Which statement about non-linear trends is accurate?

Which statement about non-linear trends is accurate?

• A. Non-linear trends cannot be modeled
• B. Non-linear trends can be modeled by adding quadratic terms
• C. They require seasonal data
• D. They are always best modeled by moving average

Answer: (B)

Non-linear trends can be captured by including polynomial terms for time in a model. By adding a quadratic term (time squared), the trend is allowed to curve rather than stay on a straight line, so the fitted line can bend upward or downward as time progresses. This directly models the curvature that characterizes non-linear trends. This is why the statement is best: using a quadratic term provides a simple, interpretable way to describe non-linearity in the trend. Other choices aren’t as accurate: non-linear trends can be modeled (there are many methods beyond linear regression), seasonality is not a prerequisite for non-linearity, and moving averages are primarily smoothing tools that don’t explicitly fit a curved trend form.

Non-linear trends can be captured by including polynomial terms for time in a model. By adding a quadratic term (time squared), the trend is allowed to curve rather than stay on a straight line, so the fitted line can bend upward or downward as time progresses. This directly models the curvature that characterizes non-linear trends.

This is why the statement is best: using a quadratic term provides a simple, interpretable way to describe non-linearity in the trend. Other choices aren’t as accurate: non-linear trends can be modeled (there are many methods beyond linear regression), seasonality is not a prerequisite for non-linearity, and moving averages are primarily smoothing tools that don’t explicitly fit a curved trend form.