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Question
Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y)
|
X |
65 |
66 |
57 |
67 |
68 |
69 |
70 |
72 |
|
Y |
67 |
56 |
65 |
68 |
72 |
72 |
69 |
71 |
Solution
| X | Y | XY | X2 | Y2 |
| 65 | 67 | 4355 | 4225 | 4489 |
| 66 | 56 | 3696 | 4356 | 3136 |
| 57 | 65 | 3705 | 3249 | 4225 |
| 67 | 68 | 4556 | 4489 | 4624 |
| 68 | 72 | 4896 | 4624 | 5184 |
| 69 | 72 | 4968 | 4761 | 5184 |
| 70 | 69 | 4830 | 4900 | 4761 |
| 72 | 71 | 5112 | 5184 | 5041 |
| ∑X = 534 | ∑Y = 540 | ∑XY = 36118 | ∑X2 = 35788 | ∑Y2 = 36644 |
r = `(sumXY - ((sumX)(sumY))/N)/(sqrt(sumX^2 - (sumX)^2/N) sqrt(sumY^2 - (sumY)^2/N))`
= `(36118 - (534 xx 540)/8)/(sqrt(35788 - (534)^2/8)sqrt(36644 - (540)^2/8))`
= `(36118 - 288360/8)/(sqrt(35788 - 285156/8)sqrt(36644 - 291600/8))`
= `(36118 - 36045)/(sqrt(35788 - 35644.5)sqrt(36644 - 36450))`
= `73/(sqrt143.5 sqrt(194))`
= `73/(11.98 xx 13.93)`
= `73/166.88`
= 0.44
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