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Finding Equation of an LSRL Using Means and Standard Deviations

APSTAT-IYGYRN

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:

$$\bar { x } =4, \quad {s }_{ x }=8$$

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

$$\bar { y } =12, \quad { s }_{ y }=6$$.

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

A

$\hat { y } = 11.2 + 0.2x$

B

$\hat { y } = 8 + 0.75x$

C

$\hat { y } = 4+1.333x$

D

$\hat { y } = 2x$

E

$\hat { y } = 4+2x$