Strong Correlation

A strong correlation is a correlation (a single number) that describes the degree of strong relationship between two variables.

Or we can say that,two numbers are said to be in strong correlation if they are highly related to each other.

Let us first understand the meaning of Correlation first..

What is a correlation? (Pearson correlation)

A correlation is a number between -1 and +1 that measures the degree of association between two variables (call them X and Y). A positive value for the correlation implies a positive association (large values of X tend to be associated with large values of Y and small values of X tend to be associated with small values of Y). A negative value for the correlation implies a negative or inverse association (large values of X tend to be associated with small values of Y and vice versa).

The formula for the Pearson correlation

Suppose we have two variables X and Y, with means x and y respectively and standard deviations SX and SY respectively. The correlation is computed as

r = `sum_(i=1)^n((X-x)(Y-y))/(n Sx. Sy)`

Interpretation of strong correlation

 

Here is how we tend to interpret strong correlations.

  • -1.0 to -0.7 strong negative association.In other words if X increases, Y also increases.
  • +0.7 to +1.0 strong positive association.In other words if X increases, Y on contrary decreases

 

The correlation coefficient measures the strength of a linear relationship between two variables.

The correlation coefficient is always between -1 and +1. The closer the correlation is to +/-1, the closer to a perfect linear relationship. and this relationship is said to be as strong correlation.

Example of a strong positive association.

The correlation between blood viscosity and packed cell volume is 0.88.

Notice that small volumes tend to have low viscosity and large volumes tend to have high viscosity.Thus blood viscosity and packed cells have strong correlation.

numerical example of strong correlation for practice.

Example

This table shows some sample data. Each person reported income and years of education.Find the correlation between the income and years of education.

Also determine whether it is a strong correlation or not..?

Participant Income Years of Education
#1 125,000 19
#2 100,000 20
#3 40,000 16
#4 35,000 16
#5 41,000 18
#6 29,000 12
#7 35,000 14
#8 24,000 12
#9 50,000 16
#10 60,000 17

 

Answer: The correlation here is .79.

Being closer to 1, we can say  that there is a strong correlation between income and years of education.



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