Multivariate regression on 11 patients

Sorry for mistake, i have two groups: treated and not, the treated group consist in children intollerant to lactos and the control are not intollerant. So i would like to investigate if into the treat group the gravity of intollerance, bmi,age and sex influence the speed of growth but i have only 11 patients.
It is called multiple regressionn. It does seem not make sense to perform multiple regression
with 4 predictors and only n=11 observations.
Generally speaking, what do you expect from complex statistical analyes based on n=11
subjects only?

With kind regards

in fact I didn't think it made sense but I wasn't sure. however, do you think there would be another type of analysis to be performed on only 11 patients to understand if the severity of the disease can have an effect on the speed of growth?
Can lactos e intolerance be considered a medelian randomization (instrumental variable)? However with 11 covariates things may still not be balanced. Why cant you have more subjects??
You probably don't have enough data to power a simple linear regression and meet its assumptions, and definitely not enough to control for patient characteristics in the model. A general rule which may not always hold, is you need 10 or more outcome observations for each predictor. To put it in perspective, you may have one male baby with a high BMI and certain age in the treatment group. What conclusions can you make off a single baby, none with confidence. Also, child measurements are typically not evenly collected, so if you want to say growth at 1 year, etc. do all kids really show up at exactly 1 year, if not you would need to also control for discrepancies between time intervals between growth measurement.
You can run linear regression with a best model approach with 1 or 2 predictors or if you first want to see if there is a treatment effect, a simple ANOVA might work. You can try
a PLS regression
if there is a multivariate structure in your data it will extract it (PLS regression is available in several R packages, SAS, XLSTAT ...). But collecting more data would definitely help.