When a scatter chart of data shows a nonlinear relationship, the nonlinear model can be expressed as:
A)Y = β₀ + β₁X + β₂X² + ε
B)Y = β₀+ β₁X + (β₂X)² + ε
C)Y = β₀ + β₁X + β₂X
D)Y = β₀ + β₁X² + β₂X² + ε

Question

Quizplus · Accepted Answer

The formula Y = β₀ + β₁X + β₂X² + ε represents a curved, nonlinear relationship. The presence of the squared term indicates that the curve changes direction at some point, creating a parabolic shape. This formula is often used to model relationships where the response variable Y increases or decreases at an increasing rate as the predictor variable X increases.

When a Scatter Chart of Data Shows a Nonlinear Relationship