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Finding the Equation of an LSRL Using Means and SD

APSTAT-RJW0YL

Consider a set of $n$ ordered pairs given by:

$$({ x }_{ 1 },y_{ 1 }), ({ x }_{ 2 },y_{ 2 }), ({ x }_{ 3 },y_{ 3 }),...,({ x }_{ n },y_{ n })$$

The mean and standard deviation of the $x$-values are:

$\bar { x } =10$
${ s }_{ x }=12$

The mean and standard deviation of the $y$-values $\bar { y } =15$ and ${ s }_{ y }=6$.

Which of the following could represent the least squares regression line?

A

$\widehat { y } =-25+4x$

B

$\hat { y } = 8 + 0.5x$

C

$\hat { y } = 6+2x$

D

$\hat { y } = 4x$

E

$\widehat { y } =11+0.4x$