Answer:
B)[tex]-0.70x^2+2.37x+11.96[/tex]
Step-by-step explanation:
No. of second Height
0 12
1 13
2 15
3 13
4 9
5 7
Quadratic Regression Equation: [tex]y = a + b x + c x^2[/tex]
[tex]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 }[/tex]
[tex]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 }[/tex]
[tex]a = [ \sum y / n ] - { b \cdot [ \sum x / n ] } - { a \cdot [ \sum x^2 / n ] }[/tex]
Where ,
[tex]\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 ][/tex]
Using these formulas the required equation is :[tex]-0.696 X^2 +2.368 X +11.964[/tex]
So, option B is true
B)[tex]-0.70x^2+2.37x+11.96[/tex]
