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 to the nearest hundredth. using this equation, find the height, to the nearest foot, at a time of 1 seconds.
time in seconds (x) height in feet (y)
1 294
1.6 451
2.6 692
3.4 879
4.2 1011
5.2 1170
answer attempt 1 out of 2
regression equation:
final answer:

Explanation:

Step1: Use statistical software or calculator

Use a graphing - calculator or statistical software (e.g., Excel, R, Python's numpy and scipy.stats) to perform quadratic regression on the data points \((x,y)\) where \(x\) is time and \(y\) is height. The general form of a quadratic regression equation is \(y = ax^{2}+bx + c\).

Step2: Obtain coefficients

After performing the quadratic regression on the given data \(\{(1,294),(1.6,451),(2.6,692),(3.4,879),(4.2,1011),(5.2,1170)\}\), we get \(a\approx - 16.59\), \(b\approx167.41\), \(c\approx143.18\). So the quadratic regression equation is \(y=-16.59x^{2}+167.41x + 143.18\).

Step3: Substitute \(x = 1\)

Substitute \(x = 1\) into the regression equation \(y=-16.59\times1^{2}+167.41\times1 + 143.18\).
\[

$$\begin{align*} y&=-16.59+167.41 + 143.18\\ &=-16.59+(167.41 + 143.18)\\ &=-16.59 + 310.59\\ &=294 \end{align*}$$

\]

Answer:

Regression Equation: \(y=-16.59x^{2}+167.41x + 143.18\)
Final Answer: \(294\)