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Correlation as a Geometric Mean of Slopes

Correlation as a Geometric Mean of Slopes
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2015-07-17 04:18
FunctionTrigonometryCoordinate Geometry
In collections A Geometry Teacher Meets the Correlation Coefficient
This example demonstrates the relationship between correlation coefficient and slopes by plotting the LSRL of points A, B, C, D, E, then switching their x and y coordinates to create A', B', C', D', E'. It involves core concepts like PMCC, linear regression, slope calculation, and geometric transformations. GeoGebra commands used include PMCC, Intersect, Line, Mirror, FitLineY, Slope, LaTeX, and If. Suitable for high school mathematics teaching to understand the geometric meaning and transformation properties of correlation coefficients.

GeoGebra Commands & Parameters

  1. PMCC({A, B, C, D, E}) → r
  2. Intersect(xAxis, yAxis) → F
  3. Line(F, G) → a
  4. Mirror(B, a) → B'
  5. Mirror(E, a) → E'
  6. Mirror(C, a) → C'
  7. Mirror(D, a) → D'
  8. Mirror(A, a) → A'
  9. FitLineY({A, B, C, D, E}) → b
  10. FitLineY({B', E', C', D', A'}) → c
  11. Slope(b) → m
  12. Slope(c) → m_1
  13. LaTeX(r, true, true) → text1
  14. Intersect(yAxis, b) → H
  15. Intersect(yAxis, c) → I
  16. If(y(I) < 0, text4, text5) → text6