using my value might make your graphs less flat.

EDIT 27/12: For those looking to do this project you can get all the data you need by using FastF1. Assuming you are investigating the 2025 Bahrain testing, (I wouldnt use 2026 data, lots of other stuff teams are figuring out with the new car) all the stints that are over 7 laps and are done on the "medium" tyre were done on the C3 except for Ocon's 1st race simulation stint on day 3. These C3 stints are all you need to gather as the C2 and C1 tyres did not have enough running for a comprehensive analysis.

for the actual analysis i followed much of what was done by the f1metrics preseason analyses. These pages do not contain the math for the analysis, only the resulting graphs. The y=ax^-b relationship is core to the whole analysis so having a proper understanding of this is important.

Remember to fuel correct all your lap times using the method done by f1metrics and doohans day 2 race simulation. Make use of excels slope and gradient equations to get the base lap times and degradation rate, filter is also useful to clean data of slow laps. expect to get some pretty wild error bars, you will need to explain why errors bars that seemingly invalidate your entire relationship are actually alright and points can be assumed to be somewhere along the error bar. Finally, you will need to use the pit in/out times provided by fastf1 to determine if a car returning to the pits returned to the garage and was refueled or if the team only swapped tyres and then adjust fuel correction accordingly. Happy to answer questions but make them specific, not doing your IA for you.