Quadratic Regression calculation

[pyfgcr]

Hi, I'm learning statistic. Do you guys know how to calculate quadratic regression by hand, which is: give a data set (x,y), find a parabola f(x)=ax^2+bx+c that minimize the total square errors .
I have known how to calculate linear regression.
Thanks in advanced.

 

[Stephen Tashi]

Write out the function that is to be minimized and then write its derivative. You get a a system of simultaneous linear equations. If you cannot visualize this using the summation notation $\Sigma$ then try making up 4 (x,y) data pairs and doing it.

 

[pyfgcr]

A system of simultaneous linear equation: ax^2 + bx + c , derivative: 2ax + b ?
I don't really understand

 

[Stephen Tashi]

A system of simultaneous linear equation: ax^2 + bx + c , derivative: 2ax + b ?
I don't really understand

Perhaps you haven't studied how the formulas for linear least squares regression are derived.

In linear regression there are $n$ data points ${(x_1,y_2), (x_2,y_2),...(x_n,y_n) }.$ The function to be minimized is $G(A,B) = \sum_{i=1}^n (A x_i + B - y_i)^2$ and deriving the formulas involves taking the partial derivatives of $G(A,B)$ with respect to each of $A$ and $B$ and setting them equal to zero to obtain two simultaneous linear equations. Look up how that is done.

The method for the quadratic is similar. It involves minimzing a function of 3 variables $G(A,B,C)$.