Correlation is the degree of the relationship between two or more variables. It does not explain the cause behind the relationship.
Kinds of Correlation may be studied on the basis of:
I. Change in proportion.
II. Number of variation.
III. Change in direction.
(I) Basis of change in proportion: There are two important correlations on the basis of change in proportion. They are:
(a) Linear correlation
(b) Non-linear correlation
(a) Linear correlation: Correlation is said to be linear when one variable move with the other variable in fixed proportion
(b) Non-linear correlation: Correlation is said to be non-linear when one variable move with the other variable in changing proportion.
(II) On the basis of number of variables: On the basis of number of variables, correlation may be:
(a) Simple
(b) Partial
(c) Multiple
(a) Simple correlation: When only two variables are studied it is a simple correlation.
(b) Partial correlation: When more than two variables are studied keeping other variables constant, it is called partial correlation.
(c) Multiple correlations: When at least three variables are studied and their relationships are simultaneously worked out, it is a case of multiple correlations
(III) On the basis of Change in direction: On the basis of Chang in direction, correlation may be
(a)Positive Correlation
(b)Negative Correlation
(a) Positive Correlation: Correlation is said to be positive when two variables move in same direction.
(b) Negative Correlation: Correlation is said to be negative when two variables moves in opposite direction.
Uses of Correlation
1. It gives a precise quantitative value indicating the degree of relationship existing between the two variables.
2. It measures the direction as well as relationship between the two variables.
3. Further in regression analysis it is used for estimating the value of dependent variable from the known value of the independent variable
4. The effect of correlation is to reduce the range of uncertainty in predictions.
Limitations of correlation:
1. Extreme items affect the value of the coefficient of correlation.
2. Its computational method is difficult as compared to other methods.
3. It assumes the linear relationship between the two variables, whether such relationship exist or not.
Difference between correlation and regression:
(1) Nature of relationship: Correlation explains the degree of relationship, whereas regression explains the nature of the relationship.
(2) Causal relationship: Correlation does not explain the cause behind the relationship whereas regression studies the cause and effect relationship.
(3) Prediction: Correlation does not help in making prediction whereas regression enable us to make prediction.
(4) Origin and scale: Correlation coefficient is independent of the change of origin and scale, whereas regression coefficient is independent of change of origin but not of scale.
Degrees of Correlation:
1. Perfect Correlation: It two variables vary in same proportion, and then the correlation is said to be perfect correlation.
2. Positive Correlation: If increase (or decrease) in one variable corresponds to an increase (or decrease) in the other, the correlation is said to be positive correlation.
3. Negative Correlation: If increase (or decrease) in one variable corresponds to a decrease (or increase) in the other, the correlation is said to be positive correlation.
4. Zero or No Correlation: If change in one variable does not other, than there is no or zero correlation.