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In my AP Stats course, we just finished our chapter on least squares regression lines and are moving on to non-linear regressions. I was expecting a least squares regression parabola, but instead we are using logs to make the function linear.

I googled it and found this and this on the least squares regression parabola and this how to use it on my calculator.

Is there a reason why my teacher and my book would not know/teach us about it? Is it a knew concept? Is using taking the log more accurate?

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There are lots of different kinds of non-linear regression, but fitting a parabola by least squares is not one of them.

Say you have data points $(x_i,y_i),\quad i=1,\ldots,n$ and you find the values of $a,b,c$ that minimize the sum of squares $\sum_{i=1}^n (ax_i^2 +bx_i +c - y_i)^2$. That is linear regression, not non-linear regression. It is a commonplace mistake to think that the reason why linear regression is called linear is that one is fitting a line. See this answer.

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