Scatterplot and Correlation: Definition, Example & Analysis
A scatterplot is used to graphically represent the relationship between two variables. Explore the relationship between scatterplots and correlations, the different types of correlations, how to interpret scatterplots, and more.
Scatterplot
Imagine that you are interested in studying patterns in individuals with children under the age of 10. You collect data from 25 individuals who have at least one child. After you’ve collected your data, you enter it into a table.
Data table
Data Recorded
You try to draw conclusions about the data from the table; however, you find yourself overwhelmed. You decide an easier way to analyze the data is by comparing the variables two at a time. In order to see how the variables relate to each other, you create scatterplots.
So what is a scatterplot? A scatterplot is a graph that is used to plot the data points for two variables. Each scatterplot has a horizontal axis (x-axis) and a vertical axis (y-axis). One variable is plotted on each axis. Scatterplots are made up of marks; each mark represents one study participant’s measures on the variables that are on the x-axis and y-axis of the scatterplot.
Most scatterplots contain a line of best fit, which is a straight line drawn through the center of the data points that best represents the trend of the data. Scatterplots provide a visual representation of the correlation, or relationship between the two variables.
Types of Correlation
All correlations have two properties: strength and direction. The strength of a correlation is determined by its numerical value. The direction of the correlation is determined by whether the correlation is positive or negative.
Positive correlation: Both variables move in the same direction. In other words, as one variable increases, the other variable also increases. As one variable decreases, the other variable also decreases.
I.e., years of education and yearly salary are positively correlated.
Negative correlation: The variables move in opposite directions. As one variable increases, the other variable decreases. As one variable decreases, the other variable increases.
I.e., hours spent sleeping and hours spent awake are negatively correlated.
All positive correlations have scatterplots that move in the same direction as the positive correlation in the image above. All negative correlations have scatterplots that move in the same direction as the negative correlation in the image above.
Types of correlation
No Correlations
What does it mean to say that two variables have no correlation? It means that there is no apparent relationship between the two variables. For example, there is no correlation between shoe size and salary. This means that high scores on shoe size are just as likely to occur with high scores on salary as they are with low scores on salary.
If your line of best fit is horizontal or vertical like the scatterplots on the top row, or if you are unable to draw a line of best fit because there is no pattern in the data points, then there is little or no correlation.
No Correlation
Strength
The strength of a correlation indicates how strong the relationship is between the two variables. The strength is determined by the numerical value of the correlation. A correlation of 1, whether it is +1 or -1, is a perfect correlation. In perfect correlations, the data points lie directly on the line of fit. The further the data are from the line of fit, the weaker the correlation. A correlation of 0 indicates that there is no correlation. The following should be considered when determining the strength of a correlation:
The closer a positive correlation lies to +1, the stronger it is.
I.e., a correlation of +.87 is stronger than a correlation of +.42.
The closer a negative correlation is to -1, the stronger it is.
I.e., a correlation of -.84 is stronger than a correlation of -.31.
When comparing a positive correlation to a negative correlation, only look at the numerical value. Do not consider whether or not the correlation is positive or negative. The correlation with the highest numerical value is the strongest.
I.e., a correlation of -.80 is stronger than a correlation of +.55.
If the numerical values of a correlation are the same, then they have the same strength no matter if the correlation is positive or negative.
I.e., a correlation of -.80 has the same strength as a correlation of +.80.
Interpretations of Scatterplots
So what can we learn from scatterplots? Let’s create scatterplots using some of the variables in our table. Let’s first compare age to Internet use. Now let’s put this on a scatterplot. Age is plotted on the y-axis of the scatterplot and Internet usage is plotted on the x-axis.
Age and Internet usage scatterplot
Age and Internet Usage
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Additional Activities
Analyzing Scatter Plots
This exercise requires some light internet research to find scatter plots to look at.
Make some google inquiries that will produce good images of scatter plots. Some examples might be “CO2 emissions vs temperature scatterplot” and “internet usage vs education scatterplot” or “soda consumption vs income scatterplot” and look in google images.
Find scatter plots that seem to show some correlation and lines drawn through the data. See if you can find some with R^2 values.
Look at the x and y axes and see if they correspond to something that is meaningful to you. What is being correlated?
Answer the following questions:
Is the correlation negative or positive?
Is there a strong or weak correlation?
Is there enough data to decide?
Next, see if you can find a scatter plot that shows very little or no correlation and examine it.
What are the axes and what does a non-correlation tell you?
Are you surprised by a non-correlation between these two variables?
Suggestions
Allow students to come up with things they think might be correlated or wonder if they are.
If there are surprising or interesting correlations (or non-correlations) that come up, have students look further into the study methods.
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Supplemental Math: Study Aid
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Ch 1. Overview of Math Concepts
Less Than Symbol in Math: Problems & Applications4:10
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Trapezoid: Definition, Properties & Formulas3:58
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Zero Exponent: Rule, Definition & Examples4:32
Quotient Of Powers: Property & Examples4:58
What is Simplest Form? – Definition & How to Write Fractions in Simplest Form5:49
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Skewed Distribution: Examples & Definition5:09
Change Of Base Formula: Logarithms & Proof4:54
Transformations in Math: Definition & Graph6:27
What is Translation in Math? – Definition, Examples, & Terms4:23
Fixed Interval: Examples & Definition4:00
Scatterplot and Correlation: Definition, Example & Analysis7:48
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