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Scatterplot

Page history last edited by Nicholas Davis 7 years ago

Scatterplots are graphs that shows the relationship between two quantitative variables and usually are represented by a collection of dots. The dots have the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.  Scatterplots may be the most common displays for data.  By just looking at them, you can see patterns, trends, relationships, and even the occasional extraordinary value sitting apart from the others (an outlier). 

 

When using scatterplots, we use two variables: independent and dependent.  The independent variable represent the input and the dependent variable is the variable of interest. Independent variable causes a change in dependent variable.  Naturally, we'll plot the dependent variable on the Y-axis and the independent variable on the X-axis.  Your scatterplot may show that a relationship exists, but it does not and cannot prove that one variable is causing the other.  There could be a third factor involved which is causing both (lurking variable), some other cause, or the apparent relationship could just be a fluke.  Nevertheless, the scatterplot can give you a clue that two things might be related, and if so, how they move together.

 

The first thing that you look for when analyzing a scatterplot is the direction of the association (assuming that there is an association, which in most cases there will not be).  A pattern that runs from the upper left to the lower right is said to be negative.  A pattern that runs from the lower left to the upper right is said to be positive.  The second thing to look for in a scatterplot is its form.  A plot that appears as a cloud or swarm of points stretched out in a generally consistent, straight form is called linear.  If the relationship isn't straight, but curves gently while still increasing or decreasing steadily, we often give it the term nearly straight.  But if it curves sharply up and down, there is much less we can say about it.  The third feature to look for in a scatterplot is the strength of the relationship.  At one extreme, do the points appear tightly clustered in a single stream (whether straight, curved, or bending all over the place)?  Or, at the other extreme, does the swarm of points seem to form a vague cloud through which we can barely discern any trend or pattern?  Finally, always look for the unexpected.  Often the most interesting thing to see in a scatterplot is something you never thought to look for.  One example of such a surprise is an outlier standing away from the overall pattern of the scatterplot.

 

For example data, we used data about the number of sales and prices for pizzas.  For this example we are going to use sales for our dependent variable and prices for our independent variable because we are trying to find how the diversity of pizza prices impact pizza sales.  If we want to see if these two variables have a relationship, we can use a scatterplot. 

 

 

One can see that the outcomes for pizzas that had higher prices had less sales and that for pizzas that had lower prices had higher sales.  We chose to used "price" as the independent variable and "sales" as the dependent variable because we were trying to find how many sales were going to be predicted, based on prices.  There does not seem to be any significant outliers that would propose a problem because there are 156 data points.

 

 

Generating a Scatterplot in SPSS

  • Go to "Graphs" in the top menu.
  • Select "Chart Builder."
  • Click "OK" when the chart builder window pops up.
  • In the "Choose From" Menu, select "Scatter/Dot."  Then select the first option, which is simple scatter.
  • Click and drag the scatterplot to the preview window.
  • Put the explanatory variable (grouping variable) on the X-axis and the response variable (variable of interest) on the Y-axis.
  • Click "OK." 

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