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Linear Regression Visualizer - Residual Sum of Squares

Linear Regression Visualizer - Residual Sum of Squares
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2016-01-20 16:06
FunctionCoordinate GeometryProbability & StatisticsOptimization
This example demonstrates the calculation and visualization of the residual sum of squares in linear regression. Key math concepts include linear regression, residual sum of squares, and least squares method. It constructs data points, regression lines, and residuals using GeoGebra commands like Point, Line, OrthogonalLine, Intersect, Polygon, FitLineY, RSquare. Suitable for high school and above students to understand evaluation metrics of linear regression models.

GeoGebra Commands & Parameters

  1. Point(yAxis) → S
  2. Line(S, T) → a
  3. OrthogonalLine(B, xAxis) → b
  4. OrthogonalLine(C, xAxis) → c
  5. OrthogonalLine(A, xAxis) → d
  6. OrthogonalLine(D, xAxis) → e
  7. OrthogonalLine(E, xAxis) → f
  8. Intersect(a, b) → H
  9. Intersect(d, a) → I
  10. Intersect(c, a) → J
  11. Intersect(a, e) → K
  12. Intersect(a, f) → L
  13. Polygon(H, B, 4) → poly1, g, h, i, j, M, N
  14. Polygon(I, A, 4) → poly2, k, l, m, n, O, P
  15. Polygon(J, C, 4) → poly3, p, q, r, s, Q, R
  16. Polygon(K, D, 4) → poly4, t, a_1, b_1, c_1, S_1, T_1
  17. Polygon(L, E, 4) → poly5, d_1, e_1, f_1, g_1, U, V_1
  18. FitLineY(DataSet) → h_1
  19. Intersect(h_1, b) → F
  20. Intersect(h_1, c) → G
  21. Intersect(h_1, d) → Z
  22. Intersect(h_1, e) → A_1
  23. Intersect(h_1, f) → B_1
  24. Polygon(F, B, 4) → poly6, i_1, j_1, k_1, l_1, C_1, D_1
  25. Polygon(G, C, 4) → poly7, m_1, n_1, p_1, q_1, E_1, F_1
  26. Polygon(Z, A, 4) → poly8, r_1, s_1, t_1, a_2, G_1, H_1
  27. Polygon(A_1, D, 4) → poly9, b_2, c_2, d_2, e_2, I_1, J_1
  28. Polygon(B_1, E, 4) → poly10, f_2, g_2, h_2, i_2, K_1, L_1
  29. RSquare({(-3, 2), (-2, 1), (-1, 3), (0, 4), (1, 2), (2, 4), (3, 3), (4, 5), (6, 4)}, (0.5 * x) + 2.5) → w