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Unit 14: Correlation Analysis Vs. Regression Analysis

(5) Correlation coefficient is independent of origin and change of scale. Regression coefficient is Notes
independent of change of scale but not of origin.
Some Similarities: (1) Coefficient of correlation for two variables shall take the same sign as regression
coefficients. (2) If, at a given level of significance, the value of regression coefficients is significant, the
value of correlation coefficient shall also be significant at that level.
On examining the various definitions, it reveals that regression is a tool which helps in estimating or
predicting the unknown value of one variable from the known value of the other variable. It differs
from correlation as the later only tell the direction and extent of relationship between two variables
whereas regression is a step further.
Self-Assessment
1. Indicate whether the following statements are True or False [T/F]:
(i) Correlation always signifies a cause and effect relationship between the variables.
(ii) If r is negative both the variables are decreasing.
(iii) Regression analysis reveals average relationship between two variables.
(iv) The terms ‘dependent’ and ‘independents’ do not imply that there is necessarily any cause
and effect relationship between the variables.
(v) In regression analysis b stands for regression coefficient of X on Y.
xy
14.4 Summary

• Correlation analysis refers to the techniques used in measuring the closeness of the relationship
between the variables. A very simple definition of correlation is that given by A.M. Tuttle. He
defines correlation as: “An analysis of the covariation of two or more variables is usually called
correlation”.
• The computation concerning the degree of closeness is based on the regression equation.
However, it is possible to perform correlation analysis without actually having a regression
equation.
• Correlation analysis contributes to the economic behaviour, aids in locating the critically
important variables on which others depend, may reveal to the economist the connection by
which disturbances spread and suggest to him the paths through which stabilizing forces become
effective.
• Progressive development in the methods of science and philosophy has been characterised by
increase in the knowledge of relationships or correlations. Nature has been found to be a
multiplicity of interrelated forces.
• Correlation observed between variables that could not conceivably be causally related are called
spurious or non-sense correlation. More appropriately we should remember that it is the
interpretation of the degree of correlation that is spurious, not the degree of correlation itself.
The high degree of correlation indicates only the mathematical result. We should reach a
conclusion based on logical reasoning and intelligent investigation on significantly related
matters. It should also be noted that errors in correlation analysis include not only reading
causation into spurious correlation but also interpreting spuriously a perfectly valid association.
• In modern times term ‘estimating line’ is coming to be used instead of ‘regression line’. On
examining a few definitions, the term regression as used in statistics can be clearly described.
• The variable which is used to predict the variable of interest is called the independent variable
or explanatory variable and the variable we are trying to predict is called the dependent or
explained variable.

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