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Correlation as the Cosine of an Angle

Correlation as the Cosine of an Angle
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2015-07-17 04:04
VectorFunction
In collections A Geometry Teacher Meets the Correlation Coefficient
This example provides a new perspective on correlation. By standardizing the coordinates of points, the x-coordinates are represented as a vector and the y-coordinates as another vector. The cosine of the angle between these vectors represents the correlation. The construction involves commands such as Midpoint, Dilate, Polygon, Vector, Angle, PMCC, and FitLineY. Suitable for high school and above students learning about correlation and vectors.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → C_1
  2. Dilate(C_1, -2, (0, 0)) → C
  3. Polygon(A, C, B) → poly1, b, a, c'
  4. Vector((x(A), x(B), x(C_1))) → u
  5. Vector((y(A), y(B), y(C_1))) → v
  6. Angle((x(A), x(B), x(C_1)), (0, 0, 0), (y(A), y(B), y(C_1))) → α
  7. PMCC({A, B, C}) → r
  8. FitLineY({A, B, C}) → c

AI Drawing Prompt Reference

Draw a triangle ABC. Standardize the coordinates of points to represent x-coordinates as vector u and y-coordinates as vector v. Calculate the angle α between vectors u and v, and the Pearson correlation coefficient r for points A, B, and C. Draw a line c passing through points A, B, and C.
The prompt above was compiled from the original drawing commands and is for reference only.