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Correlation: Definition, Analysis & Examples

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  • 0:03 Correlation
  • 0:41 Types of Correlation
  • 2:30 Correlation Coefficient
  • 2:48 Example
  • 3:43 Lesson Summary
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Lesson Transcript
Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

Correlation describes the relationship between two sets of data. In this lesson, we'll delve into what correlation is and the different types of correlation that can be encountered.

Correlation

Correlation is used to describe how data sets are related to one another. Correlation can be seen when two sets of data are graphed on a scatter plot, which is a graph with an X and Y axis and dots representing the data points.


Image 1


The scatter plot in Image 1 relates two sets of data: years of education on the x axis and income on the y axis. The dots represent a data point that gives two pieces of information: years of education and income per year. For example, you can see the data point farthest to the left shows that somebody with around 6.2 years of education makes roughly $3,000 per year.

Types of Correlation

Correlation can be positive, negative, or no correlation. Positive correlation means that as one data set increases, the other data set increases as well. The data in Image 1 has a positive correlation because as years of education increases, so does income. Typically, positively correlated data sets are seen as a line the goes up and to the right on a scatter plot.

Negative correlation means that as one data set increases, the other decreases. Image 2 shows two sets of unknown data with a negative correlation. As the data set on the x axis increases, the data set on the y axis decreases. Typically, negatively correlated data sets are seen as a line the goes down and to the right on a scatter plot.


Image 2


No correlation means that the two sets of data are not related at all. In other words, this means that one set of data does not increase or decrease with the other. No correlation is typically seen when the data points are very spread out as in Image 3.


Image 3


Positive and negative is not the only way to describe correlation; correlation can also be described by its strength. Data sets can also have perfect correlation, strong correlation, or weak correlation. The closer the data points are together and the more they form a straight line, the stronger the correlation. If the data points form a perfect straight line, the data sets are said to have perfect positive or negative correlation depending on which way the line is going (up and right = positive, down and right = negative).

Image 4 shows three graphs with varying levels of correlation. The first graph has a strong positive relationship, while the second has a low or weak positive correlation. The third graph has no relationship or no correlation.


Strong, Weak, and No Correlation Examples


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