Choosing linear, quadratic, or exponential regression models

Different kinds of data call for different models. A linear model fits when the data change by a roughly constant amount for each step in x; a quadratic model fits data that rise and then fall, or fall and then rise, like the height of a thrown ball over time; and an exponential model fits data that change by a roughly constant percent or ratio, like a growing population or a cooling drink approaching room temperature once the room temperature is subtracted out. With equally spaced x-values, constant first differences suggest linear, constant second differences suggest quadratic, and constant ratios suggest exponential. Technology can fit each type by regression; compare them using the scatter plot, the residual plot (random scatter is good), the context, and the coefficient of determination, r^2, the share of the variation in y the model explains, where closer to 1 means a better fit for the same data. Use the chosen model to make predictions and decisions, being cautious about extrapolating far beyond the data.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report