Advertisements
Advertisements
प्रश्न
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 |
उत्तर
| S. NO. | X | Y | (X-A) = dx | (Y-A) = dy | dx2 | dy2 | dxdy |
| 1 | 23 | 18 | -8 | -8 | 64 | 64 | 64 |
| 2 | 27 | 22 | -4 | -4 | 16 | 16 | 16 |
| 3 | 28 | 23 | -3 | -3 | 9 | 9 | 9 |
| 4 | 29 | 24 | -2 | -2 | 4 | 4 | 4 |
| 5 | 30 | 25 | -1 | -1 | 1 | 1 | 1 |
| 6 | 31 | 26 | 0 | 0 | 0 | 0 | 0 |
| 7 | 33 | 28 | 2 | 2 | 4 | 4 | 4 |
| 8 | 35 | 29 | 4 | 3 | 16 | 9 | 12 |
| 9 | 36 | 30 | 5 | 4 | 25 | 16 | 20 |
| 10 | 39 | 32 | 8 | 6 | 64 | 36 | 48 |
| N = 10 | ∑X = 311 | ∑Y = 257 | ∑(X-A) = 1 | ∑(Y-A) = (-2) | ∑dx2 = 203 | ∑dy2 = 159 | ∑dxdy = 178 |
`barx = (sumX)/N = 311/10 = 31.1`
`barx = (sumY)/N = 257/10 = 25.7`
Take the assumed values A =31 and B =26
Therefore dr = X-A ⇒ X-31 and
dy = Y - A ⇒ Y-26
`∴ r = (NsumdXdy - (sumdx)(sumdy))/(sqrt(Nsumdx^2-(sumdx)^2)sqrt(Nsumdy^2-(sumdy)^2)`
`= (10xx178 -1xx(-3))/(sqrt(10xx203- (1)^2) xx sqrt(10xx159 -(-3)^2)`
APPEARS IN
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 |
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 |
Find the coefficient of correlation for the following:
| X | 78 | 89 | 96 | 69 | 59 | 79 | 68 | 62 |
| Y | 121 | 72 | 88 | 60 | 81 | 87 | 123 | 92 |
If r(X,Y) = 0 the variables X and Y are said to be
The correlation coefficient from the following data N = 25, ∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520
The correlation coefficient is
The variable whose value is influenced (or) is to be predicted 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
If r = – 1, then correlation between the variables
Calculate the correlation coefficient from the following data:
∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520, N = 25
A measure of the strength of the linear relationship that exists between two variables is called:
If both variables X and Y increase or decrease simultaneously, then the coefficient of correlation will be:
If the points on the scatter diagram indicate that as one variable increases the other variable tends to decrease the value of r will be:
The value of the coefficient of correlation r lies between:
State and explain the different kinds of Correlation.
