Hello Fizza Qureshi. Think about the distinction between partial and semi-partial (aka., part) correlations. What happens if you compute semi-partial correlations rather than partial correlations? My guess is the results will be consistent with what you're seeing in your regression results. HTH.

PS- To get semi-partial correlations with SPSS (which you listed as a topic), use the ZPP option on the STATISTICS sub-command of the REGRESSION command. ZPP is short for zero-order, partial & part correlations.

https://www.ibm.com/support/knowledgecenter/en/SSLVMB_26.0.0/statistics_reference_project_ddita/spss/base/syn_regression_statistics_independent_variables.html

It is most likely that one of the variables mentioned has a mediating role which, through partial correlation, is no longer significant

I think this problem due to correlation between IV(1) and IV(2) variables, indeed your problem is collinearity of the predictors.

Some of the responses make me think people are misunderstanding what Fizza described. Here is my translation of the original question. Fizza can correct me if I get anything wrong.

The multiple regression model looks like this:

Y = b0 + b1X1 + b2X2 + E

b1 > 0, b2 < 0, and both are statistically significant.

Additionally:

• The Pearson r for Y and X1 is positive (and significant, I gather)
• The Pearson r for Y and X2 is negative (and significant, I gather)
• The partial correlation between Y and X1 with X2 partialled out of both of them is not significant
• The partial correlation between Y and X2 with X1 partialled out of both of them remains significant

In my first response, I suggested that partial correlations should not be expected to show the same results as the multiple regression model, because the 3rd variable gets partialled out of both the other X and Y when you use partial correlation. If you want something that matches the regression model results, you need to look at the semi-partial (or part) correlations, where nothing is partialled out of Y. Specifically:

• The square of the semi-partial correlation between Y and X1 with X2 partialled out of X1 (but not out of Y) = the change in R2 when X1 is added to a model containing X2, or when X1 is removed from the full model with both X1 and X2.
• The square of the semi-partial correlation between Y and X2 with X1 partialled out of X2 (but not out of Y) = the change in R2 when X2 is added to a model containing X1, or when X2 is removed from the full model with both X1 and X2.

Here's an example you can study if you happen to have access to Stata.

sysuse auto, clear

* Fit a model with Y = mpg, X1 = headroom, X2 = gear_ratio

regress mpg headroom gear_ratio

* Enter X1 first, then X2, and examine change in Rsq

nestreg: regress mpg (headroom) (gear_ratio)

* Enter X2 first, then X1, and examine change in Rsq

nestreg: regress mpg (gear_ratio) (headroom)

* Now look at the squares of the partial and semi-partial correlations

pcorr mpg headroom gear_ratio

HTH.

Bruce Weaver yes that’s exactly the situation. Thank you so much for the explanation, it’s very clear and thorough!

would you recommend reporting the partial correlations as well if you’re interested in the effect of b2 on the relationship between b1 and Y ?