The correlation is an answer to the strength of the linear association between the paired variables, assuming X and Y. Regression as an extension tells us about the form of the association that in the best way predicts Y from the value of X.
To calculate correlation certain pre requisites are necessary:
- Both X and Y is measured in each subject and also quantify how much is the linear association between the two.
- The Pearson product moment correlation co efficient has to be used when the assumption made by X and Y are sampled from a population that is normally distributed.
- Correlation is not used in the case of manipulated variables.
- We use Linear Regression is used in a situation when one of the independent variable has to make prediction about the dependent Y variable.
- Both X and Y is not symmetric in the case of Linear Regression. This means that if X and Y are interchanged the regression model would be redefined. If X in terms of Y is placed against the original Y in terms of Y the regression model would be redefined. However, in the case of correlation coefficient if the variables X and Y are interchanged the value of the coefficient would remain the same.
- In the case when we target to achieve the best linear regression model we select the variable X with the least strong correlation to Y.
- A correlation is a relationship between two variables. A positive correlation indicates and signifies that one value going up the other value also goes up. If the values are plotted on a scatter plot from left to right, the height of the graph would also increase. The reverse of this is indicated in a negative correlation where the effect of the variables on each other is negative. In the case of the value of one increases, the value of the other decreases.
The regression analysis is complete and simpler to understand when applying line to a scatter plot. The purpose behind deriving the regression line is that the squared and summed across value is the smallest possible value.