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प्रश्न
Calculate the correlation coefficient between X and Y and comment on their relationship.
|
X |
1 |
3 |
4 |
5 |
7 |
8 |
|
Y |
2 |
6 |
8 |
10 |
14 |
16 |
उत्तर
| X | Y | XY | X2 | Y2 |
| 1 | 2 | 2 | 1 | 4 |
| 3 | 6 | 18 | 9 | 36 |
| 4 | 8 | 32 | 16 | 64 |
| 5 | 10 | 50 | 25 | 100 |
| 7 | 14 | 98 | 49 | 196 |
| 8 | 16 | 128 | 64 | 256 |
| ∑X = 28 | ∑Y = 56 | ∑XY = 328 | ∑X2 = 164 | ∑Y2 = 656 |
r = `(sumXY - ((sumX)(sumY))/N)/(sqrt(sumX^2 - (sumX)^2/N)sqrt(sumY^2 - (sumY)^2/N))`
= `(328 - (28 xx 56)/6)/(sqrt(164 - (28)^2/6)sqrt(656 - (56)^2/6))`
= `(328 - 1568/6)/(sqrt(164 - 784/6)sqrt(656 - 3136/6))`
= `(328 - 261.33)/(sqrt(164 - 130.67)sqrt(656 - 522.67))`
= `66.67/(sqrt33.33sqrt(133.33))`
= `66.67/(5.77 xx 11.55)`
= `66.6/66.6`
= 1.00
= 1
As the correlation coefficient between the two variables is +1, so the two variables are perfectly positively correlated.
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संबंधित प्रश्न
If rxy is positive the relation between X and Y is of the type ______
If rxy = 0 the variable X and Y are ______
Of the following three measures which can measure any type of relationship.
Can r lie outside the –1 and 1 range depending on the type of data?
Does zero correlation mean independence?
Can a simple correlation coefficient measure any type of relationship?
Interpret the values of r as 1, –1, and 0.
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 |
Calculate the correlation coefficient between X and Y and comment on their relationship:
|
X |
-3 |
-2 |
-1 |
1 |
2 |
3 |
|
Y |
9 |
4 |
1 |
1 |
4 |
9 |
