I have several small datasets of few (9 to 12) observations each, and I do have to treat these datasets separately. For each dataset, I want to test for the relative contribution of two continuous predictors on my response variable. More precisely, I am more interest in one predictor (lets call it $X1$), but I have have to take the effect of the second predictor ($X2$) into consideration to "retrieve" it from the relationship between $Y$ and $X1$.
$Y = intercept + aX1 + bX2 + e$ ($X1$ and $X2$ both continuous and non-collinear)
I know that testing the effect of two predictors with as few as 9 to 12 observations is tricky! Thus, I am using the R function
'summ' (after a classical
lm())from the package
jtools to get the mean + confidence intervals of each estimate (a and b) after standardization (R function
'standardize'); and get a general idea of the effect size of each predictor for each of my small datasets eventhough I get something non-significant (which is, expectedly, often the case).
Here are my questions:
Is that OK to do multiple linear regression to get the estimation (+CIs) of $a$ (the slope of $X1$), and only use this estimation in further analyses? In other terms: can I then consider I am actually reporting the proper, remaining effect of X1 on Y after accounting for the effect of $X2$?
Should I run a separate model first (i.e., $Y = bX2 + e$), get the residuals, and then (and only then) fit a model with residuals($Y.X2) = aX1 + e$ ? Is there any difference (I would intuitively say there is not!) between this and what I was describing formerly?
Thank you all for your answers! Still learning about secrets of statistics but hoping to get better at it very soon :-)