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 |
Advertisements
उत्तर
| Sr. 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
dx = 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(-2))/(sqrt(10xx203- (1)^2) xx sqrt(10xx159 -(-3)^2)`
= `r = (1780 + 2)/(sqrt(2030 - 1) * sqrt(1590 - 4)) = (1782)/(sqrt(2029*1586))`
= `r = (1782)/(sqrt(3219494)) = (1782)/(1793.17)`
r ≈ 0.9955
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 |
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.
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 |
Example for positive correlation is
If the values of two variables move in same direction then the correlation is said to be
If the values of two variables move in the opposite direction then the correlation is said to be
If r(X,Y) = 0 the variables X and Y are said to be
From the following data, N = 11, ∑X = 117, ∑Y = 260, ∑X2 = 1313, ∑Y2 = 6580, ∑XY = 2827 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
The coefficient of correlation describes
Calculate the coefficient of correlation from the following data:
∑X = 50, ∑Y = – 30, ∑X2 = 290, ∑Y2 = 300, ∑XY = – 115, N = 10
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 |
Calculate the correlation coefficient from the following data:
∑X = 125, ∑Y = 100, ∑X2 = 650, ∑Y2 = 436, ∑XY = 520, N = 25
Define Correlation.
State and explain the different kinds of Correlation.
