Perhaps the data doesn't support your hypotheses assuming all else is correct. Best wishes, David Booth

Hello Shehryar,

Here's some possible explanations:

1. Your independent variables overlap or are redundant with each other, to a non-negligible degree (this is referred to as multicollinearity). One common outcome of collinear IVs is that estimated regression coefficients may vary in magnitude and sign from what you might otherwise expect (given the bivariate relationship of a specific IV with scores on the DV);

2. As Professor Booth indicates, perhaps the data simply don't conform to the hypothesized relationships;

3. You may have one or more IVs of low precision or technical quality. This would be the case, for example, if a specific IV did not yield reliable scores. It could certainly be the case if the purported attribute the IV was said to represent was not in actuality that which was measured by the IV.

4.Too small a sample to get stable estimates of the relationships among the variables.

Good luck with your work.

Shehryar Khan -

Because you said "...when I conduct regression analysis separately for these two variables (IV which showed positive R/s previously) the sign revert to negative," I think the strongest possibility is collinearity.

I'd say it's as if the regression coefficients for collinear variables work together, and one may be overestimated, and the other may correct for this.

You might use principle components, but that makes interpretation problematic, and a little collinearity is often not a problem.

If collinearity is large enough to change coefficient signs, however, then either it is very substantial, perhaps redundant enough to drop a variable, or else perhaps the t-values, considering sample size, may indicate that you can drop one or more variables as not contributing substantially to the predictions.

Cheers - Jim

It may be good to step back a little and think if this in terms of correlations and partial correlations. It seems that your initial assumptions about negative dependence corresponds to thoughts about ordinary correlation coefficients, whereas your results from multiple regression correspond to results about the partial correlations.

An alternative is to think in terms of (or to experiment with) the residuals from regressions .... If you were to leave out one of the IVs from you full model and look at the residuals from fitting the reduced model, you would find that those residuals would be related to the IV you left out, with either a positive or negative correlation that corresponds in sign to the regression coefficient in your full model.

To summarise, the regression coefficients in your full model summarise the dependence between your DV and an individual IV, but specifically the dependence that is not explained by the other IVs.