The following data shows heights for some adult brother and

The following data shows heights for some adult brother and sister pairs.

Brother\'s height (inches)           Sister\'s height (inches)

71                                                69

68                                                64

66                                                65

67                                                64

70                                                65

71                                                62

73                                                64

77                                                66

65                                                59

Which is the correct value for the correlation between brother\'s height and sister\'s height?

.2185

.3362

.4675

.5928

Solution

Let x be brothers heights and y that of sisters

There are 9 reading given.

Let us find correlation coefficient.

Explanation

Step 1: Find X?Y , X2 and Y2 as it was done in the table below.

Step 2: Find the sum of every column to get:

?X=628 , ?Y=578 , ?X?Y=40370 , ?X2=43934 , ?Y2=37180

Step 3: Use the following formula to work out the correlation coefficient.

r r = n??XY??X??Y[n?X2?(?X)2]?[n?Y2?(?Y)2]??????????????????????????????????= 9?40370?628?578[9?43934?6282]?[9?37180?5782]????????????????????????????????0.4675

r =0.4675

III optin is right