Find the Least-Squares Regression Line and Use the Line to Make Predictions
-Find the equation of the regression line for the given data.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$

A) $\hat { y } = 2.097 \mathrm { x } - 0.552$
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 Least-Squares Regression Line and Use the Line to Make Predictions
-Find the equation of the regression line for the given data.
$\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}
\mathrm{x} & -5 & -3 & 4 & 1 & -1 & -2 & 0 & 2 & 3 & -4 \
\hline \mathrm{y} & -10 & -8 & 9 & 1 & -2 & -6 & -1 & 3 & 6 & -8
\end{array}$

A) $\hat { y } = 2.097 \mathrm { x } - 0.552$
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

The least-squares regression line is calculated using the formula $\hat{y} = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given the data, the correct calculation results in the equation $\hat{y} = 2.097x - 0.552$, which matches choice A. This calculation involves finding the mean of the x and y values, calculating the slope $m$ using the formula $\frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2}$, and then finding $b$ using the formula $b = \bar{y} - m\bar{x}$.