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Correlation - Definition, Variables and Types

Correlation is defined as the method of creating a relationship or link between two or more than two variables. This method is useful in measuring quantities at a higher or ordinal level. The relation between x and y, or a and b, is known as correlation. It is one of the customary methods approached to calculate the measurements. It incorporates the use of a scattering graph or ‘scatter plot’ to create the relationship between two distinct variables.

Correlation Coefficient: This is a single-valued constant that sums up the relation between any two variables. It is generally denoted by the letter ‘r’. In statistics, the value of the correlation coefficient can reach a minimum of -1 and a maximum of 1, -1 < r < 1. Important results have been deduced due to the range of correlation.

  • If the correlation coefficient is close to zero (middle), either negative to zero, positive to zero, or zero implies that there is no relationship between the variables.
  • The correlation coefficient close to +1 means there exists a positive relationship between the two variables.
  • A correlation coefficient reaching -1 implies the relationship between the two variables to be negative.
  • Spearman’s Rho is used to calculate the coefficient for ordinal scales, while Pearson’s r is the standard method to find out the coefficient in the case of interval or ratio scales.

The two variables used in making a correlation are generalized as ‘X’ and ‘Y’. They are first related with the help of Pearson’s r method and then represented graphically with the help of a scatter diagram.

Scatter diagram: A scatter diagram is a graphic showing the values of two variables X and Y, and the relationship between these two variables. Variable X values are displayed along the horizontal axis, with Y values displayed on the vertical axis.

Later, one of the parameters is established as an independent parameter when a regression model is employed, and one is specified as the dependent variable. The independent variable X is thought to have some impact or influence on the dependent component Y in regression. The correlation techniques for both variables are symmetric, with no evidence of cause or effect being included in the statistical analysis.

Types of Correlation:

With the help of 'scatter diagram', mathematicians have deduced three types of correlations, which are explained below:

Positive Correlation: Positive correlation occurs due to the values of two parameters moving in the same direction so that a rise or decrease in one variable is followed by an increase or decrease in the other variable. It is further of two types: Strong positive correlation where the points are close to the linear graph, and weak positive correlation where the points are far away from the linear graph.

Negative Correlation: Negative correlation occurs due to the values of two components moving in the opposite direction from each other so that a rise or decrease in one variable is followed by a rise or decrease in the other variable. Negative correlations are also classified into two types. Similar to positive correlation, the negative correlation has a strong negative correlation where the points are close to the linear graph and a weak negative correlation where the points are far away from the linear graph.

No Correlation: when the two variables are not linear or related, it is known as no correlation.

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