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Linear Regression by Jed Butler

Linear Regression by Jed Butler
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2014-05-12 23:36
FunctionTrigonometryCoordinate GeometryProbability & StatisticsOptimization
In collections GGBChat4: Statistics 1
This example demonstrates how users can define points by dragging or manually inputting/modifying them in a spreadsheet, and then plot a scatter plot along with the fitted linear regression line. Key math concepts include linear regression, correlation coefficient, least squares method, and analytical geometry. The construction involves commands/objects like Line, Intersect, Polygon, Vector, RSquare, SampleSD, Median, Text, FitLineY, and Circle as per the GeoGebra command summary. Suitable for high school and above learners to understand data fitting and statistical analysis methods.

GeoGebra Commands & Parameters

  1. Line(U, V) → line_{guess}
  2. Line(A, x = 0) → a
  3. Line(B, x = 0) → b
  4. Line(C, x = 0) → c
  5. Line(D, x = 0) → d
  6. Line(E, x = 0) → e
  7. Line(F, x = 0) → f
  8. Line(G, x = 0) → g
  9. Line(H, x = 0) → h
  10. Line(I, x = 0) → i
  11. Line(J, x = 0) → j
  12. Line(K, x = 0) → k
  13. Line(L, x = 0) → l
  14. Line(M, x = 0) → m
  15. Line(N, x = 0) → n
  16. Line(NP, x = 0) → np
  17. Line(O, x = 0) → p
  18. Line(P, x = 0) → q
  19. Line(R, x = 0) → s
  20. Line(S, x = 0) → t
  21. Intersect(line_{guess}, a) → A'
  22. Intersect(line_{guess}, b) → B'
  23. Intersect(line_{guess}, c) → C'
  24. Intersect(line_{guess}, d) → D'
  25. Intersect(line_{guess}, e) → E'
  26. Intersect(line_{guess}, f) → F'
  27. Intersect(line_{guess}, g) → G'
  28. Intersect(line_{guess}, h) → H'
  29. Intersect(line_{guess}, i) → I'
  30. Intersect(line_{guess}, j) → J'
  31. Intersect(line_{guess}, k) → K'
  32. Intersect(line_{guess}, l) → L'
  33. Intersect(line_{guess}, m) → M'
  34. Intersect(line_{guess}, n) → N'
  35. Intersect(line_{guess}, np) → NP'
  36. Intersect(line_{guess}, p) → O'
  37. Intersect(line_{guess}, q) → P'
  38. Intersect(line_{guess}, s) → R'
  39. Intersect(line_{guess}, t) → S'
  40. Line(Q, x = 0) → r
  41. Intersect(line_{guess}, r) → Q'
  42. Polygon(A', A, 4) → poly1, a_1, b_1, c_1, d_1, T, W
  43. Polygon(B', B, 4) → poly2, e_1, f_1, g_1, h_1, Z, A_1
  44. Polygon(D', D, 4) → poly3, i_1, j_1, k_1, l_1, B_1, C_1
  45. Polygon(E', E, 4) → poly4, m_1, n_1, p_1, q_1, D_1, E_1
  46. Polygon(C', C, 4) → poly5, r_1, s_1, t_1, a_2, F_1, G_1
  47. Polygon(F', F, 4) → poly6, b_2, c_2, d_2, e_2, H_1, I_1
  48. Polygon(G', G, 4) → poly7, f_2, g_2, h_2, i_2, J_1, K_1
  49. Polygon(H', H, 4) → poly8, j_2, k_2, l_2, m_2, L_1, M_1
  50. Polygon(I', I, 4) → poly9, n_2, p_2, q_2, r_2, N_1, O_1
  51. Polygon(J', J, 4) → poly10, s_2, t_2, a_3, b_3, P_1, Q_1
  52. Polygon(K', K, 4) → poly11, c_3, d_3, e_3, f_3, R_1, S_1
