Scatter Plots and Patterns
Two variables, one plot. You'll see clusters, lines, curves, and weirdos.
Key Points
- Linear pattern = straight line. Positive slope (up right) or negative (down right).
- Nonlinear = curved. Examples: U‑shape, exponential growth, logarithmic.
- Clusters = distinct groups. May need separate models per cluster.
- Outliers = extreme points. Could be errors or rare events.
- No pattern = random scatter. Variables likely unrelated.
- Always check for overplotting when many points overlap.
What it is
A scatter plot puts one variable on the x‑axis, another on the y‑axis. Each point is one observation. The pattern tells you the relationship. Linear: points form a line. Nonlinear: they form a curve. Clusters: separate groups. Outliers: lonely points far from the crowd. Scatter plots are the workhorse of bivariate EDA.
Why it exists
Correlation coefficients (like Pearson's r) only detect linear relationships. A perfect U‑shape gives r near 0, but the relationship is strong. Scatter plots reveal the truth. They also show clustering and outliers that summary stats hide.
Intuition
When to use
- Whenever you want to see relationship between two continuous variables.
- Before calculating Pearson correlation – the plot tells you if linear is appropriate.
- To spot clusters that could be different segments or groups.
- To identify outliers that might be data errors.
Common mistakes
- Relying on correlation without plotting. A U‑shape or outlier‑driven line can lie.
- Ignoring overplotting – use transparency (alpha), hexbin plots, or sampling.
- Claiming a nonlinear pattern is random just because correlation is near zero.
Notes
- Add a trend line (linear regression) to help the eye, but beware of forcing linearity.
- For categorical vs continuous, use box plots or violin plots, not scatter.
In practice
Scatter plots are everywhere in EDA, diagnostic plots for regression (residuals vs fitted), and visualizing clustering results (PCA scatter plots). Also used in correlation heatmaps as a matrix of scatter plots.
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