After fitting several models (linear, quadratic, exponential…), you need to decide which fits the data best - R² is the key tool.
In short: R², the coefficient of determination, measures the proportion of the variation in y explained by the fitted model, so a value closer to 1 suggests a better fit. Compare R² across candidate models fitted to the same data, but also check the residuals and that the model makes sense in the context of the question.
When you'd use this
You've fitted more than one type of model (e.g. linear and quadratic) to the same data.
Deciding which model to actually use in the rest of the question.
An R² close to 1 for one model but not another is strong evidence for the better-fitting shape.
A question explicitly asks you to justify your choice of model using R².
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
Turn DiagnosticOn first (2nd → 0, scroll to DiagnosticOn, ENTER) - then R² appears after every regression.
R² (displayed as r²) appears in the regression output; run CALC → REG for each model type and compare.
R² is shown automatically after each regression calculation in the Statistics menu.
On a TI-84 Plus CE
Fit each candidate model in turn and note the R² value each time.
Turn DiagnosticOn first (2nd → 0, scroll to DiagnosticOn, ENTER) - then R² appears after every regression.
The model with R² closest to 1 explains the most variation in y - but also consider whether the model makes sense for the context.
An exponential model with R² = 0.98 is better than a linear model with R² = 0.91 for the same data.
Tip: R² alone doesn't tell you whether the model is appropriate - always look at the scatter plot too. A high R² on a model that shouldn't apply (e.g. sinusoidal for steadily growing data) is meaningless.
On a Casio fx-CG50 and fx-CG100
Fit each candidate model in turn and note the R² value each time.
R² (displayed as r²) appears in the regression output; run CALC → REG for each model type and compare.
The model with R² closest to 1 explains the most variation in y - but also consider whether the model makes sense for the context.
An exponential model with R² = 0.98 is better than a linear model with R² = 0.91 for the same data.
Tip: R² alone doesn't tell you whether the model is appropriate - always look at the scatter plot too. A high R² on a model that shouldn't apply (e.g. sinusoidal for steadily growing data) is meaningless.
On a TI-Nspire CX
Fit each candidate model in turn and note the R² value each time.
R² is shown automatically after each regression calculation in the Statistics menu.
The model with R² closest to 1 explains the most variation in y - but also consider whether the model makes sense for the context.
An exponential model with R² = 0.98 is better than a linear model with R² = 0.91 for the same data.
Tip: R² alone doesn't tell you whether the model is appropriate - always look at the scatter plot too. A high R² on a model that shouldn't apply (e.g. sinusoidal for steadily growing data) is meaningless.
Here's a real IB-style question that uses exactly this technique.
HardCalculatorPaper 2[4 marks]
For the data (1,2), (2,5), (3,10), (4,17), (5,26), compare a linear and a quadratic model using R², and state which fits better.
Linear R² = 0.963; quadratic R² = 1 (exact fit, since y = x² + 1)
Mark it
Correct4 / 4 marks
Worked solution & mark scheme:
M1 Run linear regression and record R²
M1 Run quadratic regression and record R²
A1 Linear R² = 0.963
R1 Quadratic model fits better (R² = 1)
Common questions
When would I need to compare regression models using R² in IB Maths?
After fitting several models (linear, quadratic, exponential…), you need to decide which fits the data best - R² is the key tool. You've fitted more than one type of model (e.g. linear and quadratic) to the same data. Deciding which model to actually use in the rest of the question.
How do I compare regression models using R² on a TI-84 Plus CE?
1. Fit each candidate model in turn and note the R² value each time. 2. Turn DiagnosticOn first (2nd → 0, scroll to DiagnosticOn, ENTER) - then R² appears after every regression. 3. The model with R² closest to 1 explains the most variation in y - but also consider whether the model makes sense for the context. 4. An exponential model with R² = 0.98 is better than a linear model with R² = 0.91 for the same data.
How do I compare regression models using R² on a Casio fx-CG50 and fx-CG100?
1. Fit each candidate model in turn and note the R² value each time. 2. R² (displayed as r²) appears in the regression output; run CALC → REG for each model type and compare. 3. The model with R² closest to 1 explains the most variation in y - but also consider whether the model makes sense for the context. 4. An exponential model with R² = 0.98 is better than a linear model with R² = 0.91 for the same data.
How do I compare regression models using R² on a TI-Nspire CX?
1. Fit each candidate model in turn and note the R² value each time. 2. R² is shown automatically after each regression calculation in the Statistics menu. 3. The model with R² closest to 1 explains the most variation in y - but also consider whether the model makes sense for the context. 4. An exponential model with R² = 0.98 is better than a linear model with R² = 0.91 for the same data.
What should I watch out for when I compare regression models using R²?
R² alone doesn't tell you whether the model is appropriate - always look at the scatter plot too. A high R² on a model that shouldn't apply (e.g. sinusoidal for steadily growing data) is meaningless.
How are marks awarded when I compare regression models using R² in an IB exam?
In the worked example on this page (4 marks, Paper 2), the marks are: M1: Run linear regression and record R²; M1: Run quadratic regression and record R²; A1: Linear R² = 0.963; R1: Quadratic model fits better (R² = 1).
