I am performing an analysis in which the unit of analysis is a geographical area (more precisely, an LSOA). This is a case when the sample analysed can represent the entire population (all 32000+ LSOAs in England). How do we interpret, in this case, the point and interval estimates of a, say, regression analysis?
The point estimate is the predicted point when your predictor variables are at 0, but the interval estimates don't mean anything if your entire population of interest is your sample.
I wrote about this in an earlier answer: Why do irrelevant regressors become statistically significant in large samples?
Basically, inferential statistics are there to help you generalize from a sample to the population. If your sample is your population, then any relationship you observe is the "real" one.
In other words, the confidence intervals are there to tell you what the point estimate might be if you were interested in some larger population, and you were to randomly sample from that population again.
You would probably be more interested in effect size measures that quantify how well your model predicts your DV (in this case, $R^2$). For example, you might have an $R^2$ of 1, which means your model perfectly predicts your DV, or .01, which means it explains 1% of the variance. Whether or not that is important to you is a human judgment call.