To find the equation of the regression line for the given data, we need to determine the slope ([tex]\( m \)[/tex]) and the y-intercept ([tex]\( c \)[/tex]) of the line in the form:
[tex]\[
\hat{y} = mx + c
\][/tex]
Given the data points,
[tex]\[
\begin{array}{rrrrrrrrrrr}
x & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \\
y & 11 & -6 & 8 & -3 & -2 & 1 & 5 & -5 & 6 & 7
\end{array}
\][/tex]
After performing the calculations, we find the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( c \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\(-0.206\)[/tex], rounded to the nearest thousandth.
- The y-intercept [tex]\( c \)[/tex] is [tex]\(2.097\)[/tex], rounded to the nearest thousandth.
This means the equation of the regression line is:
[tex]\[
\hat{y} = -0.206x + 2.097
\][/tex]
Thus, the correct answer is:
D. [tex]\(\hat{y} = -0.206x + 2.097\)[/tex]
