Correlation and Linear Regression

$\pm 1$ means the points lie exactly on a straight line; 0 means no linear relationship. A value outside this range is an error.

The magnitude gives the strength and the sign gives the direction: as $x$ rises, $y$ tends to fall.

$b = \dfrac{S_{xy}}{S_{xx}} = 0.8$. Each unit rise in $x$ is associated with a rise of 0.8 in $y$.

It follows from $a = \bar{y} - b\bar{x}$, and it makes a useful check on the arithmetic.

$r_s = 1 - \dfrac{6(10)}{6(35)} = 1 - \dfrac{60}{210} = 0.714$.

Nothing in the data supports assuming the linear pattern continues that far beyond the observed range.