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Interactive Linear Regression by GeoGebra Institute of Southern Connecticut

Interactive Linear Regression by GeoGebra Institute of Southern Connecticut
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2014-11-29 23:30
FunctionCoordinate GeometryCalculusProbability & StatisticsOptimization
This example demonstrates how to interactively find a line that minimizes the sum of squared errors through linear regression. Key math concepts include linear regression, least squares method, and residual analysis. GeoGebra commands and objects used in construction are Line, Mean, Sum, OrthogonalLine, Intersect, Segment, and Residual. Suitable for high school and above students to understand the process of building a linear regression model.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Mean(A2:A16) → A18
  3. Mean(B2:B16) → B18
  4. Sum(F2:F16) → F18
  5. Sum(G2:G16) → G18
  6. Line(D, C) → b
  7. OrthogonalLine(O11, xAxis) → c
  8. Intersect(b, c) → E
  9. Segment(E, O11) → d
  10. Residual(O1, b) → e
  11. Residual(O2, b) → f
  12. Residual(O10, b) → g
  13. Residual(O3, b) → h
  14. Residual(O12, b) → i
  15. Residual(O4, b) → j
  16. Residual(O13, b) → k
  17. Residual(O5, b) → l
  18. Residual(O14, b) → m
  19. Residual(O6, b) → n
  20. Residual(O8, b) → p
  21. Residual(O15, b) → q
  22. Residual(O9, b) → r
  23. Residual(O7, b) → s
  24. Residual(O10, a) → t
  25. Residual(O11, a) → a_1
  26. Residual(O1, a) → b_1
  27. Residual(O2, a) → c_1
  28. Residual(O12, a) → d_1
  29. Residual(O3, a) → e_1
  30. Residual(O13, a) → f_1
  31. Residual(O4, a) → g_1
  32. Residual(O14, a) → h_1
  33. Residual(O5, a) → i_1
  34. Residual(O6, a) → j_1
  35. Residual(O15, a) → k_1
  36. Residual(O7, a) → m_1
  37. Residual(O8, a) → n_1
  38. Residual(O9, a) → p_1
  39. Sum(I2:I16) → I18
  40. Sum(J2:J16) → J18

AI Drawing Prompt Reference

Draw a scatter plot to demonstrate linear regression by minimizing the sum of squared errors. First, plot the best-fit line, then show all residuals from data points to this line. Also, calculate and display residuals of all data points to the best-fit line and the mean line. Finally, draw a perpendicular line from the mean point to the best-fit line and mark its intersection point.
The prompt above was compiled from the original drawing commands and is for reference only.