A trend needs context.
A scatterplot places two numerical measurements together for each observation. Describe direction, form and strength, then identify unusual points. An association alone does not establish cause: another variable may influence both measurements.
A fitted line summarises a linear trend. A residual is observed minus predicted. Predicting within the observed x-range is interpolation; predicting beyond it is extrapolation and may be unreliable. A larger sample does not automatically remove selection bias.
Try it. Watch it change.
Illustrative observations. Change one point to investigate sensitivity. A fitted association alone does not establish causation.
Explore: Move the unusual observation vertically. Watch how a single point changes the fitted line.
A fitted model predicts 72 marks, but the observed result is 68. Find the residual.
- Residual = observed − predicted.
- 68 − 72 = −4 marks; the point lies below the fitted line.
Assumed knowledge
Coordinates, averages and reading scales.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Describe scatterplots and interpret a fitted line.
- Recognise outliers, sampling bias and limits of prediction.