Linear Regression with Random Data Set

Linear Regression with Random Data Set
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2014-05-16 05:17
This example demonstrates linear regression analysis using a randomly generated set of data points. Key math concepts include linear regression, data fitting, and statistical probability. GeoGebra commands and objects used in the construction are Random (for point generation), Line (for drawing lines), Intersect (for intersection calculations), Polygon (for polygons), Vector (for vectors), RSquare (for coefficient of determination), SampleSD (for sample standard deviation), Median (for median calculation), FitLineY (for fitting a line), Circle (for circles), and Text (for annotations). Suitable for high school mathematics or statistics courses, teaching linear regression models and data visualization.

GeoGebra Commands & Parameters

  1. Random(1, 20) → A2
  2. Random(1, 20) → A1
  3. Random(1, 20) → A3
  4. Random(1, 20) → A4
  5. Random(1, 20) → A5
  6. Random(1, 20) → A6
  7. Random(1, 20) → A7
  8. Random(1, 20) → A8
  9. Random(1, 20) → A9
  10. Random(1, 20) → A10
  11. Random(1, 20) → A11
  12. Random(1, 20) → A12
  13. Random(1, 20) → A13
  14. Random(1, 20) → A14
  15. Random(1, 20) → A15
  16. Random(1, 20) → A16
  17. Random(1, 20) → A17
  18. Random(1, 20) → A18
  19. Random(1, 20) → A19
  20. Random(1, 20) → A20
  21. Random(-2, 2) → slope_1
  22. Line(U, V) → line_{guess}
  23. Line(A, x = 0) → a
  24. Line(B, x = 0) → b
  25. Line(C, x = 0) → c
  26. Line(D, x = 0) → d
  27. Line(E, x = 0) → e
  28. Line(F, x = 0) → f
  29. Line(G, x = 0) → g
  30. Line(H, x = 0) → h
  31. Line(I, x = 0) → i
  32. Line(J, x = 0) → j
  33. Line(K, x = 0) → k
  34. Line(L, x = 0) → l
  35. Line(M, x = 0) → m
  36. Line(N, x = 0) → n
  37. Line(NP, x = 0) → np
  38. Line(O, x = 0) → p
  39. Line(P, x = 0) → q
  40. Line(R, x = 0) → s
  41. Line(S, x = 0) → t
  42. Intersect(line_{guess}, a) → A'
  43. Intersect(line_{guess}, b) → B'
  44. Intersect(line_{guess}, c) → C'
  45. Intersect(line_{guess}, d) → D'
  46. Intersect(line_{guess}, e) → E'
  47. Intersect(line_{guess}, f) → F'
  48. Intersect(line_{guess}, g) → G'
  49. Intersect(line_{guess}, h) → H'
  50. Intersect(line_{guess}, i) → I'
  51. Intersect(line_{guess}, j) → J'
  52. Intersect(line_{guess}, k) → K'
  53. Intersect(line_{guess}, l) → L'
  54. Intersect(line_{guess}, m) → M'
  55. Intersect(line_{guess}, n) → N'
  56. Intersect(line_{guess}, np) → NP'
  57. Intersect(line_{guess}, p) → O'
  58. Intersect(line_{guess}, q) → P'
  59. Intersect(line_{guess}, s) → R'
  60. Intersect(line_{guess}, t) → S'
  61. Line(Q, x = 0) → r
  62. Intersect(line_{guess}, r) → Q'
  63. Polygon(A', A, 4) → poly1, a_1, b_1, c_1, d_1, T, W
  64. Polygon(B', B, 4) → poly2, e_1, f_1, g_1, h_1, Z, A_1
  65. Polygon(D', D, 4) → poly3, i_1, j_1, k_1, l_1, B_1, C_1
  66. Polygon(E', E, 4) → poly4, m_1, n_1, p_1, q_1, D_1, E_1
  67. Polygon(C', C, 4) → poly5, r_1, s_1, t_1, a_2, F_1, G_1
