Harmonic regression model coefficient interpretation

I am learning harmonic regression techniques and need a hand interpreting the results of the regression model.

I followed the example in the question answer here. and the equation here but I don't quite understand

Zti = β0 + βC cos(2πωti) + βS sin(2πωti) + εti

My question is how to interpret βC and βS. I understand β0 is the mean of Zti at baseline but I am not sure what the other two coefficients are. An explanation of the error term would be appreciated too.

• This post contains some discussion of the connection of functions those two coefficients to the amplitude and phase of the curve. As for interpreting the error term, how are you interpreting it for any other regression fit? Commented Sep 3, 2021 at 5:19
• @Glen_b thank you for your response, yes of course the error term is the difference of the observations from the fitted line (I was over worked and exhausted when I asked that). So from what I understand from your answer in the linked post, BC and BS coefficients are somewhat meaningless alone and the linear combination of these terms is what creates the general sine wave with an amplitude and phase. So when you interpret the output of your model - can you intuitively look at the estimate for sin(2*piToY) = -5.916 and cos(2*piToY) = -4.046 and imagine what the sine wave looks like? Commented Sep 7, 2021 at 22:03
• I wouldn't claim they're meaningless alone, I simply gave a way to interpret them (aside from the obvious "they're the coefficients of the sin and cos terms"). Don't assume there could not be multiple other ways to look at things. Commented Sep 8, 2021 at 2:14
• "can you intuitively look at the estimates [...] and imagine what the sine wave looks like?" ... well, sure, if you have some intuition about how the functions relating phase and amplitude to the coefficients behave. So for example, immediately the amplitude is going to be more than 6 (since one coefficient is almost 6 and the other isn't tiny), but not as big as 9 (since even two coefficients of 6 couldn't get you above 6√2). A little further thought - without actually calculating it - suggests it's something between 7 and 8 and nearer to 7. A quick mental approximation puts it at about 7.2 Commented Sep 8, 2021 at 2:21