GeoGebra: How Input Scaling Affects Regression and Quadratic Fitting
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This example demonstrates what changes when you scale the input variables ("Scaling the Inputs") in a regression workflow, highlighting how the displayed fit and parameter scale can differ even when the underlying model relationship remains interpretable. It connects core ideas such as linear regression, quadratic equations / quadratic functions, and the intuition behind hypothesis testing and model comparison under preprocessing. Construction-wise, the provided GeoGebra construction summary indicates the use of text objects (text1, text2) to clearly label and contrast the “before scaling” versus “after scaling” situation directly on the figure, turning the geometric/numerical result into a readable explanation. Suitable for upper-secondary students and introductory university courses in modeling, statistics, and data preprocessing (feature scaling) using GeoGebra.
AI Drawing Prompt Reference
Create a side-by-side comparison plot. On the left, show a scatter plot of original input data with a quadratic regression curve fitting closely, labeled 'before scaling'. On the right, show the same data points but with rescaled axes, where the quadratic fit curve appears differently shaped, labeled 'after scaling'. Include brief text annotations explaining that the underlying model relationship remains interpretable despite the visual change in fit and parameter scale.
The prompt above was compiled from the original drawing commands and is for reference only.