MathPlotAI Logo MathPlotAI

Least Squares Regression Line Demo

Least Squares Regression Line Demo
Loading the math board and drawing, please wait…
2013-01-09 04:33
FunctionCoordinate GeometryProbability & StatisticsOptimization
In collections AP Statistics
This example demonstrates how to estimate the least squares regression line for a dataset using visual aids. Key math concepts include regression analysis, residuals, slope, intercept, and correlation coefficient (PMCC). It utilizes commands like Random, Line, Polygon, Intersect, Point, Sequence, Zip, FitLineY, Sum, PMCC, along with objects such as n, list3, list2, etc. Ideal for high school students or beginners in statistics learning linear regression models.

GeoGebra Commands & Parameters

  1. Random(0, 1) → list3
  2. Line(If[Element[list2, 1] ≟ 1, (0, list3 * 5 + RandomUniform[0, 5]), (RandomUniform[0, 8], list3 * 10)], If[Element[list2, 2] ≟ 1, (16, 5 * (1 - list3) + RandomUniform[0, 5]), (8 + RandomUniform[0, 8], 10 - 10 * list3)]) → f
  3. Polygon((-1, -1), (-1, 10), (16, 10), (16, -1)) → poly1, b, c, d, e
  4. Intersect(f, poly1) → F, G
  5. Point(poly1) → D
  6. Point(poly1) → E
  7. Line(D, E) → g
  8. Sequence(RandomUniform[x(F) + n, x(G)], t, 1, Random[8, 17]) → list1
  9. Zip((A, Slope[f] * A + y(Intersect[f, yAxis]) + RandomUniform[-Random[0, 3] + n, RandomUniform[0, 3]]), A, list1) → list4
  10. FitLineY(list4) → h
  11. Zip((x(A), x(A) * Slope[g] + y(Intersect[g, yAxis])), A, list4) → list5
  12. Zip(Segment[A, B], A, list4, B, list5) → list6
  13. Zip(Polygon[A, B, 4], A, list4, B, list5) → list7
  14. Sum(Zip[Polygon[B, (A, Slope[h] * A + y(Intersect[h, yAxis])), 4], A, list1, B, list4]) → list8
  15. PMCC(list4) → r

AI Drawing Prompt Reference

Draw a coordinate system with a randomly generated line and multiple points. Highlight the points in different colors and plot their fitted line. Show residual line segments and points, and calculate the correlation coefficient. Enclose all points with a polygon and fill it with color.
The prompt above was compiled from the original drawing commands and is for reference only.