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Find the equation of the regression line for the given data. Round values to the nearest thousandth.

[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]

A. [tex]\(\hat{y}=-2.097x+0.206\)[/tex]

B. [tex]\(\hat{y}=2.097x-0.206\)[/tex]

C. [tex]\(\hat{y}=0.206x-2.097\)[/tex]

D. [tex]\(\hat{y}=-0.206x+2.097\)[/tex]

Sagot :

GinnyAnswer
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]
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