Question

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 three different x-values. Drawing on his mathematical expertise, the researcher realizes that he can fit the second-order model $E\left(y\right)={\beta }_0+{\beta }_{1}x+{\beta }_2{x}^2$and it will pass exactly through all three 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 he encounter in attempting to make inferences?

Short answer

The researcher has fit a second-order model to the data and taken one measurement on y at 3 different values for x. The SSE value is coming out to be zero indicating that the data points lie perfectly on the line. However, since the SSE value is zero, the researcher might face issues while testing the significance of beta parameters or the goodness of fit test for the model.

Step-by-step solution

Second-order model

The researcher has fit a second-order model to the data and taken one measurement on y at 3 different values for x. The SSE value is coming out to be zero indicating that the data points lie perfectly on the line.

Problems with second-order model

However, since the SSE value is zero, the researcher might face issues while testing the significance of beta parameters or the goodness of fit test for the model.