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+cÂ whereÂ aâ‰ 0y=ax2+bx+cÂ the placeÂ aâ‰ 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:

âŽ¡âŽ£âŽ¢âˆ‘xi4âˆ‘xi3âˆ‘xi2âˆ‘xi3âˆ‘xi2âˆ‘xiâˆ‘xi2âˆ‘xinâŽ¤âŽ¦âŽ¥âŽ¡âŽ£âŽ¢abcâŽ¤âŽ¦âŽ¥=âŽ¡âŽ£âŽ¢âˆ‘xi2yiâˆ‘xiyiâˆ‘yiâŽ¤âŽ¦âŽ¥[âˆ‘xi4âˆ‘xi3âˆ‘xi2âˆ‘xi3âˆ‘xi2âˆ‘xiâˆ‘xi2âˆ‘xin][abc]=[âˆ‘xi2yiâˆ‘xiyiâˆ‘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=1âˆ’SSESSTÂ whereÂ SSE=âˆ‘(yiâˆ’axi2âˆ’bx+iâˆ’c)2Â SST=âˆ‘(yiâˆ’yÂ¯)2r=1âˆ’SSESSTÂ the placeÂ SSE=âˆ‘(yiâˆ’axi2âˆ’bx+iâˆ’c)2Â SST=âˆ‘(yiâˆ’yÂ¯)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 y -3 -2 -1 0 1 2 3 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.

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