Correlation Coefficient Properties

What Is the Correlation Coefficient?

The term correlation coefficient is a statistical measure of the strength of the relationship between the relative movements of two variables. The values fall between -1.0 and 1.0. There will be an error in the correlation measurement if the estimated number is larger than or less than 1.0. A perfect negative correlation is represented by a correlation of -1.0, and a perfect positive correlation is represented by a correlation of 1.0. The movement of the two variables has no linear relationship, with a correlation of 0.0.

In finance and investment, correlation statistics are useful. A correlation coefficient, for example, might be used to measure the degree of correlation between the price of crude oil and the stock price of an oil-producing corporation like Exxon Mobil Corporation. Because oil firms make more money when oil prices rise, there is a strong positive link between the two variables.

Body

Correlation coefficients are used to assess the strength of a relationship between two variables. The Pearson correlation is the most widely used in statistics. A linear link between two variables is measured by the strength and direction of the relationship. The values are always in the range of -1 (very negative relationship) to +1 (strongly positive association) (strong positive relationship). A weak or non-linear relationship is shown by values at or near zero. Correlation coefficients of less than +0.8 or more than -0.8 are not considered statistically significant.

Correlation Coefficient Properties

It’s all about establishing relationships between two variables when using the correlation coefficient. The following are some properties of the correlation coefficient:

1. The correlation coefficient remains constant in the same measurement as the two variables.
2.  The variance’s sign will always be the same as the sign of the coefficient correlations.
3. The correlation coefficient will have a numerical value ranging from -1 to 1, also known as the real number value.
4. The coefficient’s negative value indicates a strong and negative association. If ‘r’ continues to approach -1, the relationship is going almost towards the negative side.
5. A correlation coefficient is a pure number that is unaffected by the units. When we add the same number to all the values of a variable, it has no effect. 
6. All the variables can be multiplied by a single positive value. The correlation coefficient is unaffected by this. Because ‘r’ is a scale-invariant, as previously stated, it is unaffected by any unit.
7. Correlation is used to measure association, but it does not imply causation. This means that if two variables are correlated, the third variable may have an impact on them.
8. When ‘r’ reaches the side of + 1, it indicates a strong and positive relationship. We can conclude that if the correlation result is +1, the relationship is in a positive state.
9. When the coefficient of correlation approaches 0, it indicates a weak correlation. We can determine that the association is weak when ‘r’ is close to zero.
10. The correlation coefficient is risky because we don’t know whether the participants are telling the truth or not.
11. When the two variables are swapped, the coefficient of correlation remains unchanged.

Conclusion

In a broader sense, correlation measures a relationship between variables. In correlated data, a change in one variable’s magnitude is linked to a change in another variable’s magnitude, either in the same (positive correlation) or opposite (negative correlation) direction. Correlation is most commonly used to describe a linear relationship between two continuous variables, written as Pearson product-moment correlation.

The Correlation Coefficient is a unitless statistic. Depending on the sign of scale factors, the coefficient of correlation stays invariant when the origin and/or scale of the variables under examination are changed. The correlation coefficient is always between –1 and 1, including both limiting values. The correlation coefficient, which measures a linear relationship between two variables, shows how much variation in one variable is accounted for by the other. The square of the correlation coefficient, often known as the ‘coefficient of determination,’ is a better measure for this purpose. This can be considered as the ratio of explained variation to total variance or vice versa.