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

Question

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

.2185

.3362

.4675

.5928

Explanation / Answer

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

X Y X?Y X?X Y?Y 71 69 4899 5041 4761 68 64 4352 4624 4096 66 65 4290 4356 4225 67 64 4288 4489 4096 70 65 4550 4900 4225 71 62 4402 5041 3844 73 64 4672 5329 4096 77 66 5082 5929 4356 65 59 3835 4225 3481

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