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Exploring R-squared

Exploring R-squared
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2019-09-05 02:06
FunctionCoordinate GeometryProbability & Statistics
This example demonstrates the concept of R-squared, a measure of how well a linear regression model fits the data. Through the commands and objects in the construction summary, one can visually understand the calculation and significance of R-squared. The core mathematical concepts include linear regression, correlation coefficient, and variance. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Max(A1:A20) → a
  2. Max(B1:B20) → b
  3. mean(B1:B20) → c
  4. Min(A1:A20) → d
  5. Segment((d, c), (a, c)) → f
  6. Line(A, B) → g
  7. Polygon(E1, D1, G1, H1) → q1, f1, c1, h1, i1
  8. Polygon(E2, D2, G2, H2) → q2, f2, c2, h2, i2
  9. Polygon(D3, E3, H3, G3) → q3, c3, f3, i3, h3
  10. Polygon(D4, E4, H4, G4) → q4, c4, f4, i4, h4
  11. Polygon(D5, G5, H5, E5) → q5, c5, h5, i5, f5
  12. Polygon(E6, H6, G6, D6) → q6, f6, i6, h6, c6
  13. Polygon(D1, K1, L1, I1) → q7, h, l1, m1, j1
  14. Polygon(D2, K2, L2, I2) → q8, i, l2, m2, j2
  15. Polygon(D3, I3, L3, K3) → q9, j, j3, m3, l3
  16. Polygon(D4, I4, L4, K4) → q10, k, j4, m4, l4
  17. Polygon(I5, L5, K5, D5) → q11, j5, m5, l5, l
  18. Polygon(I6, L6, K6, D6) → q12, j6, m6, l6, m
  19. FitLineY({D1, D2, D3, D4, D5, D6}) → r
  20. PMCC({D1, D2, D3, D4, D5, D6}) → s
  21. Sum(F10:F15) → F16
  22. Sum(J10:J15) → J16

AI Drawing Prompt Reference

Draw a coordinate system with data points and a fitted line to illustrate the concept of R-squared in regression analysis. First, plot multiple polygons representing data points, then draw a horizontal segment for the mean of y, fit a best-fit line, calculate the correlation coefficient, and combine the polygons and line to visualize the concept.
The prompt above was compiled from the original drawing commands and is for reference only.