
IB Math AI HL 4.13 – Regression Analysis
This lesson explores non-linear regression models and the use of technology to evaluate least-squares regression curves for data that does not fit a straight line.
Students learn how to model complex relationships between variables by transforming data to achieve a more linear pattern and then applying regression techniques. The slide deck introduces the concept of the sum of squared residuals (Σr²) as a key measure of how well a model fits observed data—the smaller the residuals, the better the fit. The lesson also introduces the coefficient of determination (R²), explaining how it quantifies the proportion of variance in the dependent variable that can be explained by the model. Examples demonstrate how to compute R² using technology and interpret it in context (e.g., an R² of 0.85 means 85% of variation in y is explained by the model).
Practice problems include comparing exponential and power models, determining which best fits the data, and making predictions based on regression equations. By the end of the lesson, students can evaluate multiple regression models, use calculator or software tools to perform curve fitting, and critically assess the reliability of predictions.
Fully aligned with IB Math AI HL Topic 4.13 – Regression Analysis, this resource develops analytical and technological proficiency for modeling real-world relationships and interpreting statistical results in context.
IB M
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