MathPlotAI Logo MathPlotAI

Scatter Plots and Fitted Functions

Scatter Plots and Fitted Functions
Loading the math board and drawing, please wait…
2022-01-20 12:25
FunctionCoordinate GeometryProbability & Statistics
This example demonstrates how to visualize data points through scatter plots and generate linear, polynomial, exponential, and logarithmic functions using GeoGebra's fitting tools. Key math concepts include probability & statistics, function fitting, least squares method, and geometric transformations. Construction highlights the use of commands like Line, If, FitPoly, FitExp, FitLog, RSquare, Corner, and objects such as LinFit, QuadFit, ExpFit. Ideal for high school and above, focusing on data visualization, model selection, and evaluation.

GeoGebra Commands & Parameters

  1. Line(F, D) → LinFit
  2. If(Linear ≟ true ∨ Quad ≟ true ∨ Cubic ≟ true ∨ Exp ≟ true ∨ Logarithmic ≟ true, 1, 0) → k
  3. FitPoly({D, G, F}, 2) → QuadFit
  4. FitExp({D, F}) → ExpFit
  5. FitPoly({A, D, G, F}, 3) → CubicFit
  6. FitLog({D, F}) → LogFit
  7. RSquare({E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17}, LinFit) → LinR2
  8. RSquare({E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17}, QuadFit(x)) → QuadR2
  9. RSquare({E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17}, CubicFit(x)) → CubR2
  10. RSquare({E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17}, ExpFit(x)) → ExpR2
  11. RSquare({E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17}, LogFit(x)) → LogR2
  12. Corner(text3, 1) → fc1
  13. Corner(text3, 3) → fc3
  14. Corner(text3, 4) → fc4
  15. Corner(text3, 2) → fc2

AI Drawing Prompt Reference

In a single coordinate plane, plot a scatter set of discrete data points that will be used for fitting. Then construct five fitted curves over the same domain: a linear best-fit line, a quadratic polynomial fit, a cubic polynomial fit, an exponential fit, and a logarithmic fit. Ensure each curve is tied to its corresponding fitted function derived from the same data points. Compute a goodness-of-fit score for each model and display these values alongside the curves. Finally, place four corner label callouts at distinct corner-like positions to annotate the figure.
The prompt above was compiled from the original drawing commands and is for reference only.