Regression Analysis Equation Relationship Demo

Regression Analysis Equation Relationship Demo
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2014-08-12 11:21
In collections Complex Math
This example demonstrates the geographic relationship of the Regression Analysis Equation Y=XB+e. It involves core math concepts like linear regression, data fitting, and error analysis. Construction highlights include using GeoGebra commands such as Polygon, Mirror, Angle, Point, Segment, Line, OrthogonalLine, Vector, Translate, Intersect, Rotate, CircleArc, and Circle. Suitable for high school students and beginners in data analysis.

GeoGebra Commands & Parameters

  1. Polygon(A, B, Y, D) → poly1, a, b, c, d
  2. Polygon(D, B, A) → poly2, a_1, d_1, b_1
  3. Mirror(D, a) → D'
  4. Mirror(B, a) → B'
  5. Mirror(A, a) → A'
  6. Polygon(D', B', A') → poly2', a', d', b'
  7. Polygon(A, B, Y) → poly3, c_1, a_2, b_2
  8. Angle(b', d) → α
  9. Angle(Y, B, A) → β
  10. Point(a) → E
  11. Segment(Y, E) → e
  12. Angle(Y, A, D) → γ
  13. Angle(e, a) → δ
  14. Polygon(C, F, G) → poly4, g, c_2, f
  15. Line(H, b_1) → h
  16. Line(I, a_1) → i
  17. Point(h) → J
  18. Point(h) → K
  19. Segment(J, K) → j
  20. Point(i) → L
  21. Point(i) → M
  22. Segment(L, M) → k
  23. Segment(N, O) → l
  24. Segment(P, Q) → m
  25. OrthogonalLine(R, xAxis) → n
  26. Mirror(P, n) → P'
  27. Mirror(Q, n) → Q'
  28. Segment(P', Q') → m'
  29. Mirror(N, n) → N'
  30. Mirror(O, n) → O'
  31. Segment(N', O') → l'
  32. Vector(T, U) → u
  33. Translate(A, u) → A'_1
  34. Translate(B, u) → B'_1
  35. Translate(Y, u) → Y'
  36. Polygon(A'_1, B'_1, Y') → poly3', y', a'_1, b'_1
  37. Vector(V, W) → v
  38. Translate(F, v) → F'
  39. Translate(G, v) → G'
  40. Segment(F', G') → p
  41. Segment(G', G) → q
  42. Vector(Z, A_1) → w
  43. Translate(L, w) → L'
  44. Translate(M, w) → M'
  45. Segment(L', M') → k'
  46. Vector(B_1, C_1) → s
  47. Translate(J, s) → J'
  48. Translate(K, s) → K'
  49. Segment(J', K') → j'
  50. Vector(D_1, E_1) → t
  51. Translate(B, t) → B'_2
  52. Translate(A, t) → A'_2
  53. Segment(B'_2, A'_2) → e_1
  54. Intersect(g, f) → F_1
  55. Segment(A, E) → f_1
  56. Intersect(y', b'_1) → G_1
  57. Segment(Y, G_1) → g_1
  58. Line(H_1, f) → h_1
  59. Line(I_1, f) → i_1
  60. Line(J_1, f) → j_1
  61. Point(h_1) → K_1
  62. Segment(K_1, H_1) → k_1
  63. Point(i_1) → L_1
  64. Point(j_1) → M_1
  65. Segment(L_1, M_1) → l_1
  66. Point(i_1) → N_1
  67. Point(k_1) → O_1
  68. Segment(N_1, O_1) → m_1
  69. Point(j_1) → P_1
  70. Segment(O_1, P_1) → n_1
  71. Rotate(O_1, 90*°, O_1) → Q_1
  72. Rotate(P_1, -90*°, P_1) → S_1
  73. Segment(N_1, P_1) → q_1
  74. Rotate(N_1, 22*°, N_1) → T_1
  75. Rotate(P_1, 22*°, N_1) → U_1
  76. Segment(T_1, U_1) → r_1
  77. Rotate(P_1, -88*°, P_1) → V_1
  78. Rotate(O_1, -85*°, P_1) → W_1
  79. Rotate(P_1, -85*°, P_1) → Z_1
  80. Segment(Z_1, U_1) → p_1
  81. Segment(E, Q_1) → s_1
  82. Intersect(y', a'_1) → R_1
  83. Intersect(a'_1, b'_1) → A_2
  84. Segment(Y, B_2) → t_1
  85. Segment(Q_1, C_2) → d_2
  86. Point(i_1) → D_2
  87. Point(d_2) → F_2
  88. Segment(A, G_2) → g_2
  89. Vector(H_2, Z_1) → u_1
  90. Vector(I_2, Q_1) → v_1
  91. Vector(J_2, T_1) → w_1
  92. Vector(K_2, L_2) → u_2
  93. Vector(M_2, N_2) → v_2
  94. Intersect(j, k) → O_2
  95. Intersect(k', j') → P_2
  96. Point(g_2) → Q_2
  97. Vector(O_2, Q_2) → w_2
  98. Point(k) → R_2
  99. Point(k) → S_2
  100. Vector(R_2, S_2) → h_2
  101. Segment(G', F_1) → i_2
  102. Segment(F', T_2) → r
  103. Segment(F_1, T_2) → j_2
  104. Point(i_2) → x_j
  105. Segment(E, x_j) → k_2
  106. Segment(U_2, V_2) → l_2
  107. Segment(W_2, Z_2) → m_2
  108. Segment(A_3, B_3) → n_2
  109. Segment(C_3, D_3) → p_2
  110. Segment(W_2, E_3) → q_2
  111. Intersect(m_2, n_2) → F_3
  112. Point(p_2) → G_3
  113. Segment(F_3, G_3) → r_2
  114. CircleArc(Z_1, U_1, Q_1) → s_2
  115. Vector(H_3, I_3) → u_3
  116. CircleArc(T_1, Z_1, U_1) → t_2
  117. Segment(Z_1, M_1) → e_2
  118. Point(p) → E_2
  119. Segment(K_3, L_3) → f_2
  120. Line(M_3, f_2) → a_3
  121. Mirror(K_3, a_3) → N_3
  122. Mirror(L_3, a_3) → O_3
  123. Segment(N_3, O_3) → b_3
  124. Vector(Y, Z_1) → v_3
  125. Segment(D_3, E_3) → c_3
  126. Point(q_2) → P_3
  127. Segment(B_3, P_3) → d_3
  128. Point(p_2) → Q_3
  129. Segment(B_3, Q_3) → e_3
  130. Point(q_2) → R_3
  131. CircleArc(P_3, R_3, B_3) → g_3
  132. Point(q_2) → S_3
  133. CircleArc(S_3, P_3, R_3) → f_3
  134. Segment(P_3, R_3) → h_3
  135. Segment(R_3, Q_3) → i_3
  136. Segment(R_3, T_3) → j_3
  137. Segment(P_3, E_3) → k_3
  138. Circle(V_3, W_3) → p_3
  139. Circle(Q_1, Z_3) → q_3

AI Drawing Prompt Reference

Draw a geometric representation of the regression analysis equation Y=XB+e, involving multiple polygons and geometric relationships to illustrate data fitting and error analysis. Start by creating two symmetric polygons, then use mirroring and rotation to generate new shapes. Add error lines and parallel lines based on angles and vectors, and finally demonstrate the transformation of the equation through translation, showcasing the geographic relationship of linear regression.
The prompt above was compiled from the original drawing commands and is for reference only.