>> You might want to use Fourier analysis instead.
Yep. There error plot clearly shows a 3rd harmonic dominating. IIRC the length of day is constant at the equator and the light/time function is a distorted sinewave as you go north or south from there. I am curious about the slope within a day. It seem to "get dark quickly" these day vs July.
https://searke.github.io/2017/01/08/TemperatureGraph.html
Also, coincidentally enough, for Chicago using Wolfram Language. Great minds think alike I guess.