Are there situations where univariate analysis should be carried out in addition to multi variate analysis? After reading this answer https://stats.stackexchange.com/a/239583/353716 and the article cited, I wonder if there are any situations where one would want to carry out an analysis where we try to explain a variable $y$ with only one independent variable $x_1$ ($y = \alpha x_1 + c$ ) if they have the possibility* to carry out a multivariable analysis $y = \alpha x_1 + \beta x_2 + ... + c$. I know everything isn't linear but for the sake of simplicity, let's only consider linear regressions for this question.
* by possibility I mean, because in the data available, we have $y, x_1, x_2, ...$ for all patients.
For example predicting the number of infections of a patient. Or the value of the concentration of a certain molecule in the patient's bloodstream. And the independent variables could be age, how long they exercise a day, etc ... And the question my analysis could try to answer is: does sex have an impact on the molecule's concentration (looking at the p_value of the coefficient could be useful)? If yes, what's the impact (looking at the value of the slope $\alpha$ could be useful)?
If not, why are articles still full of boxplots and stuff, which are univariate (can I say univariate here?) in essence?
Scientific papers studying this or intuitions are welcome!
 A: *

*If you want to predict, there may be situations where for future observations you won't have all predictors that are in your current data set, and there may even be only one of them, in which case you'd need a univariate model. Observing certain variables may also be costly, so there may be good reason to not observe them even if in principle you could. (You may also be interested in a potential one-variable situation for interpretative reasons, even if when predicting in the future you won't be in that situation.)


*You may be in an essentially univariate situation in which either only one variable is really informative, or where all variables are so strongly correlated that every single variable is good enough to predict. (Variable selection may lead to a univariate model.)


*If you have very many variables, you could use forward selection, which starts from fitting every model with one of the variables, then takes the best and goes on adding variables - but univariate models are used in the first step. (This will often not be the best method for variable selection, but very occasionally it can be.)


*"Why are articles still full of boxplots and stuff?" Because the distributions of the individual variables are often interesting in their own right, to check model assumptions, diagnose outliers, make statements like 99% percent of babies weigh more than 2 kilo etc. Note by the way that, as opposed to boxplots, univariate regression actually looks at two variables, x and y. Papers and screen show 2-d information, so 2-d displays such as residuals vs. fitted are essential for diagnosing model assumptions and all kinds of exploratory data analysis also for higher dimensional data.
That said, item 1-3 refer to particular situations, and if you have several predictors, it is indeed not normally recommended to fit univariate regressions. (At least not if you intend to take them seriously... just out of curiosity, why not?)
