Introduction to Correlation and Linear Regression Analysis

This chapter gives some concepts of correlation and regression analysis. Correlation comes prior to regression analysis. It starts with the concept of simple correlation coefficient; which gives the degree of linear relationship between two variables. One should draw scatter diagram in order to judge whether there exists any linear relation between the two variables. The correlation coefficient is not only invariant under changes of unit of measurements but also unaffected by changes of origin for both variables. The value of the correlation coefficient always lies in-between –1 and +1. As the scatter points move closer to the straight line, it moves to –1 or +1 depending on whether the relation is negative or positive. The straight-line relation between the two variables can be found by Least Squares (LS) method. The goodness of fit of the linear regression can be measured by the square of the simple correlation coefficient. Multiple Linear Regression Model is an extension of Simple Linear Regression Model. In a multiple linear regression model, we have more than two independent variables. The goodness of fit in this case is measured by coefficient of determination which is the square of the multiple correlation coefficient.