Correlation: Overview, Questions, Preparation

Correlation is the process by which you can relate two variables in mathematics. While there are various measures to understand the relation between two variables, correlation is one of the most common approaches. Correlation as a concept is important and is relevant in statistics, higher mathematics, and applied mathematics. 

The Correlation Coefficient

A correlation coefficient is the measure of the relation between two variables. It is close to the number 0 and may have a positive or a negative value. This correlation coefficient has a range between +1 and -1 and is usually denoted by the symbol ‘r’.

Types of Correlation

One can use scatter plots or diagrams to find the correlation between two statistical variables. It represents how two statistical variables are correlated. 

• No Correlation: When the statistical variables are not linearly dependent on one another, or if there is no relationship between the two statistical variables.

• Positive Correlation: When the value of one of the two statistical variables increases concerning another component in correlation.

• Negative Correlation: When the value of one of the two statistical variables decreases concerning another component in correlation.

Correlation Formula

The correlation coefficient for ordinal scales is calculated using Spearman’s rho coefficient. 
Correlation gives you the measure of the relationship between two statistical variables---correlation coefficient in this respect shows this correlation. 
A few of the formulas are:

Karl Pearson’s Correlation Formula

The most common correlation formula is the Karl Pearson method to find the linear dependency between 2 defined sets of data. The following equation gives the formula:

Σx = Sum of First Variable Value
Σy = Sum of Second Variable Value
Σxy = Sum of the Product of Both Variable Values
Σx² = Sum of the Squares of the First Variable Value
Σy² = Sum of the Squares of the Second Variable Value

Correlation is a major statistics’ topics which are taught in class 11. This topic carries a major weightage of 5-10 marks in the final examination. This is also covered in Maths for economics in class 11. 

1. Consider the table of observations below:

The X mean: 12.4
The Y means: 17.8

If we solve using the Karl Pearson formula, we can find its correlation coefficient as well.
A scatter diagram can be used to understand the correlation between the X and Y values.

2. What is the range of the correlation coefficient:
(a) 0 to infinity
(b) -1 to +1
(c) minus infinity to infinity

Solution.
(b) -1 ≤ r ≤ 1. 

3. If rXY has a positive value, the relationship between X and Y is:
(a) when Y increases X does not change
(b) when Y decreases X increases
(c) when Y increases X increases
Solution.
(c) If r is positive, the two variables move in the same direction. 

Q: What is a correlation in mathematics?

Q: What is a correlation coefficient in mathematics?

Q: What is the formula for correlation of 2 variables?

Q: What are the different types of correlation in math?

Q: What is the use of a scatter diagram for correlation?