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Regression lines, residuals and r²

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Useful for: IB Math AA SL & HL IB Math AI SL & HL AP® Statistics

Learn it A least-squares line ŷ = a + bx predicts y from x. Residual = actual − predicted (positive: the point is above the line). r² is the fraction of the variation in y explained by the line. Don't predict far outside the data (extrapolation).

Example: ŷ = 12 + 3.5x. A student who studied 6 h scored 38. Residual?

  1. Predicted: 12 + 21 = 33.
  2. Residual = 38 − 33 = 5.

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