Answer to Question #214663 in Statistics and Probability for Umair

Question

Find the co-efficient of correlation between persons employed(X) and cloth manufactured(Y) in a textile Mill. Interpret the results.                                                     

X

137

209

113

189

176

200

219

Y

23

47

22

40

39

51

49

Answer 1

$r = \frac{ \sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y}) }{ \sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar{y})^2}}$

From the table above;

$r = \frac{ 2693.142857 }{ \sqrt{9155.71429}\times \sqrt {853.428571}}$

$=0.96345$

The coefficient of correlation between persons employed(X) and cloth manufactured(Y) in a textile Mill is 0.96345. There is a strong positive association between persons employed and cloth manufactured.