Go here... http://lmgtfy.com/?q=Quadratic+Regression
Go here... http://lmgtfy.com/?q=Quadratic+Regression
Forget about regression. First learn least squares.
That's where we find a curve that fits the data as best we can.
(In this case minimizing the square of the vertical distance.)
NOW we need more data points than unknown parameters.
Otherwise we get a perfect fit.
Then if we assume that our random errors have a certain distribution then we can do statistics, which is called regression.
If those errors are normally distributed, the squared errors will all be chi-square rvs creating a lot of t and F statistcs.
But first learn ohw to do least squares VIA MATRICES.
Doing least sqaures by hand is painful and quite worthless.