Question

given the data set of the angle at which a baseball is hit and the distance it travels.
angle baseball is hit (degrees) | horizontal distance traveled (feet)
10 | 113
18 | 185
20 | 200
32 | 231
38 | 224
46 | 182
50 | 155
perform a quadratic regression on this data and fill in the equation
y = □ x² + □ x + □ round your answers to the nearest thousandth.

Explanation:

Step1: Define quadratic regression model

The quadratic regression model is $y = ax^2 + bx + c$, where $x$ is the hit angle, $y$ is the distance, and $a, b, c$ are coefficients to calculate.

Step2: Use regression formula/tool

Using statistical methods (or calculator/software for quadratic regression) with the given data points $(10,113), (18,185), (20,200), (32,231), (38,224), (46,182), (50,155)$:

1. Calculate sums needed for regression:

$\sum x = 10+18+20+32+38+46+50 = 214$
$\sum y = 113+185+200+231+224+182+155 = 1290$
$\sum x^2 = 10^2+18^2+20^2+32^2+38^2+46^2+50^2 = 7628$
$\sum x^3 = 10^3+18^3+20^3+32^3+38^3+46^3+50^3 = 292296$
$\sum x^4 = 10^4+18^4+20^4+32^4+38^4+46^4+50^4 = 11713736$
$\sum xy = (10*113)+(18*185)+(20*200)+(32*231)+(38*224)+(46*182)+(50*155) = 39134$

1. Solve the system of linear equations for $a, b, c$:

$$\begin{cases} 7c + 214b + 7628a = 1290 \\ 214c + 7628b + 292296a = 39134 \\ 7628c + 292296b + 11713736a = 1390276 \end{cases}$$

Solving this system gives $a \approx -0.178$, $b \approx 11.732$, $c \approx -10.627$.

Answer:

$y = -0.178x^2 + 11.732x - 10.627$