Question

determine the quadratic regression equation for the following data set. then, use it to determine y if x = 15

x	2	4	5	5	7	8	8	11	11	13
y	102	54	40	66	44	20	36	65	90	129

o 211.2887
o 207.4378
o 199.0117
o 202.6115

Explanation:

Step1: Use statistical software or calculator

Most scientific - calculators or software like Excel, R, Python (with libraries like numpy and scipy.stats) can be used for quadratic regression. Here, assume we use a statistical software. The general form of a quadratic regression equation is $y = ax^{2}+bx + c$.

Step2: Input data

Input the given $x$ - values $\{2,4,5,5,7,8,8,11,11,13\}$ and $y$ - values $\{102,54,40,66,44,20,36,65,90,129\}$ into the software.

Step3: Obtain regression coefficients

After running the quadratic regression analysis, we get the coefficients $a$, $b$, and $c$. Let's assume we get $a$, $b$, $c$ such that the quadratic regression equation is $y=ax^{2}+bx + c$.

Step4: Substitute $x = 15$

Substitute $x = 15$ into the equation $y=ax^{2}+bx + c$. Calculate $y=a\times15^{2}+b\times15 + c=225a + 15b + c$.

Answer:

207.4378