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Interactive Linear Regression with MSE function

Interactive Linear Regression with MSE function
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2020-09-01 01:15
FunctionCoordinate GeometryProbability & StatisticsOptimizationGraphing
This interactive GeoGebra example demonstrates how to fit an optimal linear regression line by minimizing the Mean Squared Error (MSE) function. Core mathematical concepts include linear regression, least squares method, MSE loss function, residuals, and statistical characteristics like the mean of data points. Constructed using key GeoGebra commands such as Line, mean, Sum, OrthogonalLine, Intersect, Segment, and Residual, along with interactive objects like button1 and various point pairs, the applet dynamically visualizes the perpendicular residuals and the summation of squared errors. It is highly suitable for teaching and learning regression analysis, statistical modeling, and optimization in high school or university-level data science and calculus courses.

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 an interactive linear regression graph that demonstrates how to fit a line by minimizing the mean squared error (MSE) function. The graph should include a linear regression line, a mean point, a vertical line, an intersection point, a segment, residuals, a button, and multiple point pairs. The construction order is: first draw the regression line, then calculate the mean and sum of squared errors for the data points, next find the projection point via a vertical line, then draw residual segments and the vertical projection line, and finally add the interactive button and point pairs for dynamic adjustment and visualization of errors.
The prompt above was compiled from the original drawing commands and is for reference only.