A residual is the gap between the actual y-value and the model's prediction. Large residuals reveal outliers or a poor model fit.
In short: A residual is the difference between an observed value and the value predicted by a regression model. Plotting residuals helps show whether the model suits the data: a random scatter supports it, while a clear pattern suggests a better model exists. Unusually large residuals flag possible outliers worth checking.
When you'd use this
Checking whether a data point lies unusually far from the fitted regression line.
A question asks for the residual at a specific x-value, not just the fitted equation.
Deciding whether an outlier should be removed before refitting a model.
Assessing whether a linear model is appropriate by looking at the pattern of residuals.
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
After LinReg, the residuals are automatically stored in the list RESID (2nd → STAT → RESID). Plot them: STAT PLOT → Scatter with Xlist = L1, Ylist = RESID.
After regression, the residuals are stored as a list; access via List → RESID or compute (y-value − fitted value) for each point.
In a Lists & Spreadsheet page, add a column with the formula = y_data − f1(x_data) to compute residuals manually; or use the residuals option in the regression output.
On a TI-84 Plus CE
After fitting a regression model, residual = actual y − predicted y (positive means the point is above the line).
After LinReg, the residuals are automatically stored in the list RESID (2nd → STAT → RESID). Plot them: STAT PLOT → Scatter with Xlist = L1, Ylist = RESID.
Plot residuals against x: a random scatter around zero means a good fit; a curved or fanning pattern means a different model is needed.
A point with a residual much larger than the others (in absolute value) is a potential outlier - consider removing it and refitting.
Tip: If the residual plot shows a clear curve, the model is wrong - try a quadratic or exponential instead. Residual plots reveal what R² can hide.
On a Casio fx-CG50 and fx-CG100
After fitting a regression model, residual = actual y − predicted y (positive means the point is above the line).
After regression, the residuals are stored as a list; access via List → RESID or compute (y-value − fitted value) for each point.
Plot residuals against x: a random scatter around zero means a good fit; a curved or fanning pattern means a different model is needed.
A point with a residual much larger than the others (in absolute value) is a potential outlier - consider removing it and refitting.
Tip: If the residual plot shows a clear curve, the model is wrong - try a quadratic or exponential instead. Residual plots reveal what R² can hide.
On a TI-Nspire CX
After fitting a regression model, residual = actual y − predicted y (positive means the point is above the line).
In a Lists & Spreadsheet page, add a column with the formula = y_data − f1(x_data) to compute residuals manually; or use the residuals option in the regression output.
Plot residuals against x: a random scatter around zero means a good fit; a curved or fanning pattern means a different model is needed.
A point with a residual much larger than the others (in absolute value) is a potential outlier - consider removing it and refitting.
Tip: If the residual plot shows a clear curve, the model is wrong - try a quadratic or exponential instead. Residual plots reveal what R² can hide.
Here's a real IB-style question that uses exactly this technique.
HardCalculatorPaper 2[3 marks]
For the data (1,2), (2,4), (3,6), (4,8), (5,20), find the residual at x = 5 using the linear regression line.
Residual = 4
Mark it
Correct3 / 3 marks
Worked solution & mark scheme:
M1 Find the regression line's predicted value at x = 5
A1 Residual = actual − predicted = 4, a clear outlier
Common questions
When would I need to find residuals and spot outliers in a regression in IB Maths?
A residual is the gap between the actual y-value and the model's prediction. Large residuals reveal outliers or a poor model fit. Checking whether a data point lies unusually far from the fitted regression line. A question asks for the residual at a specific x-value, not just the fitted equation.
How do I find residuals and spot outliers in a regression on a TI-84 Plus CE?
1. After fitting a regression model, residual = actual y − predicted y (positive means the point is above the line). 2. After LinReg, the residuals are automatically stored in the list RESID (2nd → STAT → RESID). Plot them: STAT PLOT → Scatter with Xlist = L1, Ylist = RESID. 3. Plot residuals against x: a random scatter around zero means a good fit; a curved or fanning pattern means a different model is needed. 4. A point with a residual much larger than the others (in absolute value) is a potential outlier - consider removing it and refitting.
How do I find residuals and spot outliers in a regression on a Casio fx-CG50 and fx-CG100?
1. After fitting a regression model, residual = actual y − predicted y (positive means the point is above the line). 2. After regression, the residuals are stored as a list; access via List → RESID or compute (y-value − fitted value) for each point. 3. Plot residuals against x: a random scatter around zero means a good fit; a curved or fanning pattern means a different model is needed. 4. A point with a residual much larger than the others (in absolute value) is a potential outlier - consider removing it and refitting.
How do I find residuals and spot outliers in a regression on a TI-Nspire CX?
1. After fitting a regression model, residual = actual y − predicted y (positive means the point is above the line). 2. In a Lists & Spreadsheet page, add a column with the formula = y_data − f1(x_data) to compute residuals manually; or use the residuals option in the regression output. 3. Plot residuals against x: a random scatter around zero means a good fit; a curved or fanning pattern means a different model is needed. 4. A point with a residual much larger than the others (in absolute value) is a potential outlier - consider removing it and refitting.
What should I watch out for when I find residuals and spot outliers in a regression?
If the residual plot shows a clear curve, the model is wrong - try a quadratic or exponential instead. Residual plots reveal what R² can hide.
How are marks awarded when I find residuals and spot outliers in a regression in an IB exam?
In the worked example on this page (3 marks, Paper 2), the marks are: M1: Find the regression line's predicted value at x = 5; A1: Residual = actual − predicted = 4, a clear outlier.
