**Correlation**

- It measures extent of relationship between two or more variables which is important in statistics
- Predictions about expectations can be made. (say if there is proper rain, the food position is likelyto be rood)
- Where value of one variable is known. the value of other variable can beworked out.

**Types of correlation**

The important types of correlation may be positive (direct) and negative (indirect) OR linear and nonlinear correlation. Other may be simple and multiple correlation OR partial and total correlation, OR logical and illogical Correlation.

** Positive correlation** : Where two variables move in the same direction i.e. if there is decline in one variable and 2nd variable also shows decline, the correlation- is direct or positive. For example at increasing price of a commodity, the supply of the commodity is likely to be increasing. Hence, between price and supply, the correlation is positive.

** Negative correlation **: Where two variables move in the opposite direction i.e. if there is decline in one variable and 2″ variable shows increase, the correlation is -indirect or negative. For example, at increasing price of a . commodity, the demand of the commodity is-likely to be decreasing.

** Linear correlation **: If change in one variable brings change in the other variable constantly at the same rate over the entire range of values. Two variables are linearly related if there is a relation of the form Y = a + b X, between them.

** Non-Linear (or curvi-linear) correlation :** If change in one variable brings change in the other variable constantly at the different rate, over the entire range of values.

**Degree and interpretation of correlation coefficient:**

The coefficient of correlation lies between two limits i.e. + or— I. For perfect positive correlation, the value would be +1 and for perfect negative, the value would be -I . When value is 0, there is no relationship

**Regression**

The statistical technique of estimating or predicting. Unknown value of a dependent Variable from – the known Value of an independent variable, called regression :analysis If it is known that the two Variables say ‘price (X) and demand (Y), are closely related, most probable value of Y can be found with given value of x. The regression analysis ‘can be classified on the basis of Change in proportion and Number of variables.

**Regression on the basis of Change in proportion:** On the basis ‘of -change in proportion, regression can be Classified as linear regression and non-linear regression.

** Linear regression **: When the dependent variable moves in a fixed proportion of the unit movement of the independent variable, it is called linear regression. When it is plotted on graph ‘paper, it forms a straight line..

Mathematically it can be expressed as:, – . .

yi.=.a.+bxi+ei (where a and b are known as regression parameters, ei denotes residual terms , xi presents value of independents variable and yi is the value of dependent variable say y when ‘the value of independent’ variable, that is x, is zero).

Again b denotes slope of regression line of y on x axis. ei denotes the combined effect of all other variable on Y axis.

** Non-linear regression **: In such regression the value of dependent variable say y does not change by a constant absolute amount for unit change in the value of the independent variable, say x. If the data is plotted on the graph, it would form a curve instead of a straight line. Hence it is called, curvi-linear regression.

**Regression on the basis of no. of variables:** Regression analysis can be simple, partial or multiple regression.

** Simple regression **: When only two variables are studied, it is knows as simple regression. One of these variables is independent and other the dependent. Functional relationship between price and demand of a product is an example of such regression.

** Partial regression **: When more than two variables are studied in a functional relationship but the relationship of only two variables is analysed at a time keeping the other constant it is partial regression.

** Multiple regression :** When more than 2 variables are studied and their functional relationship are simultaneously worked out, it is case of multiple regression. Study of growth in bank deposits in relation, to occupation and wealth of people, is an example of such regression.