Question

Calculate Pearson’s coefficient of correlation from the following
taking 100 and 50 as the assumed average of X and Y respectively.
X 104 111 104 114 118 117 105 108 106 100 104 105
Y 57 55 47 45 45 50 64 63 66 62 69 61
(b) Calculate multiple correlation coefficients R1.23 and R2.13 from the following
information: r13= 0.64, r23 0.79 and r12 0.80

Answer 1

a) Calculate

x = X-Xmean

y = Y-Ymean

then we find that

$$\sum x^2 = 1128 \\ \sum y^2 = 1380 \\ \sum xy = 312 \\ \rho(X,Y) = \frac {\sum xy}{\sqrt{\sum x^2} \sqrt{\sum y^2}} = \frac{312}{\sqrt{1128} \sqrt{1380}} = 0.2501$$

b)

$R1.23 = \sqrt{ \frac{r_{12}^2 + r_{13}^2 - 2r_{12}r_{13}r_{23}}{1-r_{23}^2}} = 0.8$

$R2.13 = \sqrt{ \frac{r_{12}^2 + r_{23}^2 - 2r_{12}r_{12}r_{23}}{1-r_{13}^2}} = 0.878$