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Residuals and Rsquared

Residuals and Rsquared
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2016-10-17 04:27
FunctionCoordinate GeometryProbability & StatisticsGraphing
In collections Correlation and Regression
This example illustrates the concepts of residuals and Rsquared. By fitting a line, calculating the correlation coefficient, slope, standard deviation, etc., it shows the residuals between data points and the fitted line. Key mathematical concepts include fitting a line, correlation coefficient, standard deviation, mean, etc. It uses GeoGebra commands such as FitLineY, PMCC, Slope, SDX, SDY, MeanX, MeanY, etc. Suitable for high school math education, helping students understand the basic principles of regression analysis.

GeoGebra Commands & Parameters

  1. FitLineY({A, B, C, D, E}) → a
  2. PMCC({A, B, C, D, E}) → r
  3. Slope(a) → m
  4. SDX({A, B, C, D, E}) → d
  5. SDY({A, B, C, D, E}) → e
  6. MeanX({A, B, C, D, E}) → Xmn
  7. MeanY({A, B, C, D, E}) → Ymn
  8. Line(MMpt, MoveThis) → f
  9. Line(A, yAxis) → g
  10. Line(B, g) → h
  11. Line(E, h) → i
  12. Line(C, i) → j
  13. Line(D, j) → k
  14. Intersect(f, g) → F
  15. Intersect(f, h) → G
  16. Intersect(f, j) → H
  17. Intersect(f, i) → I
  18. Intersect(f, k) → J
  19. Segment(A, F) → l
  20. Segment(G, B) → n
  21. Segment(E, I) → p
  22. Segment(C, H) → q
  23. Segment(J, D) → s
  24. Polygon(A, F, 4) → poly1, t, c, f_1, g_1, K, L
  25. Polygon(G, B, 4) → poly2, h_1, i_1, j_1, k_1, M, N
  26. Polygon(H, C, 4) → poly3, l_1, m_1, n_1, p_1, O, P
  27. Polygon(E, I, 4) → poly4, q_1, r_1, s_1, t_1, Q, R
  28. Polygon(J, D, 4) → poly5, a_1, b_1, c_1, d_1, S, T
  29. Slope(f) → mh
  30. ResidualPlot(ListPts, fh) → list1

AI Drawing Prompt Reference

Plot points A, B, C, D, and E, then fit a line through them. Calculate the correlation coefficient, slope, standard deviation, and mean. Draw the intersection of the line with the y-axis at point F, and connect F to points A, B, C, and D. Draw perpendicular segments from each point to the line, forming five residual rectangles, and then draw the diagonals of each rectangle.
The prompt above was compiled from the original drawing commands and is for reference only.