Uncertainty and models
Confidence-band chart
Shows uncertainty around an estimated mean, function or model quantity across X.
- Plot
- Uncertainty
- Model fit
What it answers
How uncertain is an estimated curve?
- Shape
- Estimate curve within a shaded band
- What it shows
- Precision changes across the fitted domain.
Example
The question
How sure are we about the trend line linking price and units sold?
Units sold against price with fitted line and 95% confidence band (illustrative)
Illustrative data. It belongs to no company.
When to use it
Use it when
Showing uncertainty around estimated means/functions.
Avoid it when
When confused with individual-outcome prediction ranges.
How to read it
Read the estimate line and confidence-band coverage definition.
Note
Not a prediction interval for individual outcomes.
The data you need
- Layout
- Wide interval summary
- Fields
- X or Time: number/date; Estimate,Lower,Upper: numbers
- One row is
- One ordered curve position and its estimate and bounds. What is the grain?
- Rules
- Sort X/time, pair all bounds and specify interval meaning and coverage. Compute intervals using an appropriate model.
- Optional
- Alternative Estimate,LowerError,UpperError distances. Distinguish bounds from distances.
- Preparation
- Fit or obtain a suitable model/estimate first, then pair estimates with correctly labelled bounds or standard errors. Preserve coverage and scale information.
- Units
- Estimates and interval endpoints share an effect/measurement unit unless transformed. Coverage such as 95% is a model-based probability statement, not a data-share denominator.
Worked example
AtX1 mean 10 with 95% confidence interval 8-12; X2 mean 12 with 9-15. The second interval iswider under the supplied model.
| X | Estimate | Lower | Upper |
|---|---|---|---|
| 1 | 10 | 8 | 12 |
| 2 | 12 | 9 | 15 |
| 3 | 14 | 10 | 18 |