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I think you can proceed as follows: Denote by J(\alpha, \beta_1, \beta_2) the obj. function. Then write down the FOC (the gradient should be zero). You will get a 3x3 linear system to solve w/r to \alpha, \beta_1, \beta_2. You can find the system here Least Squares Fit of a Quadratic Curve to...

Hi all, my name is Iulian and I work as a quant developer. I have 2 MSc and a PhD in applied math. Iulian