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प्रश्न
Find Karl Pearson’s coefficient of correlation between the variables X and Y for the following data
| X | 11 | 7 | 9 | 5 | 8 | 6 | 10 |
| Y | 10 | 8 | 6 | 5 | 9 | 7 | 11 |
उत्तर
Let X = xi , Y = yi
| Total | ||||||||
| `x_i` | 11 | 7 | 9 | 5 | 8 | 6 | 10 | 56 |
| `y_i` | 10 | 8 | 6 | 5 | 9 | 7 | 11 | 56 |
| `x_i^2` | 121 | 49 | 81 | 25 | 64 | 36 | 100 | 476 |
| `y_i^2` | 100 | 64 | 36 | 25 | 81 | 49 | 121 | 476 |
| `x_iy_i` | 110 | 56 | 54 | 25 | 72 | 42 | 110 | 469 |
From the table, we have
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संबंधित प्रश्न
In the following data, one of the values of Y is missing. Arithmetic means of X and Y series are 6 and 8
|
X |
6 |
2 |
10 |
4 |
8 |
|
Y |
9 |
11 |
? |
8 |
7 |
(a) Estimate the missing observation.
(b) Calculate correlation coefficient.
For 10 pairs of observations on two variables X and Y, the following data are available:
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Find the correlation coefficient between X and Y.
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| `l_x` | 1000 | 900 | 700 |
| `T_x` | - | - | 11500 |
Find Karl Pearson's correlation coefficient for the following data :
| X | 3 | 2 | 1 | 5 | 4 |
| Y | 8 | 4 | 10 | 2 | 6 |
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| Distance (Km) | 80 | 120 | 160 | 200 | 240 |
| Time (Hr) | 2 | 3 | 4 | 5 | 6 |
Draw scatter diagram and identify the type of correlation.
If r = 0.5, σx = 1 and σy = 4, then find Cov.(X,Y).
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Find: (a) Correlation coefficient.
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`n = 15 ,bar x = 25, bary = 18, σ_x = 3.01, σ_y = 3.03,`
`sum ("x"_i - bar x) ("y"_i - bar y) = 122`
Compute rank correlation coefficient for the following data :
| Rx | 1 | 2 | 3 | 4 | 5 | 6 |
| Ry | 6 | 3 | 2 | 1 | 4 | 5 |
If the rank correlation coefficient is `2/3` and `Σ"d"_1^2` = 55` , then find the number of pairs of observations. (Assume that no rank is repeated.)
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| Length (cm) | 3 | 4 | 6 | 7 | 10 |
| Weight (gm) | 9 | 11 | 14 | 15 | 16 |
Calculate Karl Pearson's coefficient of correlation between the length and weight and interpret the result.
