Linear Regression Example 3: Least Squares Fit and Geometric Construction

① This example demonstrates how to perform a least-squares linear regression on a set of scattered data points using GeoGebra's FitLineY command, and visualizes the geometric relationship between the fitted line and the data points. ② Core mathematical concepts include linear regression, least squares method, correlation, geometric mean, orthogonal projection of points onto a line, and polygon area calculations (to visualize residual sum of squares). ③ Construction highlights: uses Line, OrthogonalLine, and Intersect commands to construct auxiliary lines and intersection points, Polygon and Sum commands to compute residual-related areas, and finally FitLineY to generate the regression line; objects include multiple points (A to R), lines (a to s), and polygons (poly1 to poly4). ④ Suitable for high school to university-level teaching that integrates statistics and geometry, providing an intuitive understanding of the geometric meaning of regression lines and the least squares principle.