What Is Correlation?

Correlation measures how one variable moves with another. It is a number between -100% and +100% and can be decomposed into two quantities:

  • the sign: negative or positive,
  • the magnitude: between 0% and 100%.

A positive sign means that as one variable moves up, the other variable tends to move up as well. In other words, the two variables tend to move in the same direction. In such a case, one speaks of positively correlated variables. Examples are height of father & height of son; temperature & sales of ice cream; years of education & income.

A negative sign means that as one variable moves up, the other variable tends to move down. In other words, the two variables tend to move in opposite directions. In such a case, one speaks of negatively correlated variables. Examples are age & testosterone (in adult males); price of a good & demand for the good; years of education & likelihood of being unemployed.

The magnitude measures the strength of the relationship. A magnitude of 0% means there is no relationship at all. An example is weight & income. A magnitude of 100% means there is a perfect relationship (so knowing the value of one variable will exactly tell you the value of the other variable). Such examples are rare, one is temperature in Celsius & temperature in Fahrenheit. In most cases, the magnitude of a correlation is larger than 0% and less than 100%. It can be interpreted as a `percentage of perfection’ of the relationship. So the larger the magnitude of the correlation, the stronger is the correlation. For example, the correlation between height of father and height of son is around 60% in most countries. This means that the relationship is quite strong but far from perfect.

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