Testing for nonlinearities

Problem

Consider the Crime data at https://www.oswego.edu/~kane/econometrics/data.htm .

y = crime, x2 = pov, x3 = metro, x4 = popdens. \(α=0.05\) .

It is suggested that popdens has a nonlinear effect on crime. Masha suggests running the regression

\[y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+β_4x_{i,4}+β_5x_{i,4}^2+ε_i\]

The bear wants to go with the linear model

\[y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+β_4x_{i,4}+ε_i\]

How can we decide between these two models? (Do this problem in Eviews)