Regression (Beta weights and correlation) I have used regression to explain a dependent variable with a number of independent variables.
I expected independent variables which have higher correlations with the dependent variable to have higher beta weights in the regression model but this is not the case for some variables. That is, there are some independent variables with very small correlations with the dependent variable but with large and statistically significant betas. And some independent variables with greater correlations with the dependent variable but smaller betas.
Can someone explain why this has happened? Thanks
Anthony 
 A: One possibility is that your independent variables have different scales. This would affect weights in the regression model, but not correlations with the dependent variable. For example, if you were to multiply one of the independent variables by two, its weight in the model would be halved. But, its correlation with the dependent variable would remain the same because correlation is scale invariant.
Another possibility is multicollinearity, which means some of the independent varaibles are correlated with each other. In this case, the weights of the correlated variables can behave unexpectedly. But, correlations with the dependent variable won't change. For example, imagine an extreme case where two of the independent variables are perfect duplicates of each other. In this case, there's no unique choice of weights that best predicts the dependent variable. One of the duplicate variables might have its weight set to 0, while the other receives all the weight. But, there are infinitely many ways to weight the two duplicate variables that will produce the same output.
