Mathematics: Which equation is the quadratic regression equation for the data shown in the table? x 3 6 5 10 5 4 7 2 9 y 7 2 4 5 3 5 1 12 2 y=3x∧2 + 6x+5 y=0.392x - 5.583x y=0.392x∧2 - 5.583x + 21.167 y= -0.006x∧2 - 0.431x + 0.407

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Which equation is the quadratic regression equation

misst002

11.03.2022

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

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