Well if say gender is such a variable it means that there's a.difference by gender. Why are you doing hierarchical regression anyway? Best wishes David Booth

1. So, it means that, irrespective of the model, if the control variable comes out significant, it means they have some effect on the dependent variable along with other significant variables in the model. Right? How do I connect the control variable with the other significant independent variables in the model (lets say, in model 2 and 3).

2. Also, in the results, I need to mention this point and justify the difference by citing proper references. Am I right? Now, in order to find which of the two, male or female has more significant effect on the dependent variable, is it okay if I do independent t-test?

3. I’m doing heirarchical regression analysis because I want to study the interrelationships theoretically.

1. Not quite. The test of an effect of an individual predictor in a regression model is the test of its unique effect and ignores any variance in the outcome (Y) that is explained by the shared contribution with other predictors. If a variable like gender is significant in model 2 but not 1 then there are two (not mutually exclusive) ways this could happen:

a. Adding predictors that explain Y decreases the error term and makes tests of the effects of gender more precise/sensitive. If this happens the unstandardized slope for gender should be fairly similar across models.

b. gender is correlated with other predictors. if this happens the slope for gender could be very different (indeed in some cases it change direction - something known as suppression). collinearity diagnostics can be useful here.

I don't really know know what you mean by "How do I connect the control variable with the other significant independent variables in the model". The effects in the model are independent/additive. So you can interpret them separately unless you have interaction effects. However, you do need to consider the collinearity between predictors. (The unique effects are independent but the predictors themselves are correlated in your data set. That might be hard to interpret. If gender is highly correlated with X then it will be statistically difficult to estimate their unique effects - certainly without huge samples).

2. If its a control variable I'm not sure you need to justify it that much, but it makes sense to report whether the effect is consistent with what is known in the literature. You don't need to do a t test to see the direction. This is given by the sign of the gender coefficient. If positive the group coded 1 (assuming dummy coding) has bigger Y than the group coded 0. If this isn't flagged by your software - create a new variable such as "female" coded 1 if female and zero if male and replace gender with female. A positive slope means the female Y > male Y. The value of the unstandardized b coefficient/slope gives the difference in Y between genders.

3. I'm assuming this is just entering groups of predictors in blocks (e.g., demographics -> theoretical predictors etc.) as is common in some social science fields. David Eugene Booth may be concerned that you are doing stepwise regression (which is not a good idea).

Thom Baguley so it means, I should just ignore that (let's say gender came out significant) in Models 2 and 3. I am studying the interaction effects in Model 3. So, I should just ignore that gender came out significant in Model 3 and just focus on that interaction effect of independent and moderator variables was significant in Model 3. Right?

Usually you include such control variables in a non-experimental study because of potential confounding. So you are probably trying to address whether after accounting for them your theoretical variables have additional impact. So to that extend the main focus is on the theoretical variables. I wouldn't ignore them but I'd generally just report them with minimal interpretation - maybe just noting that the finding is consistent or inconsistent with other research.