Question

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

Answer 1

y= 0.392x^2 − 5.583x + 21.167

Step-by-step explanation:

Answer 2

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=(\sum y)/(n)-b(\sum x)/(n)-a(\sum x^2)/(n)`

Where,

`\sum xx=\sum x^2-((\sum x)^2)/(n)`

`\sum xy=\sum xy-(\sum x\sum y)/(n)`

`\sum xx^2=\sum x^3-(\sum x\sum x^2)/(n)`

`\sum x^2y=\sum x^2y-(\sum x^2\sum y)/(n)`

`\sum x^2x^2=\sum x^4-((\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`