Advertisements
Advertisements
प्रश्न
Find the coefficient of correlation for the following data:
| X | 35 | 40 | 60 | 79 | 83 | 95 |
| Y | 17 | 28 | 30 | 32 | 38 | 49 |
Advertisements
उत्तर
| X | Y | dx = X − 65 | dy = Y − 32 | dx2 | dy2 | dxdy |
| 35 | 17 | − 30 | − 15 | 900 | 225 | 450 |
| 40 | 28 | − 25 | − 4 | 625 | 16 | 100 |
| 60 | 30 | − 5 | − 2 | 25 | 4 | 10 |
| 79 | 32 | 14 | 0 | 196 | 0 | 0 |
| 83 | 38 | 18 | 6 | 324 | 36 | 108 |
| 95 | 49 | 30 | 17 | 900 | 289 | 510 |
| 392 | 194 | 2 | 2 | 2970 | 570 | 1178 |
`bar"X" = 392/6` = 65.33
`bar"Y" = 194/6` = 32.33
Coefficient of correlation
r(X, Y) = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/(sqrt("N"sum"dx"^2 - (sum"dx")^2) xx sqrt("N"sum"dy"^2 - (sum"dy")^2))`
= `(6(1178) - 2(2))/(sqrt(6(2970) - 4) xx sqrt(6(570) - 4))`
= `7064/(sqrt17816 xx sqrt3416)`
= `7065/((133.48) (58.45))`
= `7064/7801.91`
= 0.906
APPEARS IN
संबंधित प्रश्न
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 between X and Y series from the following data.
| Description | X | Y |
| Number of pairs of observation | 15 | 15 |
| Arithmetic mean | 25 | 18 |
| Standard deviation | 3.01 | 3.03 |
| Sum of squares of deviation from the arithmetic mean | 136 | 138 |
Summation of product deviations of X and Y series from their respective arithmetic means is 122.
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 which influences the values or is used for prediction is called
If two variables moves in decreasing direction then the correlation is
If Cov(x, y) = – 16.5, `sigma_"x"^2` = 2.89, `sigma_"y"^2` = 100. Find correlation coefficient.
Calculate the correlation coefficient from the following data:
∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520, N = 25
If both variables X and Y increase or decrease simultaneously, then the coefficient of correlation will be:
Calculate the Karl Pearson Correlation Co-efficient for the following data:
| Demand for Product X: | 23 | 27 | 28 | 29 |
30 |
31 | 33 | 35 | 36 | 39 |
| Sale of Product Y: | 18 | 22 | 23 | 24 | 25 | 26 | 28 | 29 | 30 | 32 |
