Ninth Grade · Math · week 33

Statistics: scatter plots and correlation

Describe bivariate data with scatter plots, judge correlation, and match a data pattern to a linear, quadratic, or exponential model.

A scatter plot shows two variables at once, one point per pair. The pattern reveals correlation: points trending up together are positively correlated, trending in opposite directions are negatively correlated, and a shapeless cloud shows no real correlation at all. A line of best fit estimates the trend, and a residual (actual value minus predicted value) measures how far any one real point strays from that trend line - small residuals mean a good-fitting model.

Correlation is not causation: two variables can move together because a hidden "lurking" variable drives them both (ice cream sales and drownings both rise in summer - heat drives both, one does not cause the other). This term also gave you three model shapes - spot which one fits a pattern by checking its differences: a constant FIRST difference means linear, a constant RATIO means exponential, and a constant SECOND difference (the differences of the differences) means quadratic.

📋 For the grown-up teacher
Teach it (10–15 min):
  • Plot a real, easy data set together (height vs. shoe size across the family, minutes practiced vs. a skill score) before ever discussing correlation vocabulary.
  • Make the ice-cream/drowning example a genuine discussion, not a punchline - land firmly on "a THIRD variable can drive both" as the real lesson.
  • Practice the three-way differences check (constant difference / constant ratio / constant second difference) on fresh number lists until identifying the pattern feels quick.
  • Have them predict a value from their own trend line, then discuss what a large residual there would mean about the model's reliability.
Talk about it:
  • What is the difference between correlation and causation, in your own words?
  • How would you tell, just from a list of y-values, whether a pattern is linear, quadratic, or exponential?
  • What does a small residual tell you about how well a model fits a data point?

Mastery looks like: They classify correlation from a scatter plot, distinguish correlation from causation, and identify whether a numeric pattern is linear, quadratic, or exponential.

Common stumbles: Assuming any correlation implies causation; checking only first differences and mislabeling an exponential pattern as "not linear, so it must be quadratic."

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
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