What you’ll learn
Identify linear/nonlinear association.
Key idea
An exact straight-line pattern has constant rate; direction and shape are different properties.
Compare rates over equal horizontal intervals; positive trend and different output values do not decide linearity.
Worked example
Classify examples and non-examples for the concept 'Identify linear/nonlinear association'.
Classify displayed observations {(0,2),(1,3),(2,6),(3,11)} as linear or nonlinear, with difference evidence.
- Equal horizontal increments allow direct comparison of y differences [1, 3, 5].
- Nonlinear: equal unit x steps give y differences [1, 3, 5], which are not constant; increasing output alone does not determine straightness.
Answer: Nonlinear — equal unit x steps give y differences [1, 3, 5], which are not constant.
Quick Check
Classify examples and non-examples for the concept 'Identify linear/nonlinear association'.
Classify displayed observations {(0,2),(1,5),(2,8),(3,11)} as linear or nonlinear, with difference evidence.