# Difference between Correlation and Regression

9th February 2020

Correlation

The term correlation is a combination of two words ‘Co’ (together) and relation (connection) between two quantities. Correlation is when, at the time of study of two variables, it is observed that a unit change in one variable is retaliated by an equivalent change in another variable, i.e. direct or indirect. Or else the variables are said to be uncorrelated when the movement in one variable does not amount to any movement in another variable in a specific direction. It is a statistical technique that represents the strength of the connection between pairs of variables.

Correlation can be positive or negative. When the two variables move in the same direction, i.e. an increase in one variable will result in the corresponding increase in another variable and vice versa, then the variables are considered to be positively correlated. For instance: profit and investment.

On the contrary, when the two variables move in different directions, in such a way that an increase in one variable will result in a decrease in another variable and vice versa, This situation is known as negative correlation. For instance: Price and demand of a product.

The measures of correlation are given as under:

• Karl Pearson’s Product-moment correlation coefficient
• Spearman’s rank correlation coefficient
• Scatter diagram
• Coefficient of concurrent deviations

Regression

A statistical technique for estimating the change in the metric dependent variable due to the change in one or more independent variables, based on the average mathematical relationship between two or more variables is known as regression. It plays a significant role in many human activities, as it is a powerful and flexible tool which used to forecast the past, present or future events on the basis of past or present events. For instance: On the basis of past records, a business’s future profit can be estimated.

### Difference

 Correlation Regression Meaning Correlation is a statistical measure which determines co-relationship or association of two variables. Regression describes how an independent variable is numerically related to the dependent variable. Usage To represent linear relationship between two variables. To fit a best line and estimate one variable on the basis of another variable. Dependent and Independent variables No difference Both variables are different. Indicates Correlation coefficient indicates the extent to which two variables move together. Regression indicates the impact of a unit change in the known variable (x) on the estimated variable (y). Objective To find a numerical value expressing the relationship between variables. To estimate values of random variable on the basis of the values of fixed variable.