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I have a question that I want to check an equation, formulated with coefficients, as a whole is significantly different from zero. Such as the formula below. How can I test it? I know how to test whether two coefficients are equal or joint significant but how can we test the significant of the equation as a whole. Many thanks.

\beta_1*\beta_2-\beta_3*\beta_4

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One easy answer it to use Bayesian Monte Carlo methods. Simulate values of the parameters that are consistent with the data, then plug them into your function. Repeat thousands of times, getting thousands of values of your function. Count how many are more (less) than zero, and divide by the number of simulations. These probabilities give a sensible answer to your question.

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  • $\begingroup$ Thanks for your answering. I've used the Bayesian Monte Carlo method. Does that means I need to use the random subset of the original data and obtain the parameters? Or I have to simulate data? If you are familiar to the MC method, could you please give any suggestions about the steps for Bayesian Monte Carlo method for regression method？ $\endgroup$
    – drexel star
    Dec 20, 2020 at 2:29

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