  68. Polygon(F', F, 4) → poly6, b_2, c_2, d_2, e_2, H_1, I_1
  69. Polygon(G', G, 4) → poly7, f_2, g_2, h_2, i_2, J_1, K_1
  70. Polygon(H', H, 4) → poly8, j_2, k_2, l_2, m_2, L_1, M_1
  71. Polygon(I', I, 4) → poly9, n_2, p_2, q_2, r_2, N_1, O_1
  72. Polygon(J', J, 4) → poly10, s_2, t_2, a_3, b_3, P_1, Q_1
  73. Polygon(K', K, 4) → poly11, c_3, d_3, e_3, f_3, R_1, S_1
  74. Polygon(L', L, 4) → poly12, g_3, h_3, i_3, j_3, T_1, U_1
  75. Polygon(M', M, 4) → poly13, k_3, l_3, m_3, n_3, V_1, W_1
  76. Polygon(N', N, 4) → poly14, p_3, q_3, r_3, s_3, Z_1, A_2
  77. Polygon(NP', NP, 4) → poly15, t_3, a_4, b_4, c_4, B_2, C_2
  78. Polygon(P', P, 4) → poly16, d_4, e_4, f_4, g_4, D_2, E_2
  79. Polygon(O', O, 4) → poly17, h_4, i_4, j_4, k_4, F_2, G_2
  80. Polygon(Q', Q, 4) → poly18, l_4, m_4, n_4, p_4, H_2, I_2
  81. Polygon(R', R, 4) → poly19, q_4, r_4, s_4, t_4, J_2, K_2
  82. Polygon(S', S, 4) → poly20, a_5, b_5, c_5, d_5, L_2, M_2
  83. Vector((x(A), 0), (x(A), y(A) - y(A'))) → V_A
  84. Vector((x(B), 0), (x(B), y(B) - y(B'))) → V_B
  85. Vector((x(C), 0), (x(C), y(C) - y(C'))) → V_C
  86. Vector((x(D), 0), (x(D), y(D) - y(D'))) → V_D
  87. Vector((x(E), 0), (x(E), y(E) - y(E'))) → V_E
  88. Vector((x(F), 0), (x(F), y(F) - y(F'))) → V_F
  89. Vector((x(G), 0), (x(G), y(G) - y(G'))) → V_G
  90. Vector((x(H), 0), (x(H), y(H) - y(H'))) → V_H
  91. Vector((x(I), 0), (x(I), y(I) - y(I'))) → V_I
  92. Vector((x(J), 0), (x(J), y(J) - y(J'))) → V_J
  93. Vector((x(K), 0), (x(K), y(K) - y(K'))) → V_K
  94. Vector((x(L), 0), (x(L), y(L) - y(L'))) → V_L
  95. Vector((x(M), 0), (x(M), y(M) - y(M'))) → V_M
  96. Vector((x(N), 0), (x(N), y(N) - y(N'))) → V_N
  97. Vector((x(NP), 0), (x(NP), y(NP) - y(NP'))) → V_{NP}
  98. Vector((x(P), 0), (x(P), y(P) - y(P'))) → V_P
  99. Vector((x(Q), 0), (x(Q), y(Q) - y(Q'))) → V_Q
  100. Vector((x(R), 0), (x(R), y(R) - y(R'))) → V_R
  101. Vector((x(O), 0), (x(O), y(O) - y(O'))) → V_O
  102. Vector((x(S), 0), (x(S), y(S) - y(S'))) → V_S
  103. RSquare(data, line_{guess}) → Strength
  104. SampleSD(list_y) → SD_y
  105. Median(list_x) → Median_x
  106. FitLineY(data) → line_{actual}
  107. Circle(((Median_x * 1.5), (2 * SD_y)), (Strength * Max[list_y] / 6)) → CorrelationCircle
  108. Circle(((Median_x * 1.5), (2 * SD_y)), (Strength * Max[list_y] / 6)) → CorrelationCircle_1
  109. Random(-10, 10) → yint_1
  110. Vector((Min[list_x] - 2, 0), (Min[list_x] - 2, over)) → Vector_{over}
  111. Vector((Min[list_x] - 2, 0), (Min[list_x] - 2, (-under))) → Vector_{under}
  112. Text(((Strength * 100) * "%"), (Max[list_x] + 2, 0)) → text1

AI Drawing Prompt Reference

Create a scatter plot using a randomly generated set of data points. Fit a line to these points to demonstrate linear regression. Draw several vertical lines from each point to the x-axis and label the values at the intersections. Include statistical annotations like the title and axis labels.
The prompt above was compiled from the original drawing commands and is for reference only.