Does anyone know how to do non-linear regression by hand?

[John Leak67]

I have been given data points and asked to find a sin function for it. I made the function using the regression feature in desmos, however, was wondering how to do it Desmos.

 

[Harry_the_cat]

Do you mean without Desmos?

 

[John Leak67]

yeah without it. like the mechanical maths.

 

[Harry_the_cat]

I'll assume you do mean that.
If you plot the real data points, you can estimate the parameters a, b, c and d by considering the transformation of the graph of y = sin x to get the graph of y = a sin [b(x-c)] + d. You need to know how each of those parameters change the position and shape of the curve. Have you learnt that?

 

[John Leak67]

My data has varying amplitudes, hence, a normal sin function will not do. However I figured out that if u use y = a sin [b(x-c)] + a sin [b(x-c)] + d you can create a sin function with varying amplitudes. BTW my data is the high and low tides on a particular day that's why I need different amplitudes. I already have the function to model the data, however, I need to know how to come up with the function with sinusoidal/ non-linear regression. Thanks for replying btw means a lot.