Question

Is regression possible with less than 30 observation?

Answer 1

When sample size is less than 30 so we call it small sample, but when our sample size is 38 (observation) we also call it small sample size.

Let me expand on the time series issue.

Time series analysis may require as many as over 100 observations or as few as 4, depending on what it is that you are attempting to model. ARIMA models generally require many observations to correctly capture seasonal components and trend. However this is for forecasting purposes. If you are using regression models (which are much more flexible than ARIMA models and avoid the many specification issues that plague the ARIMA approach), then fewer observations are needed (however many is always preferred over fewer). Additionally, if you are using these models for causal inference, then even as few as 4 observations in each pre-post period may be sufficient.

I am attaching two papers that I have written on time series analysis. The first is for forecasting, and the second is when it is used for causal inference.

I hope this helps