Ramsey’s RESET test

Summary

Ramsey’s RESET (Regression Equation Specification Error Test) test:

$$y_i=β_1+β_2x_{2i}+β_3x_{3i}+…+β_kx_{ki}+ε_i i=1,…,n$$

• Save the fitted values   ${\hat{y}}_i$
• Add the variable   ${\hat{y}}_i^2$ to you LRM and re-estimate it:

$$y_i=β_1+β_2x_{2i}+β_3x_{3i}+…+β_kx_{ki}+γ{\hat{y}}_i^2+ε_i i=1,…,n$$

• Test $H_0:γ=0$ . If rejected, this indicates signs of misspecification, particularly nonlinearity in the data.

It is also possible to add higher order powers, such as ${\hat{y}}_i^3$ to the second regression.