I'm trying to code a regression calculator, because I like setting stupid challenges for myself that have been done before. I know what the formula for linear regression is already (I think):
$a= \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2}$
$b= \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}$
But I do need to know what the non-linear formula is. I've looked it up, but I'm currently learning in Integrated Math II, so I don't understand much. I understood everything that wasn't greek, basically - so just the $f$. Is there some kind of formula that's more like the one above than what I've found?
This is my first time posting on this forum, so I probably overlooked something...
All in all, is there an equation like the one above, preferably on the same level, that describes a non-linear regression equation? If you can only find one for quadratic equations, that's honestly fine as well. I am familiar with matrixes as well, just need to brush up on my skills, so if the solution has that (which I know it might, I've seen them everywhere, like least-squares method which I don't totally understand) then you can show me that as well. Sorry for rambling on, but help appreciated!