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Regression Line and Sum Of Squares

Regression Line and Sum Of Squares
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2016-04-19 08:55
FunctionCoordinate GeometryOptimization
This example demonstrates how to draw a regression line through data points and calculate the sum of squares. Core math concepts include linear regression, sum of squares, and coordinate geometry. Construction involves commands like Point, Segment, Polygon, and FitLineY for plotting points, segments, polygons, and fitting a regression line. Suitable for high school mathematics teaching, focusing on data fitting and error analysis.

GeoGebra Commands & Parameters

  1. Point(f) → A1
  2. Segment(A, A1) → a
  3. Point(f) → B1
  4. Segment(B, B1) → b
  5. Point(f) → C1
  6. Segment(C, C1) → c
  7. Point(f) → D1
  8. Segment(D, D1) → d
  9. Point(Circle[C1, abs(c)]) → C2
  10. Segment(C1, C2) → e
  11. Point(Circle[C, abs(c)]) → C3
  12. Segment(C3, C2) → h
  13. Polygon(C, C1, C2, C3) → polyc, c_1, c1, c2, c3
  14. Point(Circle[D1, abs(d)]) → E
  15. Segment(D1, E) → i
  16. Point(Circle[D, abs(d)]) → F
  17. Segment(D, F) → j
  18. Segment(F, E) → k
  19. Polygon(D, D1, E, F) → polyd, d_2, d1, e_2, f_1
  20. Point(Circle[A, abs(a)]) → G
  21. Segment(A, G) → l
  22. Point(Circle[A1, abs(a)]) → H
  23. Segment(A1, H) → m
  24. Segment(G, H) → n
  25. Polygon(A, G, H, A1) → polya, a_2, g_2, h_1, a1
  26. Point(Circle[B1, abs(b)]) → I
  27. Segment(B1, I) → p
  28. Point(Circle[B, abs(b)]) → J
  29. Segment(B, J) → q
  30. Polygon(B, B1, I, J) → polyb, b_2, b1, i_2, j_2
  31. FitLineY({A, B, C, D}) → g

AI Drawing Prompt Reference

Draw a set of data points and fit a regression line through them to show the trend. Then, for each point, draw a circle with the radius equal to the corresponding line segment, connecting the intersection points to form polygons that represent error ranges. Finally, combine all points and the fitted line to create a complete illustration for analyzing data fitting and error.
The prompt above was compiled from the original drawing commands and is for reference only.