# How to estimate the sample sized required to achieve a lower p-value in multivariate linear regression?

Suppose I obtain a coefficient $$\hat{\beta_i}$$ and it has 0.01 < p < 0.05. I believe the effect is real so I want to gather more data. Assuming $$\hat{\beta_i}$$ is close to the correct coefficient, how many more data points are required to obtain p < 0.01?

• A p-value is a random variable, so you can at best calculate the probability Pr(P<0.01). Given the distribution of $\hat{\beta}_i$ this shouldn't be too hard. Nov 21, 2019 at 8:32
• @Knarpie Well we know the normalized coefficient is t-distributed. The problem is that with more samples you’d expect the standard deviation to decrease and the degrees of freedom to go up...so it’s complicated. Nov 21, 2019 at 16:40
• It seems, we're look for the same Nov 22, 2019 at 10:07