Question

age: 41=350 bone density age:49=345bone densityage :57=340 bone density age : 61=325 bone density age:69=310 bone density calculate the correlation coefficient ,r.Round to three decimal places.

Answer 1

Given:

$\bar{x}=\frac{41+49+57+61+69}{5}$$\bar{x}=55.4$$\bar{y}=\frac{350+345+340+325+310}{5}$$\bar{y}=334$

Formula for the correlation coefficient:

$r=\frac{\Sigma(x-\bar{x})(y-\bar{y)}}{\sqrt[]{\Sigma(x-\bar{x})^2\Sigma(y-\bar{y})^2}}$$\Sigma(x-\bar{x})(y-\bar{y})=-668$$\Sigma(x-\bar{x})^2=467.2$$\Sigma(y-\bar{y})^2=1070$$r=\frac{-668}{\sqrt[]{(467.2)(1070)}}$$r=\frac{-668}{\sqrt[]{499904}}$$r=-0.9448$$r=-0.945$