Find the equation of the regression line for the given data. Round values to the nearest thousandth. $\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & 11 & -6 & 8 & -3 & -2 & 1 & 5 & -5 & 6 & 7
\end{array}$
A) $\hat { y } = - 0.206 \mathrm { x } + 2.097$
B) $\hat { y } = 2.097 \mathrm { x } - 0.206$
C) $\hat { y } = 0.206 x - 2.097$
D) $\hat { y } = - 2.097 x + 0.206$

Question

Find the equation of the regression line for the given data. Round values to the nearest thousandth. $\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & 11 & -6 & 8 & -3 & -2 & 1 & 5 & -5 & 6 & 7
\end{array}$
A) $\hat { y }  = - 0.206 \mathrm { x } + 2.097$
B) $\hat { y } = 2.097 \mathrm { x } - 0.206$
C) $\hat { y } = 0.206 x - 2.097$
D) $\hat { y } = - 2.097 x + 0.206$

Quizplus · Accepted Answer

To find the equation of the regression line, we first calculate the slope ($m$) and the y-intercept ($b$) of the line. The formula for the slope is $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$ and for the y-intercept is $b = \frac{\sum y - m(\sum x)}{n}$, where $n$ is the number of data points. After calculating these using the given data, we find the equation of the regression line to be $\hat { y }  = - 0.206 \mathrm { x } + 2.097$, rounding the coefficients to the nearest thousandth.

Find the Equation of the Regression Line for the Given