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Lecture 29

Correlation

DATA 8

Fall 2023

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Announcements

  • Homework 9 is due Wednesday at 11pm
  • Project 2 checkpoint due this Friday
    • Final deadline on November 10th
    • Get started early and come to OH/Project Party!
  • My OH are today: 5-7pm @ FSM

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Weekly Goals

  • Today
    • A measure of linear association
  • Wednesday
    • Predicting one numerical variable based on another
    • The regression line
  • Friday
    • The “best” linear predictor
    • The method of least squares

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Prediction

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Guessing the Future

  • Based on incomplete information

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  • One way of making predictions:
    • To predict an outcome for an individual,
    • find others who are like that individual
    • and whose outcomes you know.
    • Use those outcomes as the basis of your prediction.

(Demo)

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Association

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Two Numerical Variables

  • Trend
    • Positive association
    • Negative association
  • Pattern
    • Any discernible “shape” in the scatter
    • Linear
    • Non-linear

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Visualize, then quantify

(Demo)

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Correlation Coefficient

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The Correlation Coefficient r

  • Measures linear association
  • Based on standard units
  • -1 ≤ r ≤ 1
    • r = 1: scatter is perfect straight line sloping up
    • r = -1: scatter is perfect straight line sloping down
  • r = 0: No linear association; uncorrelated

(Demo)

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Definition of r

average of

product of

x in standard units

and

y in standard units

Correlation Coefficient (r) =

Measures how clustered the scatter is around a straight line

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Care in Interpretation

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Watch Out For ...

  • False conclusions of causation
  • Nonlinearity
  • Outliers
  • Ecological Correlations

(Demo)

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Chocolate and Nobel Prizes

Source