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最小二乘回归

最小二乘回归
几何画板及绘图内容加载中，请稍等……
2019-02-19 19:43
函数解析几何概率统计最值优化
①本范例演示了如何通过最小二乘法拟合数据点生成最佳拟合直线；②涉及的核心数学概念包括线性回归、残差平方和、相关系数等；③作图要点——使用了OrthogonalLine(正交线), Line(直线), Intersect(交点), Polygon(多边形), FitLineY(拟合直线), PMCC(相关系数)等GeoGebra命令；④适合高中及以上数学学习者，用于理解数据拟合和统计建模的基本原理。

GeoGebra 命令及参数

  1. OrthogonalLine(A, xAxis) → f
  2. OrthogonalLine(C, xAxis) → g
  3. OrthogonalLine(E, xAxis) → h
  4. OrthogonalLine(B, xAxis) → i
  5. OrthogonalLine(D, xAxis) → j
  6. OrthogonalLine(G, xAxis) → k
  7. OrthogonalLine(F, xAxis) → l
  8. OrthogonalLine(H, xAxis) → m
  9. OrthogonalLine(I, xAxis) → n
  10. Line(J, K) → p
  11. Intersect(p, f) → L
  12. Intersect(p, g) → M
  13. Intersect(p, h) → N
  14. Intersect(p, i) → O
  15. Intersect(p, j) → P
  16. Intersect(p, k) → Q
  17. Intersect(p, l) → R
  18. Intersect(p, m) → S
  19. Intersect(p, n) → T
  20. Polygon(A, L, 4) → poly1, q, r, s, t, U, V
  21. Polygon(C, M, 4) → poly2, a, b, c, d, W, Z
  22. Polygon(E, N, 4) → poly3, e, f_1, g_1, h_1, A_1, B_1
  23. Polygon(B, O, 4) → poly4, i_1, j_1, k_1, l_1, C_1, D_1
  24. Polygon(D, P, 4) → poly5, m_1, n_1, p_1, q_1, E_1, F_1
  25. Polygon(G, Q, 4) → poly6, r_1, s_1, t_1, a_1, G_1, H_1
  26. Polygon(F, R, 4) → poly7, b_1, c_1, d_1, e_1, I_1, J_1
  27. Polygon(H, S, 4) → poly8, f_2, g_2, h_2, i_2, K_1, L_1
  28. Polygon(I, T, 4) → poly9, j_2, k_2, l_2, m_2, M_1, N_1
  29. FitLineY({A, B, C, D, E, F, G, H, I}) → n_2
  30. Intersect(f, n_2) → O_1
  31. Intersect(g, n_2) → P_1
  32. Intersect(i, n_2) → Q_1
  33. Intersect(j, n_2) → R_1
  34. Intersect(l, n_2) → S_1
  35. Intersect(h, n_2) → T_1
  36. Intersect(m, n_2) → U_1
  37. Intersect(k, n_2) → V_1
  38. Intersect(n, n_2) → W_1
  39. Polygon(A, O_1, 4) → poly10, p_2, q_2, r_2, s_2, Z_1, A_2
  40. Polygon(P_1, C, 4) → poly11, t_2, a_2, b_2, c_2, B_2, C_2
  41. Polygon(B, Q_1, 4) → poly12, d_2, e_2, f_3, g_3, D_2, E_2
  42. Polygon(D, R_1, 4) → poly13, h_3, i_3, j_3, k_3, F_2, G_2
  43. Polygon(S_1, F, 4) → poly14, l_3, m_3, n_3, p_3, H_2, I_2
  44. Polygon(E, T_1, 4) → poly15, q_3, r_3, s_3, t_3, J_2, K_2
  45. Polygon(H, U_1, 4) → poly16, a_3, b_3, c_3, d_3, L_2, M_2
  46. Polygon(G, V_1, 4) → poly17, e_3, f_4, g_4, h_4, N_2, O_2
  47. Polygon(W_1, I, 4) → poly18, i_4, j_4, k_4, l_4, P_2, Q_2
  48. PMCC({A, B, C, D, E, F, G, H, I}) → ς