Scatter plot correlation coefficient Scatter plot

Scatter plot correlation coefficient

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What is Scatterplot?

Analysing large data in a table with number of rows and columns can be pretty challenging. But it gets easier when you try to compare two variables together, side-by-side. And this is where scatterplots come into the picture. 

Scatterplot helps you figure out how the two variables relate to each other. Scatterplot looks like nothing but a graph that plots the data points for two variables under study. 

As with any graph, a scatterplot has a vertical y-axis and a horizontal x-axis and both the variables are plotted on one axis each. Scatterplots are marks on the graph which represents one participant’s measure on the variables both on the y-axis and x-axis. 

Most of the scatterplots contain a Line of best fit, which is nothing but a straight line drawn from between the data points to make it a clear trend differentiator.

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What is the correlation coefficient?

Correlation is nothing but a statistical relationship between two variables. And a correlation coefficient ( r ) is a measure of strength and direction of a relationship between two variables. Strength is determined by a numerical value, whereas direction is determined on whether the correlation is positive or negative or zero. 

  • r = 1 represents positive linear correlation. If one variable increases, the other variable increases too.
Scatter plot correlation coefficient Scatter plot
  • r = 0 represent no correlation.
Scatter plot correlation coefficient Scatter plot
Scatter plot correlation coefficient Scatter plot
  • r = -1 represents negative linear correlation. If one variable increases, the other variable decreases.
Scatter plot correlation coefficient Scatter plot

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Correlation coefficient with scatterplots

A scatterplot is nothing but a visual representation of the correlation or a relationship between the variables. 

In both positive correlation and negative correlation, all the scatterplots move in the same direction.

Scatter plot correlation coefficient Scatter plot

In the below two examples of the scatterplot, we can say both are a good representation of data. Since the data points are very close to the line of best fit, we have a strong correlation. 

  • In the figure below, as the line of best fit is a negative slope and as one variable increases the other decreases, we have a strong negative linear correlation.

Hence, r is going to be close to -1.

Scatter plot correlation coefficient Scatter plot
  • In figure (2), as the line of best fit a positive slope and as one variable increases the other increases too, we have a strong positive linear correlation. 

Hence, r is going to be close to +1.

Scatter plot correlation coefficient Scatter plot

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As for the scatterplots that makes the correlation zero or correlation coefficient r = 0, the examples would look something like these:

  • In the below figure, although the scatterplots are far away from each other, we still have shown the positive linear correlation between them but it won’t be as strong as the above example.
Scatter plot correlation coefficient Scatter plot
  • In the below figure, although the scatterplots are far away from each other, we still have shown the negative linear correlation between them but it won’t be as strong as the above example.
Scatter plot correlation coefficient Scatter plot

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As for the scatterplots that makes the correlation zero or correlation coefficient r = 0, the examples would look something like these:

  • In the below figure, although the scatterplots are far away from each other, we still have shown the positive linear correlation between them but it won’t be as strong as the above example.
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