Is using correlation matrix to select predictors for regression correct? A few days ago, a psychologist-researcher of mine told me about his method to select variables to linear regression model. I guess it's not good, but I need to ask someone else to make sure. The method is: 

Look at correlation matrix between all variables (including Dependent
  Variable Y) and choose those predictors Xs, that correlate most with Y.  

He didn't mention any criterion. 
Q: Was he right? 
[I think that this selection method is wrong, because of many things, like it's the theory that says which predictors should be selected, or even  omitted variable bias (OVB).] 
 A: You could run a step-wise regression analysis and let the software choose the variables based on F values. You could also look at Adjusted R^2 value when you run the regression each time, to see if adding any new variable contributing to your model. Your model may have the problem of multicollinearity if you just go by correlation matrix and choose variables with strong correlation. Hope this helps!
A: Theres nothing wrong with this method, particularly if you know about multicollinearity. Avoiding multicollinearity is very easy.
Simply steer clear of adding independent variables that correlate with one another, since using only one of said variables is necessary. If x1 and x2 both correlate with y and correlate with each other, use reasonable judgement to assess which is higher in the causal chain, and omit the latter. A strong theoretical framework can help with such a selection process.
I.e. using a correlation matrix, or even better a scatterplot matrix, can work if you know what to look for.
