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

Question

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

Quizplus · Accepted Answer

To find the equation of the regression line, we need to calculate the slope (m) and the y-intercept (b) of the line. The formula for the slope (m) is given by $$m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$$ and the y-intercept (b) by $$b = \frac{\sum y - m(\sum x)}{n}$$, where n is the number of data points. Calculating these values with the given data points would yield the slope and y-intercept that match the equation in choice A, $\hat { \mathrm { y } }$ = -1.885x + 0.758.

Find the Equation of the Regression Line for the Given