Hi durantz, interesting question.

Is this your null hypothesis? How would you judge whether the change in R-Squared is significant or not? Drop of 2%, 5%? (Never seen hypothesis defined in terms of R-2).Now my hypothesis is that each IV will contribute significantly to the change in R-squared.

The negative correlation makes sense, as if there are more protective factors (support from friends and family etc..)around the patient, the less likely they are to commit a suicide.

I think it would be wrong to exclude this as this is an important variable that you need to take into account.

As you've just 3 IV, I think you can use all of these 3 variables to perform a multiple regression and assess their significance in the presence of other variables in the model.

In any case, if you have more IV in the model, it should help in predicting better.