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3.2.1: Graphing Bivariate Data with Scatterplots

  • Page ID
    28701
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    A scatterplot is a useful graph for looking for relationships between two numeric variables. This relationship is called correlation. When performing correlation analysis, ask these questions:

    1. What is the direction of the correlation?
    clipboard_e83f2fdb460bae91f7d7a3f84912b470d.png
    Positive
    clipboard_ecfbeabeee23d5d6cff200fdcb8a42f05.png
    Negative
    1. What is the strength of the correlation?  
    clipboard_ec28d58ce1a3a75dd459d1822a36f882f.png
    Perfect
    clipboard_e36c4c11b5512e2cb7b625eae38272ab7.png
    None
    clipboard_e133bc017ed34866d99c9e04662977a59.png
    Strong
    clipboard_ed9ae2467a0af5a374906c5fa850fb828.png
    Weak
    clipboard_ed239116879f1f3b982e2eb411e578178.png
    Moderate
    1. What is the shape of the correlation?
    clipboard_ef7bde812f1beaa306a3889018dd80ccc.png
    Linear
    clipboard_ead4ea6eeeec9ab251107083fe9757cc6.png
    Non-linear

    Example: Cucumber yield and rainfall

    This scatterplot represents randomly collected data on growing season precipitation and cucumber yield. It is reasonable to suggest that the amount of water received on a field during the growing season will influence the yield of cucumbers growing on it.32

    clipboard_e341700db63f5072097efe5ec63c97a6b.png

    Solution

    Direction: Correlation is positive, yield increases as precipitation increases.

    Strength:  There is a moderate to strong correlation.

    Shape: Mostly linear, but there may be a slight downward curve in yield as precipitation increases.

    Example: GPA and missing class

    A group of students at Georgia College conducted a survey asking random students various questions about their academic profile.  One part of their study was to see if there is any correlation between various students’ GPA and classes missed.33

    clipboard_eb89108db0a426bd4ff3de4b26c9d0d06.png

    Solution

    Direction: Correlation, if any, is negative. GPA trends lower for students who miss more classes.

    Strength:  There is a very weak correlation present.

    Shape: Hard to tell, but a linear fit is not unreasonable.

    Example: Commute times and temperature

    A mathematics instructor commutes by car from his home in San Francisco to De Anza College in Cupertino, California. For 100 randomly selected days during the year, the instructor recorded the commute time and the temperature in Cupertino at time of arrival.

    clipboard_edc4139ee1b181907e7f809610c13ea43.png

    Solution

    Direction: There is no obvious direction present.

    Strength:  There is no apparent correlation between commute time and temperature.

    Shape: Since there is no apparent correlation, looking for a shape is meaningless.

    Other: There are two outliers representing very long commute times.

    Example: Age of sugar maple trees

    Is it possible to estimate the age of trees by measuring the diameters of the trunks? Data was reconstructed by a comprehensive study by the US Department of Agriculture. The researchers collected data for old growth sugar maple trees in northern US forests.34

    clipboard_e5da4b85d94e14cebb4b82f6c86f51963.png

    Solution

    Direction: There is a positive correlation present. Age increases as trunk size increases.

    Strength:  The correlation is strong.

    Shape: The shape of the graph is curved downward meaning the correlation is not linear.

    Example: Gun ownership and gun suicides

    This scatterplot represents gun ownership and gun suicides for 73 different countries. The data is adjusted to rates per population for comparison purposes.35

    clipboard_e14b3c4eb73d8fd26ecd891b9c694b04c.png

    Solution

    Direction: There is a positive correlation present. More gun ownership means more gun suicides.

    Strength:  The correlation is moderate for most data.  

    Shape: The shape of the graph is linear for most of the data.

    Other: There are a few outliers in which gun ownership is much higher. There is also an outlier with an extremely high suicide rate.

    This final example demonstrates that outliers can make it difficult to read graphs. For example, The United States has the highest gun ownership rates and the highest suicide by gun rates among these countries, making the United States stand far away from the bulk of the data in the scatterplot. Montenegro had the second highest suicide by gun rate, but with a much lower gun ownership rate.

     


    3.2.1: Graphing Bivariate Data with Scatterplots is shared under a CC BY-SA license and was authored, remixed, and/or curated by LibreTexts.

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