a rocket is shot off from a launcher. the accompanying table represents the height of the rocket at given…

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.\ntime in seconds (x) height in feet (y)\n1 294\n1.6 451\n2.6 692\n3.4 879\n4.2 1011\n5.2 1170\nanswer attempt 1 out of 2\nregression equation:\nfinal answer:

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.\ntime in seconds (x) height in feet (y)\n1 294\n1.6 451\n2.6 692\n3.4 879\n4.2 1011\n5.2 1170\nanswer attempt 1 out of 2\nregression equation:\nfinal answer:

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)