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Sample Linear Regression with Least Squares

Sample Linear Regression with Least Squares
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2015-07-22 23:26
Coordinate Geometry
This example demonstrates how to visualize linear regression and least squares methods using geometric constructions in GeoGebra. Key mathematical concepts include linear equations, minimizing the distance from points to a line, and coordinate geometry functions. Construction involves commands like Line, OrthogonalLine, Intersect, Polygon, and FitLineY to create lines and fit curves. Suitable for high school students or college undergraduates to understand the geometric interpretation of linear regression and apply least squares in data analysis.

GeoGebra Commands & Parameters

  1. Line(M, G) → a
  2. OrthogonalLine(A, xAxis) → b
  3. OrthogonalLine(B, xAxis) → c
  4. OrthogonalLine(C, xAxis) → d
  5. OrthogonalLine(D, xAxis) → e
  6. OrthogonalLine(E, xAxis) → f
  7. Intersect(a, b) → F
  8. Intersect(c, a) → H
  9. Intersect(d, a) → I
  10. Intersect(e, a) → J
  11. Intersect(f, a) → K
  12. Polygon(F, A, 4) → poly1, g, h, i, j, L, N
  13. Polygon(H, B, 4) → poly2, k, l, m, n, O, P
  14. Polygon(I, C, 4) → poly3, p, q, r, s, Q, R
  15. Polygon(J, D, 4) → poly4, t, a_1, b_1, c_1, S, T
  16. Polygon(K, E, 4) → poly5, d_1, e_1, f_1, g_1, U, V
  17. FitLineY({A, B, C, D, E}) → h_1