I have a set of numeric predictor variables $X_1, X_2, X_3, X_4,$ and $X_5$ that are all correlated with each other to varying degrees (from 0.2 to 0.6). My response variable Y is also correlated with the predictor variables. My aim is to see what is the effect of each predictor variable on response $Y$.

I know that partial correlation gives the correlation between two variables when another variable is held constant. For example, I can calculate the correlation between $X_1$ and $Y$ keeping $X_2$ constant. Does partial correlation also work with all variables included? Such as, can I find the partial correlation between $X_1$ and $Y$, keeping $X_2, X_3, X_4,$ and $X_5$ constant? Is there any other way to derive the effect of each predictor?

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    $\begingroup$ The multiple-regression tag you applied to your post answers your question. $\endgroup$ – whuber Feb 4 '19 at 14:19
  • $\begingroup$ I think the correlation among the predictor variables in multiple regression makes it hard to distinguish the effects of each predictor variable on the response. My question is how I can distinguish the effect of each predictor on Y as though there were no correlation among the predictors. If I use all the predictors in multiple regression ignoring the correlations, would the Beta values be biased? $\endgroup$ – teknoinsan Feb 4 '19 at 14:26
  • $\begingroup$ You cannot "distinguish the effect," because the variables are intertwined. Your hypothetical "as though there were" posits a situation that simply does not exist and therefore cannot be answered. $\endgroup$ – whuber Feb 4 '19 at 14:40
  • $\begingroup$ As I understand from other posts, multicollinarity is not an issue if the concern is the total prediction power of the model. Multicollinearity is a concern when the aim is to infer the significance of each predictor. My aim is to see what variables are significant on Y and what are their coefficients. That`s how I can calculate how much Y changes given one unit increase in one of the predictors. Now because my variables are correlated, is there a way to get unbiased (or less biased) coefficients for each predictor? $\endgroup$ – teknoinsan Feb 4 '19 at 15:19
  • $\begingroup$ Regardless of how the independent variables might be correlated, the coefficients will be unbiased when you use Ordinary Least Squares, which thoroughly addresses all your objectives. $\endgroup$ – whuber Feb 4 '19 at 16:51

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