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?
