What is the quadratic regression equation that fits these data

Asked by admin @ 27/10/2021 in Mathematics viewed by 355 People

What is the quadratic regression equation that fits these data?

A. y = -2.04x2 +1.46x + 13.92
B. y= -0.70x2 +2.37x + 11.96
c. y = 14.77(0.89)
D. y = -1.04x2+3.04x + 9.68

Answered by admin @ 27/10/2021

Answer:

B) $-0.70x^2+2.37x+11.96$

Step-by-step explanation:

No. of second Height

0 12

1 13

2 15

3 13

4 9

5 7

Quadratic Regression Equation: $y = a + b x + c x^2$

$c = \frac{ [ \sum x^2 y * \sum xx ] - [\sum xy \cdot \sum xx^2 ] } { [ \sum xx \cdot \sum x^2 x^2] - [\sum xx^2 ]^2 }$

$b =\frac{ [ \sum xy \cdot \sum x^2 x^2 ] - [\sum x^2y \cdot \sum xx^2 ] } { [ \sum xx \cdot \sum x^2 x^2] - [\sum xx^2 ]^2 }$

$a = [ \sum y / n ] - { b \cdot [ \sum x / n ] } - { a \cdot [ \sum x^2 / n ] }$

Where ,

$\sum x x = [ \sum x^2 ] - [ ( \sum x )^2 / n ]\\\\\sum x y = [ \sum x y ] - [ ( \sum x \cdot \sum y ) / n ]\\\\\sum x x^2 = [ \sum x^3 ] - [ ( \sum x^ 2 \cdot \sum x ) / n ]\\\\\sum x^2 y = [ \sum x^2 y] - [ ( \sum x^2 \cdot \sum y ) / n ]\\\\\sum x^2 x^2 = [ \sum x^4 ] - [ ( \sum x^2 )^2 / n ]$

Using these formulas the required equation is : $-0.696 X^2 +2.368 X +11.964$

So, option B is true

B) $-0.70x^2+2.37x+11.96$

What is the quadratic regression equation that fits these data

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