Question

Calculate coefficient of correlation from the following data:

Height of fathers (inches)	66	68	69	72	65	59	62	67	61	71
Height of Sons (inches)	65	64	67	69	64	60	59	68	60	64

Answer 1

Height of Fathers (X)	Height of Sons (Y)	X2	Y2	XY
66 68 69 72 65 59 62 67 61 71	65 64 67 69 64 60 59 68 60 64	4356 4624 4761 5184 4225 3481 3844 4489 3721 5041	4225 4096 4489 4761 4096 3600 3481 4624 3600 4096	4290 4352 4623 4968 4160 3540 3658 4556 3660 4544
$\mathit{\Sigma }\mathit{X}$=660	$\mathit{\Sigma }\mathit{Y}$=640	$\mathit{\Sigma }{\mathit{X}}^{\mathbf{2}}$=43726	$\mathit{\Sigma }{\mathit{Y}}^{\mathbf{2}}$=41068	$\mathit{\Sigma }\mathit{X}\mathit{Y}$=42351

N = 10

$$\begin{gathered} r=\frac{N\Sigma \mathrm{XY}-\Sigma X\Sigma Y}{\sqrt{N\Sigma X^2-{\left(\Sigma X\right)}^2}\sqrt{\mathit{}N\Sigma Y^2-{\left(\Sigma Y\right)}^2}} \\ \mathrm{or},r=\frac{10\times 42351-660\times 640}{\sqrt{10\times 43726-{\left(660\right)}^2}\sqrt{10\times 41068-{\left(640\right)}^2}} \\ \mathrm{or},r=\frac{1110}{40.74\times 32.86} \\ \Rightarrow r=0.829 \end{gathered}$$

Therefore, coefficient of correlation= 0.829YNΣX2−(ΣX)2NΣY2−(ΣY)2√√r =10×121255−1316×92010×173348−(1316)2√10×85114−(920)2√r=183040.29×68.84r =0.