Statistics - Quadratic Regression Equation

Statistics – Quadratic Regression Equation

Quadratic regression is deployed to determine an equation of the parabola which might greatest match the given set of knowledge. It’s of following type:

y=ax2+bx+c where a0y=ax2+bx+c the place a≠0

Least sq. methodology can be utilized to seek out out the Quadratic Regression Equation. On this methodology, we discover out the worth of a, b and c in order that squared vertical distance between every given level (xi,yixi,yi) and the parabola equation (y=ax2+bx+2y=ax2+bx+2) is minimal. The matrix equation for the parabolic curve is given by:

⎡⎣⎢xi4xi3xi2xi3xi2xixi2xin⎤⎦⎥⎡⎣⎢abc⎤⎦⎥=⎡⎣⎢xi2yixiyiyi⎤⎦⎥[∑xi4∑xi3∑xi2∑xi3∑xi2∑xi∑xi2∑xin][abc]=[∑xi2yi∑xiyi∑yi]

Correlation Coefficient, r

Correlation coefficient, r determines how good a quardratic equation can match the given knowledge. If r is near 1 then it’s good match. r will be computed by following components.

r=1SSESST where SSE=(yiaxi2bx+ic)2 SST=(yiy¯)2r=1−SSESST the place SSE=∑(yi−axi2−bx+i−c)2 SST=∑(yi−y¯)2

Typically, quadratic regression calculators are used to compute the quadratic regression equation.

Instance

Drawback Assertion:

Compute the quadratic regression equation of following knowledge. Verify its greatest health.

x -3 -2 -1 0 1 2 3
y 7.5 3 0.5 1 3 6 14

Answer:

Compute a quadratic regression on calculator by placing the x and y values. One of the best match quadratic equation for above factors comes as

y=1.1071x2+0.5714xy=1.1071×2+0.5714x

To examine the perfect health, plot the graph.

quadratic regression equation

So the worth of Correlation Coefficient, r for the info is 0.99420 and is near 1. Therefore quadratic regression equation is greatest match.