Answer-
Quadratic regression equation [tex]y=0.392x^2 - 5.583x + 21.167}[/tex]
Solution-
Quadratic Regression Equation,
[tex]ax^2+bx+c[/tex]
[tex]a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]
[tex]b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]
[tex]c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]
Where,
[tex]\sum xx=\sum x^2-\frac{(\sum x)^2}{n}[/tex]
[tex]\sum xy=\sum xy-\frac{\sum x\sum y}{n}[/tex]
[tex]\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}[/tex]
[tex]\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}[/tex]
[tex]\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}[/tex]
Calculating the values from the table,
a= 0.392
b= -5.583
c= 21.167
∴ Quadratic regression equation,
[tex]y=0.392x^2 - 5.583x + 21.167[/tex]
