Calculates with the help of following data by using step deviation. Price Index X : 120, 150, 190, 220, 230
Money supply in Rs. crores (y) : 1800, 2000, 2500, 2700, 3000
Let A = 100 H = 10 B = 13.0 R = 100
The table of transformed variables are as follows
Calculation of r between price Index and money supply using step deviation method
 |
 |
U2 |
V2 |
UV |
|
2 |
1 |
4 |
1 |
2 |
|
5 |
3 |
25 |
9 |
15 |
|
9 |
8 |
81 |
64 |
72 |
|
12 |
10 |
144 |
100 |
120 |
|
13 |
13 |
169 |
169 |
169 |
|
ΣU = 41 |
ΣV = 35 |
ΣU2 = 423 |
ΣV2 = 343 |
ΣUV = 378 |
Substituting these value in the formula
It shows that is strong positive correlation between price index and money supply
What do you mean by a scatter diagram? How is correlation measured by this method?
A scatter diagram : A scatter diagram is a simple visual method for getting some idea about the presence of correlation between two variables. In a scatter diagram, we plot the values of two variables as a set of points on a graph paper, the cluster of points is called scatter diagram.
Drawing of a scatter diagram involves following steps:
1. Writting down the independent variables on X axis.
2. Writting down the dependent variables on Yaxis.
3. Points with the help of given data are marked on the graph paper.
4. When the plotted points show some trend upward or downward, we know that there is some correlation between the variables. When the trend is upward, the correlation is positive. On the other hand, when the trend is downward, the correlation is negative as shown in fig.
What steps are involved in the procedure of calculating Karl Pearson’s coefficient of correlation by direct method?
Steps involved in the procedure of calculation of Karl Pearson’s coefficient of correlation by direct method.
1. Calculate mean value x and y.
2. Calculate deviations of values of x series from mean value.
3. Square the deviations.
4. Calculate deviation of values of y series from mean value.
5. Square the deviation.
6. Multiply the square of deviation of X series with the square of deviations of Y series.
7. Use the following formula for calculating correlation coefficient
Calculate r with the help of following data :
|
No. of years of schooling of farmers |
Annual yield per acre in 000 (Rs) |
|
0 |
4 |
|
2 |
4 |
|
4 |
6 |
|
6 |
10 |
|
8 |
10 |
|
10 |
8 |
|
12 |
7 |
Calculation of r between schooling of farmers and annual yields
Write down the characteristics of (properties) of correlation coefficient.
Properties of correlation coefficient:Following are main properties of correlation coefficient:
1. r has no unit. It is a pure number.
2. A negative value of r indicates an inverse relation. A change in one variable is associated with change in the other variable in the opposite direction.
3. If r is positive the two variables move in the same direction.
4. If, r = 0, the two variables ate uncorrelated. There in no linear relation between them.
5. If r = 1 r = –, the correlation is perfect. The relation between two variables is extact.
6. A high value of r indicates strong linear relationship. Its value in said to be high when it is close to+1 or –1.
7. A low value of r indicates a weak linear relation. Its value is said to be low when it is close to zero.
8. The value of correlation coefficient lies between minus one and pluse one symbolically:
–1 ≤ r ≤ 1
9. The value of r is unaffected by the change of origin and change of scale.
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