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प्रश्न
Calculate the correlation coefficient from the data given below:
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| Y | 9 | 8 | 10 | 12 | 11 | 13 | 14 | 16 | 15 |
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उत्तर
| X | Y | x = X − 5 | y = Y − 12 | x2 | y2 | xy |
| 1 | 9 | − 4 | − 3 | 16 | 9 | 12 |
| 2 | 8 | − 3 | − 4 | 9 | 16 | 12 |
| 3 | 10 | − 2 | − 2 | 4 | 4 | 4 |
| 4 | 12 | − 1 | 0 | 1 | 0 | 0 |
| 5 | 11 | 0 | − 1 | 0 | 1 | 0 |
| 6 | 13 | 1 | 1 | 1 | 1 | 1 |
| 7 | 14 | 2 | 2 | 4 | 4 | 4 |
| 8 | 16 | 3 | 4 | 9 | 16 | 12 |
| 9 | 15 | 4 | 3 | 16 | 9 | 12 |
| 45 | 108 | 0 | 0 | 60 | 60 | 57 |
Correlation coefficient
r(x, y) = `(sum"xy")/(sqrt (sum"x"^2) xx sqrt (sum"y"^2))`
= `57/(sqrt60 xx sqrt(60))`
= `57/60`
r = 0.95
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संबंधित प्रश्न
Calculate the correlation coefficient for the following data.
| X | 5 | 10 | 5 | 11 | 12 | 4 | 3 | 2 | 7 | 1 |
| Y | 1 | 6 | 2 | 8 | 5 | 1 | 4 | 6 | 5 | 2 |
Find the coefficient of correlation for the following:
| Cost (₹) | 14 | 19 | 24 | 21 | 26 | 22 | 15 | 20 | 19 |
| Sales (₹) | 31 | 36 | 48 | 37 | 50 | 45 | 33 | 41 | 39 |
Calculate the coefficient of correlation for the ages of husbands and their respective wives:
| Age of husbands | 23 | 27 | 28 | 29 | 30 | 31 | 33 | 35 | 36 | 39 |
| Age of wives | 18 | 22 | 23 | 24 | 25 | 26 | 28 | 29 | 30 | 32 |
Calculate the correlation coefficient for the following data.
| X | 25 | 18 | 21 | 24 | 27 | 30 | 36 | 39 | 42 | 48 |
| Y | 26 | 35 | 48 | 28 | 20 | 36 | 25 | 40 | 43 | 39 |
Example for positive correlation is
The variable whose value is influenced (or) is to be predicted is called
The variable which influences the values or is used for prediction is called
The correlation coefficient
If r = – 1, then correlation between the variables
Calculate the coefficient of correlation from the following data:
∑X = 50, ∑Y = – 30, ∑X2 = 290, ∑Y2 = 300, ∑XY = – 115, N = 10
