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Unit 9: Correlation: Definition, Types and its Application for Economists

effect of changes equal in amount to their respective standard deviations in the rainfall and Notes
temperature. In discussing the figures in the tables I shall accordingly utilize the partial correlation
coefficients rather than the others. Finally, I have worked out what Mr. Yule calls the coefficient of
double correlation between the crop and rainfall and accumulated temperature above 42°,
.
.
2 + r 2 − r 2r r r
12 13 12 23 13
R= ( 1 23 2 ) − r ,
or as it may also be written,
R= 1 − ( 12 2 ) − 1 r ( ρ 13 2 ) − 1 ,

a form which is quicker to calculate. This may be regarded as a measure of the joint influence of the
rainfall and the temperature upon the crop. For the sake of brevity, I shall speak of R as measuring
the effect of the ‘weather,’ using this term in the strictly limited sense of consisting only of these two
factors. . . .
“I propose to regard a coefficient between 0.3 and 0.5 as suggestive of dependence. Values below 0.3
I shall, as a rule, ignore, in the absence of any corroborative evidence. Perhaps I may remark that I
believe that some statisticians would consider themselves justified in drawing deductions from lower
coefficients than those I have adopted as my limits.”*
Mr. Yule notes that the partial or net correlation coefficient retains three of the chief properties of the
ordinary coefficients: “ (1) it can only be zero if both net regressions are zero; (2) it is a symmetrical
function of the variables (i.e., ρ 12 = ρ ); (3) it cannot be greater than unity.”
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The various illustrations which have been cited show the importance of questions of correlation in
economics. The ordinary graphic method of measuring correlation is inadequate. The coefficient of
correlation is simple and yet is sensitive to small changes. It has been used in many fields of statistics
by Galton, Pearson, Yule, Hooker, Elderton and others. The experience of these writers warrants the
adoption of the coefficient of correlation by economists as one of their standard averages.
Self-Assessment

1. Fill in the blanks:
(i) If more than one items is assigned the same rank ............ adjustment is made.
(ii) Probable error for coefficient of correlation can be found by the formula ............ .
(iii) Coefficient of determination is ............ .
(iv) Limits of correlation is ............ to ............ .
(v) The relationship between three or more variables is studied with the help of ............ correlation.
9.3 Summary

• Correlation means a relation between two groups. In statistics, it is the measure to indicate the
relationship between two variables in which, with changes in the values of one variable, the
values of other variable also change. These variables may be related to one item or may not be
related to one item but have dependence on the other due to some reason.
• The term correlation indicates the relationship between two variables in which with changes in
the value of one variable, the values of the other variable also change. Correlation has been
defined by various eminent statisticians, mathematicians and economists.
• Correlation is very useful in understanding the economic behaviour. It helps in locating those
variables on which other variables depend. In this way various economic events can be analysed.
Moreover, it also helps in identifying the stabilishing factors for a disturbed economic situation.
• Correlation measures a degree of the relationship between two or more variables but it does
not indicate any kind of cause and effect relationship between the variables. If, high degree of

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