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I have to do a logistic regression analysis. I'm attempting to understand which variables I am taking out of a model. I am doing a simple hypothesis test to understand whether I should keep an independent variable in my model or not. Would I be right in saying to test the significance level with the Wald distribution you have to see whether the p-value is higher than a 0.025 significance as we are doing a two-sided test (because we are testing whether the coefficient is non-zero)?

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The Wald test in logistic regression is often a bad approximation to the likelihood ratio test, because the logistic log likelihood function is often far from quadratic. So you are better of using the likelihood ratio test.

For more details see Why use the Wald test in logistic regression?, Rao's Score/Lagrange Multiplier Test most powerful when $\theta$ close to $\theta_0$?, Why do my p-values differ between logistic regression output, chi-squared test, and the confidence interval for the OR?, Feature selection for Logistic Regression

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