this is my first post in this forum, so if I'm doing any kind of mistake please let me know.

My situation is as follows: I'm currently writing my Thesis and I'm looking into the discrepancies of ETF NAV and their underlying assets (-> NAV premium/discount). I compare the ESG ETF premium/discount to the market premium/discount (used SPX ETF for that).

I've run now for each ESG ETF a regression against the average market premium and now wondering how to interpret the outcome. My dependent variable is ESG ETF premium and my independent variable are market premium (referenced as SPX premium in regression output) and fund flow in millions.

I would read it as the following: Y = ESG premium = 0,11397803 + 0,57905014 * market premium + 0,00239136 * fund flow

The intercept (my alpha) means that people pay more for ESG ETFs than for market(SPX) ETFs because it is positive. But what does the beta say? I've learned that beta in a regression is the slope, aka what happens when increasing 1 unit in market (SPX) premium to dependent variable (ESG premium).

Your help is very much appreciated!

There are many ways of interpreting your results and - ultimately - it depends on what you're trying to accomplish with your analysis. I won't comment on the merit (or lack thereof) of your analysis; just the statistics.

First of all, I would note that your R-Squared here is only ~1%; that is to say, in the case you have set up, only 1% of the variance in your ESG prediction can be explained by your SPX and fund flow model. In this case, the fund flow term is not even statistically significant at the confidence interval you've chose and should probably be discarded....even more so if it's correlated with your SPX input. But I would say the overall model you've built here is likely not very useful.

It's essential when building these sorts of analyses that you have covered some basics. For example, you must understand what's going on in that ANOVA table; this is simply saying that it is unlikely that the variance of your variables is unlikely to have occurred by chance alone (at least with how you've designed this study -- and, again, no comment on the merits...). But whether that data is useful to your analysis depends on your goals...and I fear that if you don't know what R-Squared is, you probably shouldn't be trying to build multiple linear regression models.

Revisit some basic statistics. Learn about the assumptions of linear regression. Learn about R-Squared. Learn what Analysis of Variance is. Learn about multicollinearity. In 2-3 hours of research on YouTube on these topics you will easily be able to fully interpret this output and design better studies.

Also, at that point, you will learn that analysing the residuals of your model is probably the most important step once you have correctly set up the study. Without knowing how to analyse the residuals / errors of your model, you won't know how and where your model is making false predictions.