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 $G(A,B,C)$.

 

[blue_raver22]

Hi there, as a scientist, I can definitely help you with calculating quadratic regression by hand. Quadratic regression is a statistical method used to find the best-fit parabola for a given data set. This parabola is represented by the equation f(x) = ax^2 + bx + c, where a, b, and c are the coefficients that we need to find.

To calculate these coefficients, we first need to find the sums of the x-values, y-values, and x^2-values in the data set. Let's call these sums Σx, Σy, and Σx^2. We also need to find the sums of the products of x and y-values, and x^2 and y-values, which we will call Σxy and Σx^2y.

Using these values, we can calculate the coefficients as follows:

a = [Σxy - (Σx * Σy)/n] / [Σx^2 - (Σx)^2/n]
b = [Σx^2 * Σy - Σx * Σxy] / [Σx^2 - (Σx)^2/n]
c = [Σy - b * Σx - a * Σx^2] / n

Where n is the total number of data points in the set.

Once we have calculated the coefficients, we can plug them into the equation f(x) = ax^2 + bx + c to get the best-fit parabola for the data set. This parabola will minimize the total square errors, meaning it will be the closest possible fit to the data points.

I hope this helps you understand how to calculate quadratic regression by hand. Let me know if you have any further questions. Best of luck with your statistics learning!