  53. Polygon(L', L, 4) → poly12, g_3, h_3, i_3, j_3, T_1, U_1
  54. Polygon(M', M, 4) → poly13, k_3, l_3, m_3, n_3, V_1, W_1
  55. Polygon(N', N, 4) → poly14, p_3, q_3, r_3, s_3, Z_1, A_2
  56. Polygon(NP', NP, 4) → poly15, t_3, a_4, b_4, c_4, B_2, C_2
  57. Polygon(P', P, 4) → poly16, d_4, e_4, f_4, g_4, D_2, E_2
  58. Polygon(O', O, 4) → poly17, h_4, i_4, j_4, k_4, F_2, G_2
  59. Polygon(Q', Q, 4) → poly18, l_4, m_4, n_4, p_4, H_2, I_2
  60. Polygon(R', R, 4) → poly19, q_4, r_4, s_4, t_4, J_2, K_2
  61. Polygon(S', S, 4) → poly20, a_5, b_5, c_5, d_5, L_2, M_2
  62. Vector((x(A), 0), (x(A), y(A) - y(A'))) → V_A
  63. Vector((x(B), 0), (x(B), y(B) - y(B'))) → V_B
  64. Vector((x(C), 0), (x(C), y(C) - y(C'))) → V_C
  65. Vector((x(D), 0), (x(D), y(D) - y(D'))) → V_D
  66. Vector((x(E), 0), (x(E), y(E) - y(E'))) → V_E
  67. Vector((x(F), 0), (x(F), y(F) - y(F'))) → V_F
  68. Vector((x(G), 0), (x(G), y(G) - y(G'))) → V_G
  69. Vector((x(H), 0), (x(H), y(H) - y(H'))) → V_H
  70. Vector((x(I), 0), (x(I), y(I) - y(I'))) → V_I
  71. Vector((x(J), 0), (x(J), y(J) - y(J'))) → V_J
  72. Vector((x(K), 0), (x(K), y(K) - y(K'))) → V_K
  73. Vector((x(L), 0), (x(L), y(L) - y(L'))) → V_L
  74. Vector((x(M), 0), (x(M), y(M) - y(M'))) → V_M
  75. Vector((x(N), 0), (x(N), y(N) - y(N'))) → V_N
  76. Vector((x(NP), 0), (x(NP), y(NP) - y(NP'))) → V_{NP}
  77. Vector((x(P), 0), (x(P), y(P) - y(P'))) → V_P
  78. Vector((x(Q), 0), (x(Q), y(Q) - y(Q'))) → V_Q
  79. Vector((x(R), 0), (x(R), y(R) - y(R'))) → V_R
  80. Vector((x(O), 0), (x(O), y(O) - y(O'))) → V_O
  81. Vector((x(S), 0), (x(S), y(S) - y(S'))) → V_S
  82. RSquare(data, line_{guess}) → Strength
  83. SampleSD(list_y) → SD_y
  84. Median(list_x) → Median_x
  85. Vector((Median_x / 2, (SD_y * 2)), (Median_x / 2, (SD_y * 2) + over)) → Vector_{over}
  86. Vector((Median_x / 2, (SD_y * 2)), (Median_x / 2, (SD_y * 2) - under)) → Vector_{under}
  87. Text(((Strength * 100) * "%"), ((Median_x * 1.425), (SD_y * 1.95))) → text1
  88. FitLineY(data) → line_{actual}
  89. Circle(((Median_x * 1.5), (2 * SD_y)), (Strength * Max[list_y] / 6)) → g_5
  90. Circle(((Median_x * 1.5), (2 * SD_y)), (Strength * Max[list_y] / 6)) → CorrelationCircle
  91. Circle(((Median_x * 1.5), (2 * SD_y)), (Strength * Max[list_y] / 6)) → CorrelationCircle_1
  92. Circle(((Median_x * 1.5), (2 * SD_y)), (Strength * Max[list_y] / 6)) → f_5

AI Drawing Prompt Reference

Draw a scatter plot with multiple points and fit a linear regression line. First, define points by dragging or manual input, then plot them in the coordinate system. Next, calculate and draw the best-fit line passing through these points to demonstrate linear regression. Finally, enclose the points with several quadrilaterals to highlight the data distribution characteristics.
The prompt above was compiled from the original drawing commands and is for reference only.