Find the equation of the regression line for the given data. Round values to the nearest thousandth. $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & 11 & 6 & -6 & -1 & 3 & 4 & 1 & -4 & -5 & 8
\end{array}$
A)$\hat { y } = -1.885 x+0.758$
B)$\hat { y } =0.758 x+1.885$
C) $\hat { y } = - 0.758 x - 1.885$
D) $\hat { y } = 1.885 x - 0.758$

Question

Find the equation of the regression line for the given data. Round values to the nearest thousandth. $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & 11 & 6 & -6 & -1 & 3 & 4 & 1 & -4 & -5 & 8
\end{array}$
A)$\hat { y }  = -1.885 x+0.758$ 
B)$\hat { y } =0.758 x+1.885$ 
C) $\hat { y } = - 0.758 x - 1.885$
D) $\hat { y } = 1.885 x - 0.758$

Quizplus · Accepted Answer

To find the equation of the regression line, we first 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, we find that the slope ($m$) is approximately -1.885 and the y-intercept ($b$) is approximately 0.758, leading to the regression equation $\hat { y } = -1.885x + 0.758$.

Find the Equation of the Regression Line for the Given