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Visualizing Linear Regression and Correlation (r)

Visualizing Linear Regression and Correlation (r)
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2025-03-25 16:04
VectorFunctionCoordinate GeometryProbability & StatisticsGraphing
This example demonstrates how to perform linear regression on a set of data points and visualize the best-fit line alongside the statistical quantities that lead to the correlation coefficient r. It highlights the roles of mean, variance, and covariance in quantifying how two variables co-vary, and how that relationship determines the regression direction and fit quality. The construction uses GeoGebra commands such as Covariance and Variance (with objects like var_x, var_y, s_{xy}), mean (to define m_x, m_y), Line to draw the regression line, and Point to plot the data sets (e.g., A1–A9 and B1–B9). It also uses Vector and Angle to provide geometric intuition for relationships between the data and the fitted model, while equation/label objects (eq1, eq2, text1, etc.) present the computation steps and results. Suitable for teaching probability & statistics and graphing-based data analysis in upper secondary school through early university.

GeoGebra Commands & Parameters

  1. Covariance(l1) → s_{xy}
  2. Variance(l2) → var_x
  3. Variance(l3) → var_y
  4. mean(l2) → m_x
  5. mean(l3) → m_y
  6. Line(Q, N) → i
  7. Line(Q, P) → j
  8. Point(xAxis) → R
  9. Angle(R, Q, N) → α
  10. Point(yAxis) → S
  11. Angle(P, Q, S) → β
  12. Point(g) → T
  13. Angle(S, Q, T) → γ
  14. Point(xAxis) → U
  15. Point(f) → V
  16. Angle(V, Q, U) → δ
  17. Vector((x(J) - 20, y(J)), K) → u
  18. Vector((x(J), y(J) - 20), L) → v
  19. Point(f) → W
  20. Point(g) → Z
  21. Point(xAxis) → A_1
  22. Point(yAxis) → B_1

AI Drawing Prompt Reference

Visualize a set of data points with a best-fit line to demonstrate linear regression and the correlation coefficient r. Include calculations of mean, variance, and covariance, with vectors showing the geometric relationship between data and the model. Label key angles and provide geometric intuition. Start by plotting data points and axes, then draw the regression line, and use vectors, angles, and labels to present statistical quantities and geometric insights.
The prompt above was compiled from the original drawing commands and is for reference only.