Question

Which equation is the quadratic regression equation for the data shown in the table?

Answer 1

Answer-

Quadratic regression equation  $y=0.392x^2 - 5.583x + 21.167}$

Solution-

Quadratic Regression  Equation,

$ax^2+bx+c$

$a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}$

$b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}$

$c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}$

Where,

$\sum xx=\sum x^2-\frac{(\sum x)^2}{n}$

$\sum xy=\sum xy-\frac{\sum x\sum y}{n}$

$\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}$

$\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}$

$\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}$

Calculating the values from the table,

a= 0.392

b= -5.583

c= 21.167

∴ Quadratic regression equation,

$y=0.392x^2 - 5.583x + 21.167$