# Minimal sample size needed univariate regression

Setup: I need to figure out how many years of data I need for $\beta_1- H_0$ to be significant at the 5% level. My plan as of now is to collect info on $y_{i1}, y_{i2},x_{i1},x_{i2}$ and run the differenced regression, $E(y_{i1}- y_{i2}) = (x_{i1}- x_{i2})$ where $y_{i1}$ refers to all observations of my deponent variable from year 1.

I will then have $\hat\beta_1$, $H_0$ (my null hypothesis) and $se(\hat\beta_1)$ How do I calculate how many more observations I need for $se(\hat\beta_1)=se^\star(\hat\beta_1)$, where $(\hat\beta_1 - H_0)/(se^\star(\hat\beta_1)) <.05$?

• (NB, I edited to your $\LaTeX$; please ensure it still says what you want it to say.) We'll need more information here to be able to answer this. Are you looking to have a certain amount of statistical power? If so, how much? How far do you believe beta hat is from H0? Are these time series data (ie is there only 1 observational unit over time)? Etc. – gung - Reinstate Monica Jan 31 '15 at 22:21
• @gung. I am looking to attain the standard statistical power, which from my quick online searching appears to be .8. Ultimately my goal is to attain statistical significance at the 5% level, assuming that my $B_1$ from my regression with a small sample will be around the same with a regression with a larger sample.I do not know how far my beta hat is from H0. For each unit of time, there are around 1000 observations. I theoretically have access to 10 years of data. If I use all 10 years of data, I would use a regression with fixed effects for each i, or unit of observation. – Zslice Feb 1 '15 at 4:15