Correlation Coefficient r - Interactive Exploration

This GeoGebra example dynamically demonstrates the calculation and visualization of Pearson's correlation coefficient r, helping learners intuitively grasp the strength and direction of linear association between two variables. Core mathematical concepts include the correlation coefficient formula, covariance, standard deviation, least-squares regression line, and the scatterplot pattern. Construction highlights: uses GeoGebra commands such as Intersect for finding intersection points, stdevp for population standard deviation, Sum for summation, FitPoly to generate a fitted polynomial (typically linear), and Textfield for input boxes to adjust data points or parameters. Objects include multiple points (A11 to A25), sliders a, b, α, the fitted function f, and equation eq1. Suitable for high school or introductory college statistics courses, also useful for AP Statistics or data analysis teaching. By dragging points or modifying parameters, users can observe real-time changes in r, deepening understanding of correlation versus causation.