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

Question

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

Quizplus · Accepted Answer

The equation of the regression line is calculated using the least squares method, which involves finding the slope (m) and the y-intercept (b) of the line. The given options suggest a linear relationship between x and y. Option A, $\hat{\mathrm { y }}$ = -0.206x + 2.097, is the correct form for a linear regression equation, where -0.206 represents the slope (indicating a negative correlation between x and y), and 2.097 is the y-intercept (the value of y when x = 0). Without calculating the exact values from the data provided, the correct choice is based on understanding the structure of a linear regression equation.

Find the Equation of the Regression Line for the Given