How Do You Fit a Non-Linear Regression Curve Using Technology?

Use a graphic display calculator (GDC) to enter the paired data, generate a scatter plot, select an appropriate non-linear regression model, and store the fitted equation. Then evaluate the model using its graph, residuals, contextual suitability, and measures such as $R^2$ or $SS_{\text{res}}$.

This is HL-only content, AHL 4.13 Non-linear regression. The method applies to all GDC-active HL paper styles.

The Method

1. Enter the explanatory-variable values into one list and the response-variable values into another, usually $x$ and $y$.
2. Produce a scatter diagram before choosing a model. The overall shape should guide your choice.
3. Open the regression menu and select the required model.
4. Store the resulting equation in the graphing application, then plot it over the scatter diagram.
5. Record the equation using the variables from the question, not calculator labels such as RegEQ.
6. Examine the fit across the whole data range, including the residuals where available.

For example, if the GDC gives $a=2.14$, $b=1.08$ for an exponential regression, write the model as $y=2.14(1.08)^x$, using the calculator's full-precision coefficients for later calculations.

A common misconception is that the model with the greatest $R^2$ is automatically best. It is not: you must also consider the scatter plot, residual pattern, domain, context, and whether the model gives sensible predictions. Avoid unreliable extrapolation beyond the observed data.

Exam Technique

An examiner expects the fitted equation with appropriate accuracy and contextual variables. If asked to compare models, cite numerical evidence such as $R^2$ or $SS_{\text{res}}$, but also justify your choice from the graph and context; do not rely on $R^2$ alone.