Question

Calculator the coefficient correlation coefficient between height of father and height of son from the following height of father inches 64 65 66 67 68 69 70 height of son inches 66 67 65 68 70 68 72

Answer 1

Answer:

Correlation Coefficient = 0.78

Step-by-step explanation:

To calculate the correlation coefficient between height of father and height of son from the following data given, we are using Spearman's rank correlation method.

The formula for Spearman's rank correlation = 1 -  $\frac{6\sum d_i^{2}}{n(n^{2}-1)}$ ,

         where $d_i$ = difference in ranks given

                     n = number of observations

 Now to use this method we will assign ranks to each height of father and son separately by marking the highest height as 1 second highest as 2 and so on...

Height of father    Rank A     Height of Son     Rank B    D=Rank B - Rank A

      64                        7                        66                    5                      -2

      65                        6                        67                    4                      -2

      66                        5                        65                    6                       1

      67                        4                        68                    3.5                   -0.5

      68                        3                        70                    2                       -1

      69                        2                        68                   3.5                      1.5

      70                         1                         72                   1                           0

Note: Here we write 3.5 rank for two number because those number were same and for same numbers we assign rank as adding both rank and divide it by 2 so we get $\frac{3+4}{2}$ = 3.5 .

Correlation Coefficient = 1 - $\frac{6((-2)^{2}+(-2)^{2} +1^{2} +(-0.5)^{2}+(-1)^{2}+1.5^{2} ) }{7(7^{2}-1) }$

                                      = 0.78

Therefore, the  correlation coefficient between height of father and height of son is 0.78 .

Note: We can use other methods also for calculation of correlation coefficient.

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