Guess the Equation: Locating Points with Zero Correlation

① This example demonstrates a dynamic exploration where dragging point A captures points that make the Pearson correlation coefficient (PMCC) exactly zero, prompting users to guess the equation of the curve on which these points lie. ② Core mathematical concepts include Pearson correlation, linear regression (FitLineY), scatter plots, curve fitting, and the geometric interpretation of zero correlation between two variables. ③ Construction details: Using GeoGebra commands such as Polygon, FitLineY, PMCC, and LaTeX, the construction involves multiple points (I, H, F, E, D, B, A, C) and polygon poly1, fitted lines b, c, a, d, correlation value r, and text objects text1 and text2. Buttons button1 and button2 control data capture and reset, while transformed points (A', C', B') and poly2 are generated, ultimately forming the locus datacap. ④ This is suitable for high school or college courses in statistics and analytic geometry, helping students understand the meaning of correlation, explore relationships between data points and equations, and develop skills in deriving mathematical models from experimental data.