I have eight independent variables and one dependent. I have run a correlation matrix, and 5 of them have a low correlation with the DV. I have then run a stepwise multiple regression to see whether any/all of the IVs can predict the DV. The regression showed that only two IVs can predict the DV (can only account for about 20% of the variance though), and SPSS removed the rest from the model. My supervisor reckons that I have not run the regression correctly, as due to the strength of the correlations, I should have found more predictors in the regression model. But the correlations were tiny, so my question is: if IVs and the DV hardly correlate, can IVs still be good predictors of the DV?
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With a correlation matrix, you are examining unconditional (crude) associations between your variables. With a regression model, you are examining the joint associations of your IVs with your DVs, thus looking at conditional associations (for each IV, its association with the DV conditional on the other IVs). Depending on the structure of your data, these two can yield very different, even contrary results.
Your question would be easier to answer if we could see quantitative detail from your software output and ideally have a sight of the data too.
What is "low correlation", in particular? What significance level are you using? Are there built-in relationships between predictors that result in SPSS dropping some?
Note that we have no scope for judging whether you used the best or most appropriate syntax for your purpose, as you don't state exactly what you did.
In broad terms, low correlations between predictors and outcomes imply that regression may be disappointing in much the same way that you need chocolate to make chocolate cake. Give us more detail, and you should get a better answer.
Also in broad terms, the disappointment of your supervisor doesn't imply that you did the wrong thing. If your supervisor knows less statistics than you do, you need to seek advice and support from other people in your institution.
Coincidentally I was just looking at an example that I had created earlier to show similar concepts (actually to show one of the problems with stepwise regression). Here is R code to create and analyze a simulated dataset:
The correlations and simple linear regressions show low (not statistically significant) relationships between $y$ and each of the $x$ variables. But $y$ was defined as a function of both $x$s, and the multiple regression shows both as significant predictors.