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For obtaining the Lagrange Multiplier Statistics I follow this steps (Wooldridge 2019, Introductory Econometrics):

  1. Regress $y$ on the restricted set of independent variables and consider the residuals $\tilde{u}$;
  2. Regress $\tilde{u}$ on all of the independent variables and obtain the R-squared $R^2_u$
  3. Compute $LM=n\cdot R^2_u$
  4. Compare $LM$ to the appropriate critical value, $c$, in a $\chi_q^2$ distribution: if $LM>c$ the null hypothesis is rejected and all the coefficients.

My doubt is about point 2., I don't understand if I should include an intercept in regressing the $\tilde{u}$ on the independent variables or not. If I do include the intercept the resulting $R^2_u$ is the same as the one from the unrestricted regression.

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