Advertisements
Advertisements
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 |
Advertisements
उत्तर
| X | Y | x = `"X" - bar"X"` = X − 6 |
y = `"Y" - bar"Y"` = Y − 4 |
x2 | y2 | xy |
| 5 | 1 | − 1 | − 3 | 1 | 9 | 3 |
| 10 | 6 | 4 | 2 | 16 | 4 | 8 |
| 5 | 2 | − 1 | − 2 | 1 | 4 | 2 |
| 11 | 8 | 5 | 4 | 25 | 16 | 20 |
| 12 | 5 | 6 | 1 | 36 | 1 | 6 |
| 4 | 1 | − 2 | − 3 | 4 | 9 | 6 |
| 3 | 4 | − 3 | 0 | 9 | 0 | 0 |
| 2 | 6 | − 4 | 2 | 16 | 4 | − 8 |
| 7 | 5 | 1 | 1 | 1 | 1 | 1 |
| 1 | 2 | − 5 | − 2 | 25 | 4 | 10 |
| 60 | 40 | 0 | 0 | 134 | 52 | 48 |
N = 10, ∑X = 60, ∑Y = 40, ∑x2 = 134, ∑y2 = 52, ∑xy = 48, `bar"X" = (sum"X")/"N" = 60/10` = 6, `bar"Y" = (sum"Y")/"N" = 40/10` = 4.
Coefficient of correlation
r = `(sum"xy")/(sqrt(sum"x"^2 sum"y"^2))`, Where x = `"X" - bar"X"`, y = `"Y" - bar"Y"`
r = `48/sqrt (134 xx 52)`
r = 0.575
APPEARS IN
संबंधित प्रश्न
In the following data one of the value of y is missing. Arithmetic means of x and y series are 6 and 8 respectively. `(sqrt(2) = 1.4142)`
| x | 6 | 2 | 10 | 4 | 8 |
| y | 9 | 11 | ? | 8 | 7 |
Estimate missing observation.
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 |
Example for positive correlation is
If the values of two variables move in the opposite direction then the correlation is said to be
Correlation co-efficient lies between
The correlation coefficient is
The variable which influences the values or is used for prediction is called
Scatter diagram of the variate values (X, Y) give the idea about
If two variables moves in decreasing direction then the correlation is
Find the coefficient of correlation for the following data:
| X | 35 | 40 | 60 | 79 | 83 | 95 |
| Y | 17 | 28 | 30 | 32 | 38 | 49 |
