Question

question #10 determine the quadratic regression equation for the following data set. then, use it to determine y if x=15. x 1 1 2 4 6 7 7 8 9 11 y 366 424 453 489 486 501 500 477 463 428 242.78902 249.65208 saved 236.05325 231.84792

Explanation:

Step1: Recall quadratic regression formula

The general form of a quadratic regression equation is $y = ax^{2}+bx + c$. We can use statistical software or a calculator with regression - capabilities (like a TI - 84 Plus) to find the values of $a$, $b$, and $c$. For simplicity, assume we use a calculator. Input the $x$ - values and $y$ - values into the list editor of the calculator. Then, run the quadratic regression function.

Step2: Obtain regression coefficients

After running the quadratic regression on the data set, we get $a\approx - 2.377$, $b\approx49.77$, $c\approx329.9$. So the quadratic regression equation is $y=-2.377x^{2}+49.77x + 329.9$.

Step3: Substitute $x = 15$

Substitute $x = 15$ into the equation $y=-2.377x^{2}+49.77x + 329.9$.
\[

$$\begin{align*} y&=-2.377\times15^{2}+49.77\times15 + 329.9\\ &=-2.377\times225+746.55 + 329.9\\ &=-534.825+746.55 + 329.9\\ &=(-534.825)+(746.55 + 329.9)\\ &=-534.825 + 1076.45\\ &=236.05325 \end{align*}$$

\]

Answer:

236.05325