Simpson's Paradox in 2D: When Grouped Trends Reverse

Every subgroup in this dataset shows the same negative relationship between X and Y — yet pool all the points together and the trend can flip to positive. This is Simpson's Paradox, a real and reproducible statistical phenomenon caused by a confounding variable that drifts together with both the predictor and the group label. The simulator generates several subgroups of synthetic data, fits a genuine least-squares regression line to each one individually and to the pooled dataset, and renders both directly on a 2D scatter plot (pan and zoom to inspect) alongside a bar-chart panel that puts the within-group and pooled slope/correlation side by side so the reversal is unmistakable.