Fit a model (quadratic, cubic, exponential, power, sinusoidal)

The heart of AI modelling - find the best-fitting curve for a data set, not just a straight line.

In short: Fitting a model means using regression to find the equation of a curve that best matches paired data, such as a quadratic, cubic, exponential, power or sinusoidal function. The GDC takes lists of x and y values and returns the model's parameters. Plot the data first to choose a sensible form, then compare how well each fits.

When you'd use this

A scatter diagram looks curved, not straight - a straight-line regression would be the wrong model.
The context suggests a specific shape: exponential growth/decay, a quadratic optimum, a periodic (sinusoidal) pattern.
Finding the parameters of that curve (a, b, etc.) directly from the data.
You need the best-fitting curve before using it to predict a value or compare it to another model.

TI-84 Plus CE Casio fx-CG50 and fx-CG100 TI-Nspire CX

At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared

	TI-84 Plus CE	Casio fx-CG50 and fx-CG100	TI-Nspire CX
Key sequence	STAT → EDIT to enter L1/L2, then STAT → CALC → QuadReg / CubicReg / ExpReg / PwrReg / SinReg.	Main menu → Statistics, enter the data in lists, then CALC → REG and pick X² / X³ / Exp / Power / Sin.	In a Lists & Spreadsheet page enter the data, then menu → Statistics → Stat Calculations → choose the regression type.

On a TI-84 Plus CE

Enter the data in two lists (x and y).
STAT → EDIT to enter L1/L2, then STAT → CALC → QuadReg / CubicReg / ExpReg / PwrReg / SinReg.

Tip: Turn DiagnosticOn (TI-84: 2nd → 0 → DiagnosticOn) to see R². Choose the model with the best R² that also makes sense for the context.

On a Casio fx-CG50 and fx-CG100

Enter the data in two lists (x and y).
Main menu → Statistics, enter the data in lists, then CALC → REG and pick X² / X³ / Exp / Power / Sin.

Tip: Turn DiagnosticOn (TI-84: 2nd → 0 → DiagnosticOn) to see R². Choose the model with the best R² that also makes sense for the context.

On a TI-Nspire CX

Enter the data in two lists (x and y).
In a Lists & Spreadsheet page enter the data, then menu → Statistics → Stat Calculations → choose the regression type.

Tip: Turn DiagnosticOn (TI-84: 2nd → 0 → DiagnosticOn) to see R². Choose the model with the best R² that also makes sense for the context.

Related guides

Try it yourself

Here's a real IB-style question that uses exactly this technique.

Hard Calculator Paper 2 [4 marks]

Fit an exponential model y = abˣ to the data (1, 6), (2, 12), (3, 24), (4, 48).

y = 3(2)ˣ

Mark it

Correct 4 / 4 marks

Worked solution & mark scheme:

M1 Run exponential regression (ExpReg) on the data

A1 y = 3(2)ˣ

Common questions

When would I need to fit a quadratic, cubic, exponential, power or sinusoidal model in IB Maths?

The heart of AI modelling - find the best-fitting curve for a data set, not just a straight line. A scatter diagram looks curved, not straight - a straight-line regression would be the wrong model. The context suggests a specific shape: exponential growth/decay, a quadratic optimum, a periodic (sinusoidal) pattern.

How do I fit a quadratic, cubic, exponential, power or sinusoidal model on a TI-84 Plus CE?

1. Enter the data in two lists (x and y). 2. STAT → EDIT to enter L1/L2, then STAT → CALC → QuadReg / CubicReg / ExpReg / PwrReg / SinReg.

How do I fit a quadratic, cubic, exponential, power or sinusoidal model on a Casio fx-CG50 and fx-CG100?

1. Enter the data in two lists (x and y). 2. Main menu → Statistics, enter the data in lists, then CALC → REG and pick X² / X³ / Exp / Power / Sin.

How do I fit a quadratic, cubic, exponential, power or sinusoidal model on a TI-Nspire CX?

1. Enter the data in two lists (x and y). 2. In a Lists & Spreadsheet page enter the data, then menu → Statistics → Stat Calculations → choose the regression type.

What should I watch out for when I fit a quadratic, cubic, exponential, power or sinusoidal model?

Turn DiagnosticOn (TI-84: 2nd → 0 → DiagnosticOn) to see R². Choose the model with the best R² that also makes sense for the context.

How are marks awarded when I fit a quadratic, cubic, exponential, power or sinusoidal model in an IB exam?

In the worked example on this page (4 marks, Paper 2), the marks are: M1: Run exponential regression (ExpReg) on the data; A1: y = 3(2)ˣ.

Practise with your calculator

Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.