To determine the quadratic regression equation for the given data set, we follow these steps:
1. Define the form of the quadratic equation:
The general form of a quadratic equation is:
[tex]\[
y = ax^2 + bx + c
\][/tex]
2. Fit the quadratic model to the data:
Using the given [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values, we fit the quadratic model to determine the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
3. Determine the coefficients:
The quadratic model, after fitting it to the given data points, yields the following coefficients:
[tex]\[
a = -6.36897
\][/tex]
[tex]\[
b = 37.3389
\][/tex]
[tex]\[
c = -200.937
\][/tex]
4. Substitute the coefficients back into the quadratic equation:
Substituting [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] into the general form of the quadratic equation, we get:
[tex]\[
y = -6.36897x^2 + 37.3389x - 200.937
\][/tex]
Therefore, the correct quadratic regression equation for the given data set is:
[tex]\[
y = -6.36897x^2 + 37.3389x - 200.937
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{y = -6.36897x^2 + 37.3389x - 200.937}
\][/tex]
