Quadratic Regression calculation

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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.
 

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  • #2
Stephen Tashi
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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 [itex] \Sigma [/itex] then try making up 4 (x,y) data pairs and doing it.
 
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A system of simultaneous linear equation: ax^2 + bx + c , derivative: 2ax + b ?
I don't really understand
 
  • #4
Stephen Tashi
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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 [itex] n [/itex] data points [itex] {(x_1,y_2), (x_2,y_2),...(x_n,y_n) }. [/itex] The function to be minimized is [itex] G(A,B) = \sum_{i=1}^n (A x_i + B - y_i)^2 [/itex] and deriving the formulas involves taking the partial derivatives of [itex] G(A,B) [/itex] with respect to each of [itex] A [/itex] and [itex] B [/itex] 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 [itex] G(A,B,C) [/itex].
 

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