Fourth-order polynomial

To model the relationship between y, a dependent variable, and x, an independent variable, a researcher has taken one measurement on y at each of five different x-values. Drawing on his mathematical expertise, the researcher realizes that he can fit the fourthorder polynomial model

E(y) = β₀ + β₁x + β₂x² + β₃x³ + β₄x⁴

and it will pass exactly through all five points, yielding SSE = 0. The researcher, delighted with the ‘‘excellent'' fit of the model, eagerly sets out to use it to make inferences. What problems will the researcher encounter in attempting to make inferences?