To Expand: Econometrics includes Multivariate Analysis as a tool (a mathematical one). At the same time it may include many other things, such as economic "fundamental" models.
Econometrics is also a certain spin on (applied) statistics, just as biostatistics (one could say biometrics) or statistics in medicine, information theory or whatever field you can imagine. The unique problems faced in any field shape the tools needed for statistical analysis.
For example Econometrics is a very frequentist, non Bayesian field (at least how it is taught) - or at least one that doesn't teach two distinct approaches. The reason for that is that the data for most problems* lends itself to classic, frequentist analysis (lots of data points available, targets are constant mechanics). It is also a pretty standard approach in econometrics to learn OLS and then the General Method of Moments.
Panel Data models (Fixed/Random Effect) are, until needed, more of a fringe thing that comes up as a sidenote in most classes.
The data is generally considered continous. Logit, Probit and models which target nominal or ordinal variables are also not at the heart of what you learn in most Econometrics courses. Of course they are taught eventually and are important for economic fields which stray more into experiments or social areas but usually dependent variables are in money units.
Many medical people will learn things like ANOVA very througoutly. Econometricians consider this to be a spin on linear regression and maybe never learn it as a distinct thing.
Before those things come up, students will study time series analysis very througoutly, with Hamilton (1994) being the premier book in that area.
Even if you study econometrics to a graduate level, many methods on this site will seem foreign to you at first. It is a applied take on statistics that goes deep where it needs to and omits things that are not important in the field of economics.
In your case I would say that learning Econometrics is the right thing to do. It includes the stuff you need to analyze problems such as the one you posted.
My recommendation would include three books on three different levels.
The first one is Introduction to Econometrics by Stock and Watson. It is written for economics undergrads without further interest in statistics - just the basic stuff without going deep in the math. On the other hand it brings you - method wise - up to topics like cointegrated analysis.
Next up are Econometrics by either Hayashi or Green. These are the standard econometric graduate textbooks. If things are not proven or analyzed completely, they at least refer to the mathematical texts that do. Those give you a pretty good understanding of the usual econometric problem.
Last up is Time Series Analysis by Hamilton. It pretty much includes everything you could know at the point when it was published (1994), though it is more on a late graduate or phd level at least for (non quant-) economists.
*One could very well argue about this though