Correlation

Indian Economy glossary

Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 6 "Correlation"; Class 11, Ch 8 "Use of Statistical Tools"

Meaning

Correlation studies whether two variables move together. It measures the direction of the relationship and how strong it is.

  • Positive correlation: both variables rise and fall together.
  • Negative correlation: one rises as the other falls.

Karl Pearson's coefficient r = Cov(X,Y) / (σx·σy). Here σx and σy are the standard deviations of X and Y.

The value of r:

  • lies between −1 and +1, where ±1 is perfect correlation;
  • has no units;
  • measures only straight-line (linear) relationships.

It measures covariation, not cause and effect.

Example

For a group of farmers, NCERT relates years of schooling to yield per acre. The result is r = 0.644, a fairly strong positive link. Another example: the price of apples and the demand for them are negatively correlated.

Don't confuse with

  • Causation: a high r does not prove that one variable causes the other.
  • Independence: r = 0 means only that there is no linear relation. For example, if Y = X² for X from −3 to 3, then r = 0, even though Y depends fully on X.

Related concepts

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