Answer:
The height at time of 12.1 seconds is approximately 729.2562 feet
Step-by-step explanation:
The general form of the quadratic regression equation is y = A + Bx + Cx²
The quadratic regression formula is given as follows;
[tex]B = \dfrac{S_{xy}S_{x'x'}-S_{x'y}S_{xx'}}{S_{xx}S_{x'x'} -(S_{xx'})^2}[/tex]
[tex]C = \dfrac{S_{x'y}S_{xx}-S_{xy}S_{xx'}}{S_{xx}S_{x'x'} -(S_{xx'})^2}[/tex]
[tex]A = \bar y - B \bar x - C \bar {x^2}[/tex]
[tex]S_{xx} = \Sigma (x_i - \bar x)^2[/tex]
[tex]S_{xy} = \Sigma (x_i - \bar x)(y_i - \bar y)[/tex]
[tex]S_{xx'} = \Sigma (x_i - \bar x)(x^2_i - \bar {x^2})[/tex]
[tex]S_{x'x'} = \Sigma (x^2_i - \bar {x^2})^2[/tex]
[tex]S_{x'y} = \Sigma (x^2_i - \bar {x^2})(y_i - \bar {y})[/tex]
Solving using an online quadratic regression calculator, gives;
A = 2.5643259
B = 246.6374865
C = -15.41986006
Substituting gives;
y = 2.5643259 + 246.6374865·x -15.41986006·x²
When time, x = 12.1, we have;
y = 2.5643259 + 246.6374865×12.1 -15.41986006×12.1²≈ 729.2562 feet
The height at time of 12.1 seconds ≈ 729.2562 feet.
