Question

Deviation of two series of X and Y are shown. Calculate coefficient of correlation.

X	+5	−4	−2	+20	−10	0	+3	0	−15	−5
Y	+5	−12	−7	+25	−10	−3	0	+2	−9	−15

Answer 1

dx	dx2	dy	dy2	dxdy
5 –4 –2 20 –10 0 3 0 –15 –5	25 16 4 400 100 0 9 0 225 25	5 –12 –7 25 –10 –3 0 2 –9 –15	25 144 49 625 100 9 0 4 81 225	25 48 14 500 100 0 0 0 135 75
∑dx= –8	∑dx2 = 804	∑dy= –24	∑dy2 = 1262	∑dxdy= 897

$$\begin{gathered} r=\frac{{\sum }_{}{d}_x{d}_y-{\displaystyle \frac{\left({\sum }_{}^{}{d}_x\right)\times \left({\sum }_{}^{}{d}_y\right)}{N}}}{\sqrt{{\sum }_{}^{}{d}_x^{\mathit{2}}-{\displaystyle \frac{{\left({\sum }_{}^{}{d}_x\right)}^2}{N}}}\times \sqrt{{\sum }_{}^{}{d}_y^{\mathit{2}}-{\displaystyle \frac{{\left({\sum }_{}^{}{d}_y\right)}^2}{N}}}} \\ \mathrm{or},r=\frac{897-{\displaystyle \frac{\left(-8\right)\times \left(-24\right)}{10}}}{\sqrt{804-{\displaystyle \frac{(-8{)}^2}{10}}}\times \sqrt{1262-{\displaystyle \frac{(-24{)}^2}{10}}}}=\frac{877.8}{28.24\times 34.70} \\ \therefore r=+0.895 \end{gathered}$$