To test a fifth-order polynomial in regression, which predictor should be included?

To test a fifth-order polynomial in regression, which predictor should be included?

• A. Time raised to the power of the order of the polynomial.
• B. Time as a binary category.
• C. Time transformed by natural log.
• D. Time squared only.

Answer: (A)

When you want to test a fifth-degree polynomial in regression, you need the term that represents that degree: time raised to the fifth power. This highest-order term lets the model capture the distinctive fifth-order curvature in the relationship between time and the outcome, so you can test whether adding this level of nonlinearity actually improves fit. If this coefficient is significant, it suggests a true fifth-degree pattern beyond simpler terms. Using time as a binary category would only compare two groups, not a smooth polynomial trend. Time transformed by a logarithm changes scale but doesn’t specifically test a fifth-degree shape. Time squared tests only a second-degree effect, not the fifth order.

When you want to test a fifth-degree polynomial in regression, you need the term that represents that degree: time raised to the fifth power. This highest-order term lets the model capture the distinctive fifth-order curvature in the relationship between time and the outcome, so you can test whether adding this level of nonlinearity actually improves fit. If this coefficient is significant, it suggests a true fifth-degree pattern beyond simpler terms. Using time as a binary category would only compare two groups, not a smooth polynomial trend. Time transformed by a logarithm changes scale but doesn’t specifically test a fifth-degree shape. Time squared tests only a second-degree effect, not the fifth order.