Find the equation of the regression line for the given data. Round values to the nearest thousandth. $\begin{array}{l|c|c|c|c|c|c|c|c|c|c}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$
A)$\hat { y } = 2.097 x - 0.552$
B) $\hat { y } = 0.522 x - 2.097$

C)$\hat { y }= 2.097 \mathrm { x } + 0.552$
D)$\hat { y } = - 0.552 \mathrm { x } + 2.097$

Question

Find the equation of the regression line for the given data. Round values to the nearest thousandth. $\begin{array}{l|c|c|c|c|c|c|c|c|c|c}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$
A)$\hat { y } = 2.097 x - 0.552$
B) $\hat { y } = 0.522 x - 2.097$

C)$\hat { y }= 2.097 \mathrm { x } + 0.552$
D)$\hat { y } = - 0.552 \mathrm { x } + 2.097$

Quizplus · Accepted Answer

To find the equation of the regression line, we calculate the slope (m) and the y-intercept (b) using the formulas for linear regression. The slope formula is $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$ and the y-intercept formula is $b = \frac{\sum y - m(\sum x)}{n}$, where n is the number of data points. After calculating these using the given data points, the equation of the regression line is found to be closest to $\hat { y } = 2.097 x - 0.552$, rounding the coefficients to the nearest thousandth.

Find the Equation of the Regression Line for the Given