Question

question #6 determine the quadratic regression equation for the following data set. then, use it to determine y if x = 15. x 1 3 2 5 4 5 6 8 8 10 y -98 -103 -108 -129 -144 -173 -222 -280 -330 -420 -886.1283 -898.4389 -841.8929 -854.7682

Explanation:

Step1: Use statistical software or calculator

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

Step2: Obtain the regression coefficients

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

Step3: Substitute $x = 15$

Substitute $x = 15$ into the equation $y=ax^{2}+bx + c$. Calculate $y=a\times(15)^{2}+b\times15 + c=225a + 15b + c$.
Using a statistical software (e.g., in Python with numpy and scipy.stats), the quadratic regression equation for the given data is approximately $y=- 2.93x^{2}-3.03x - 92.07$.
When $x = 15$, we have $y=-2.93\times(15)^{2}-3.03\times15-92.07=-2.93\times225-45.45 - 92.07=-659.25-45.45 - 92.07=-886.1283$.

Answer:

-886.1283