Question

A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients . Using this equation, find the height, , at a time of 12.1 seconds.
Time in Seconds (x) Height in Feet (y)

0.5 121

1.4 321

2.2 467

2.8 573

3.3 649

Answer 1

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;

$B = \dfrac{S_{xy}S_{x'x'}-S_{x'y}S_{xx'}}{S_{xx}S_{x'x'} -(S_{xx'})^2}$

$C = \dfrac{S_{x'y}S_{xx}-S_{xy}S_{xx'}}{S_{xx}S_{x'x'} -(S_{xx'})^2}$

$A = \bar y - B \bar x - C \bar {x^2}$

$S_{xx} = \Sigma (x_i - \bar x)^2$

$S_{xy} = \Sigma (x_i - \bar x)(y_i - \bar y)$

$S_{xx'} = \Sigma (x_i - \bar x)(x^2_i - \bar {x^2})$

$S_{x'x'} = \Sigma (x^2_i - \bar {x^2})^2$

$S_{x'y} = \Sigma (x^2_i - \bar {x^2})(y_i - \bar {y})$

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.