Correlation and Regression

·        Correlation: The correlation is the measure of extent and direction of relationship between two variables in two bivariate distribution. Two variables are said to have correlation when they are so related that the change in the value of one variable is accompanied by the change in the value of other.

·   Positive and negative correlation: If two variables vary in the same direction, i.e. if increase or decrease in the values of one variable corresponds to increase or decrease in another variable then the correlation is considered to be positive correlation.

      On the other hand if two variables very in the opposite direction, i.e. if one variable increase or decreases corresponds to the second variable decrease or increase then the two variables are considered to have negative correlation.

·  Linear and non-linear correlation

      A linear correlation coefficient is a measure of linear relationship between the two variables X and Y. If all the points in the scatter diagram seem to lie near a line, then the correlation is called linear. If the points seems to lie near to some curve, then the correlation is called non-linear.

Simple and Multiple or partial correlation

Correlation between two variable - simple

Correlation coefficient between more than two variables - multiple or partial

·   Scatter diagram: Scatter diagram is a simple and attractive method of diagrammatic representation of bivariate distribution for ascertaining the nature of correlation between two variables.

·   Coefficient of correlation: The coefficient of correlation is a number which indicates to what extent two variables are related, to what extent variations in one go with the variations in the other. The coefficient of correlation lies between –1 and 1 inclusive.

·   Karl Pearson's Coefficient of Correlation: One of the widely used mathematical methods of calculating the correlations coefficient between two variable is Karl Pearson's correlation coefficient. It is denoted by rxy or simply r and is defined by