Regression analysis

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In a data set of bivariate distribution, there present a set of pairs of observations where each pair of the observations is expressed with numerical values of two variables. Telling alternatively, the bivariate distribution is intended in finding or analyzing relationship between two variables under study. In any scientific studies, the basic interest of the researchers is to find out the possible co-movement of two or more than variables under study.

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In the process of co-movement determination, there exist two important statistical tools popularly called as correlation analysis and regression analysis. Correlation analysis simply, is a measure of association between two or more variables under study. Where as regression analysis examine the nature or direction of association between two variables. Regression analysis is analyzed by classifying the variables in two classes like the dependent variables and the independent variables. Thus it tries to estimate the average value of one variable (dependent variable) from the given value of the other variable(s) (i.e., independent variables). Where as, the condition of correlation analysis is exactly the contrast of the regression analysis. In such a case the basic focus of the researcher is on measurement of the strength of relationship between the variables. In other wards the correlation analysis measures the depth of relationship between two variables where as the regression analysis measures the width of the relationship between the variables. Again in regression analysis, the dependent variables are considered as random or stochastic and the independent variable(s) are assumed to be fixed or non-random. But in the correlation analysis all the variables are treated as symmentric and hence are considered as random.


The magnitude of association or relationship between the two variables can be measured by calculating correlation. Correlation analysis can be defined as a quantative measure of strength of relationship that exists between two variables. There are four types of relationship that may exists between two variables. They are:

  1. Positive correlation
  2. Negative correlation
  3. Linear correlation and
  4. Non-linear correlation.

1. Positive correlation:

Two variables are said to be positively correlated when the movement of the one variable lead to the movement of the other variable in the same direction. In other wards there exists direct relationship between the two variables. For example, the relationship between height of the human being to their corresponding weight, income of the person with expenditure, price of the commodities and supply of the commodity etc. In all such cases increase (or decrease) in the value of one variable leads to the increase (or decrease) in the value of corresponding other variable. The nature of positive relationship between the two variables can also be shown graphically.

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