Question

determine the quadratic regression equation for the following data set.

x	3	5	5	6	8	7	8	10	12	12
y	44	69	93	103	104	91	94	60	32	-3

o y = -3.39987x² + 47.6654x - 83.5298
o y = -3.39987x² + 47.6654x - 69.1658
o y = -2.19803x² + 47.6654x - 83.5298
o y = -2.19803x² + 47.6654x - 69.1658

Explanation:

Step1: Use statistical software or calculator

Most statistical software (e.g., Excel, R, Python's numpy and scipy.stats) or graph - ing calculators have built - in functions for quadratic regression. For simplicity, assume we use a calculator with quadratic regression functionality. Enter the x - values (3, 5, 5, 6, 8, 7, 8, 10, 12, 12) and y - values (44, 69, 93, 103, 104, 91, 94, 60, 32, - 3) into the appropriate lists.

Step2: Perform quadratic regression

Execute the quadratic regression command. The general form of a quadratic regression equation is $y = ax^{2}+bx + c$. The calculator will output the values of a, b, and c. After performing the regression, we find that $a\approx - 3.39987$, $b\approx47.6654$, and $c\approx - 83.5298$.

Answer:

$y=-3.39987x^{2}+47.6654x - 83.5298$