2.2

Scatterplots

Definition of Scatterplots

  • A scatterplot is a graphical representation that shows the relationship between two quantitative variables measured on the same individuals.
    • Explanatory Variable (x): Plotted on the horizontal axis of the scatterplot.
    • Response Variable (y): Plotted on the vertical axis of the scatterplot.
    • Each individual in the dataset appears as a point in the scatterplot, determined by the values of both variables.

Example of a Scatterplot

  • This is illustrated using a dataset that includes measurements of the girth and volume of 31 felled black cherry trees.
    • Significance of Black Cherry Trees: Utilized in the manufacturing of wooden furniture.
    • Definition of Girth: Girth refers to the circumference of the tree, measured in inches, at a height of 4 feet 6 inches above the ground.

Data Representation

Tabulated Data

  • The values for the girth and volume of the trees can be presented in the following tabular format:
    • Girth: 8, 10, 12, 14, 16, 18, 20
    • Volume: 10, 20, 30, 40, 50, 60, 70

Examining a Scatterplot

Steps to Analyze a Scatterplot

  • When analyzing a graph of data, one should search for the following:
    • Overall Pattern: Look for trends in the data.
    • Striking Deviations: Identify any significant outliers in the data.

Describing Patterns in a Scatterplot

  • The overall pattern of a scatterplot can be described through:
    • Form: Linear or nonlinear.
    • Direction: Positive or negative correlation.
    • Strength of Relationship: The degree to which the points cluster around a direction.

Associations in Scatterplots

Positive Association

  • Two variables are considered to have a positive association when:
    • Above-average values of one variable tend to accompany above-average values of the other variable.
    • Similarly, below-average values tend to occur together.

Negative Association

  • Conversely, two variables exhibit a negative association if:
    • Above-average values of one variable tend to be paired with below-average values of the other variable, and vice versa.

Categorical Variables in Scatterplots

Adding Categorical Variables

  • To incorporate a categorical variable into a scatterplot:
    • Utilize different colors or symbols to represent each category distinctively in the plot.

Example of Categorical Variables in Scatterplots

Iris Species Dataset

  • Mentioned by Anderson, Edgar (1935) in The Irises of the Gaspe Peninsula, Bulletin of the American Iris Society, 59, 2–5.
    • Categories of Species (categorical variable):
    • Setosa
    • Versicolor
    • Virginica
    • Variables analyzed: Petal length and petal width.

Visual Representation for Iris Species

  • Petal Length values are displayed on the x-axis, while Petal Width values are plotted on the y-axis. This results in distinct clusters based on species, depicted graphically as symbols or colors in the scatterplot.
  • Example values include:
    • For Setosa
    • For Versicolor
    • For Virginica