Correlation & Regression Analysis

Definition & Objective

The objective of correlation analysis is to see whether two measurements variables co vary, and also to quantify the strength of the relationship between variables. The regression, in the other hand will express the relationship in the form of an equation.

In an example, a group of students taking a maths and english test, we could use correlation to determine whether students who are good at maths tend to be good at english as well, and regression to determine whether the marks in english can be predicted for given marks in maths.

There are three main objective of this method which is :

- to test hypotheses about cause and effect relationships.

- to see whether two variables are associated, without necessarily inferring a cause and effect relationship.

- estimating the value of one variable corresponding to a particular value of the other variable.

Uses of Correlation

Correlation can be used such as the Pearson Product Moment Correlation Coefficient, to test if there is a linear relationship between the variables. To quantify the strength of the relationship, we can calculate the correlation coefficient (r). Its numerical values ranges from +1.0 to -1.0. r > 0 indicates positive linear relationship, while r < 0 indicates negative linear relationship and r = 0 indicates no linear relationship.

Uses of Regression

In the analysis of regression, the problem of interest is the nature of the relationship itself between the dependent variable and the independent variables.

The analysis consists of choosing and fitting an appropriate model, done by the method of least squares, with a view to exploiting the relationship between the variables to help estimate the expected response for a given value of the independent variable. For example, if we are interested in the effect of age on height, then by fitting a regression line, we can predict the height for a given age.

By: Hanis Jefry

References:

http://abyss.uoregon.edu/~js/glossary/correlation.html

http://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_multivariable/bs704_multivariable5.html

http://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one/11-correlation-and-regression

http://keydifferences.com/difference-between-correlation-and-regression.html