Be careful with using correlated variables as predictors. What you are asking is the effect of variation in one variable when you allow for variation in the other variable. The trouble can be that the variation in the two variables may be so "locked together" that when you allow for variation in one variable, the other hardly varies at all.

If you look at years in education and social class (negatively correlated) together in a model, you are asking what is the effect of a difference in social class for a given level of education. In other words, you are looking at a mismatch between the person's education and their current social status – social mobility. 

So you need a theory to guide the process of adding correlated variables into an analysis. The fact that they are correlated will reduce the precision of your model, but it will also material change the interpretation.

I agree with Ronan. In a multivariate analysis the correlation between some of the variables will decrease the accuracy of your model, no mater if they are positively or negatively correlated.

Let's make distinction between negative correlation and linear dependency.

Negative correlation is as good as positive correlation. For example, if you count mistakes in performance test it is negatively correlated with ability for doing that task. Your variable is just inverted in coding, more mistakes means less ability. Technically and substantially multivariate technics do not have any problem with negative correlation. In multiple regression such kind of inverted coding get negative b or betas, meaning that for reduction of result in predictor for one point (or one sigma for beta) will result by reduction increase of criteria for given b value. In factor analysis inverted variable has negative factor loading but saturation with factor is described by square of loading giving proportion of variance of variable determined (satured) by factor.

Linear dependency is extreme case of overlapping of two or more variables. Those variables are highly correlated and bring in analysis same information, thus they are redundant. Linear dependency is present even if two variables are negatively correlated (e.g. number of mistakes and number of correct answers in same test). In multivariate analysis this situation causes pure math problems, giving not enough information for solving mathematical problem. In this case we expect, for example in multiple regression that we got b-coefficients for k variables, but giving just information about k-1 variables and one that duplicate information given in one of k-1 variables. For illustration, I’ll give the case of 3 equations with 3 unknown elements (multiple regression is solving of multiple linear equations – see. Guilford Statistics published in end of fifties).

x+y+z=10

2x+2y+2z=20

2x+2y+z=18

Reasonable overlapping of predictors in multiple regression is not mathematical problem, but it complicates interpretation of shares of predictors (overlapping is divided proportionally between predictors giving larger shares to better predictors). So, neither b (beta) nor correlation is exact estimation of shares, but product of beta*r or b*c.

Dear Ronán, Rita and Ivan,

Thank you for your detailed answers and examples.

I really appreciate your helps.

Best regards.