Hi, We know that in a simple multivariate linear regression scheme, the betas have a multivariate normal distribution, with mean equal to the population beta and a variance proportional to the inverse of the matrix XTX multiplied by the variance of the error term. My question is while testing the statistical significance of any given beta, is it best to just test for that beta alone, meaning that analyze the behavior of the marginal distribution of that beta alone, or is it best to incorporate the effect of other betas, in other words analyze the mutivariate distribution. These two are distinct approaches. In the method 1, my t stat say for beta-1 is just beta-1/var(beta-1). In the second approach, I can build a test to say that, what is the probability that both beta-1 and beta-2 are zero, and use the multivariate distribution to build the right statistic. I think it'll involve the chi-square distribution in some form. What are the best practices around this?Thanks, and please let me know if I wasn't clear.