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The Correlation Coefficient

Maths Applications (Year 12) - Bivariate Data Analysis

Bhakti Sharma

We can look at scatterplots to see if there is a correlation between our two variables of interest. A correlation is a relationship between two variables, and the correlation coefficient looks at the strength of the relationship between two variables. There are different types of correlations, as seen below:


When looking at the correlation between two variables, always comment on the strength and direction of the model. Here are some notes on how to determine these characteristics in a scatter plot:

  1. A positive correlation suggests that an increase in one variable generally leads to an increase in the other variable.

  2. A negative correlation indicates that an increase in one variable generally leads to a decrease in the other variable.

  3. The closer the points are to looking like a perfect line, the stronger the correlation is between the two variables.

  4. The less the points look like a perfect line, the weaker the correlation is between the two variables.


A Numerical Approach to Correlation

Using the “eyeballing” method to describe the relationship can be useful when you are trying to make an estimate, however, if we want to follow a more accurate approach, then following a more quantitative method is more appropriate. This is done through the correlation coefficient, which can be calculated using a CAS Calculator.  

The correlation coefficient indicates the direction and strength of the data plots. The number ranges from 1 to -1, with r = 1 meaning that there is a perfect positive linear relationship and r = -1 meaning that there is a perfect linear relationship. The closer r is to 1 or -1, the stronger the relationship between the plots. The closer r is to 0, the weaker the relationship is between the plots. The table below shows interpretation of different correlation coefficients:


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