Correlation From a Summary Table

A greenhouse trial recorded, for each of $n = 10$ plots, the daily hours of sunlight $x$ and the yield $y$ in grams. The raw pairs have been lost, but the lab notebook still holds the totals:

$\sum x = 50, \qquad \sum y = 80, \qquad \sum xy = 470$

$\sum x^2 = 300, \qquad \sum y^2 = 800$

Pearson's correlation coefficient is

$r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \; \sum (y_i - \bar{y})^2}}$

and the three deviation sums it needs can be rebuilt from raw totals using

$S_{xy} = \sum xy - \frac{(\sum x)(\sum y)}{n}, \qquad S_{xx} = \sum x^2 - \frac{(\sum x)^2}{n}, \qquad S_{yy} = \sum y^2 - \frac{(\sum y)^2}{n}$

What is Pearson's $r$ for sunlight and yield?

Round your answer to 3 decimal places.