# Interpretation hierarchical regression

I'm running hierarchical regression to determine whether or not a number of independent variables are able to explain a dependent variable. I have following models:

• Model 1: only controlvariables
• Model 2: Model 1 + independent variables
• Model 3: Model 2 + interaction term

When interpreting the significance of the different terms, should I only consider the last model or should I consider the model where I entered the terms. For instance, to investigate which controlvariables are significantly significant to the dependent variable, should I look at Model 1, and then, for the independent variables, consider Model 2? Or should I just look at the last model for the significance of the different terms?

Interpretation of hierarchical regression

1. Model Summary Box:

Read 3rd column named 'R square' for all your models and interpret like this. Check the R Square in the Model Summary box. Variables entered in Block 1 (control variable) explained X (depends on your output) % of the variance in DV.

After Block 2 variables (IDV's) has been included , the model as a whole explained Y (depends on your output) % of variance in DV.

Adding Block 3 variable (interaction term), the model as a whole explained Z (depends on your output) % of variance in DV.

1. Now look at change statistics

The column labelled R Square Change shows how much change in R square (explained variation) as compare to previous model. For example, for model 1, it is same as X, for model 2, it is same as (Y - X) and so on.

To infer if this change is statistically significant or not, you need to look at the last column (Sig. F Change)

1. The ANOVA table:

It indicates that the models as a whole are significant or not.

Hope it helps!

• Thank you very much for your kind and comprehensible reply. However, if I want to determine the significance of individual variables, should I consider the last model or the model where I entered the considered variable? I would expect that I have to consider the last model, as for in this model I control for all variables (control, independent and interaction). However I'm not quite sure if this is correct? – Bensa Jun 22 '16 at 8:50
• You need to consider the last model (If it is statistically significant_as supported by ANOVA table) and if the R square change is also statistically significant for the same. – Dr Nisha Arora Jun 22 '16 at 8:54
• Hope you understand unstandardized (B) and standardized coefficients (Beta). – Dr Nisha Arora Jun 22 '16 at 8:57
• Would you mind accepting/up voting my answer, if you find it worthy. – Dr Nisha Arora Jun 22 '16 at 8:59
• Of course I don't mind upvoting your answer! You helped me a lot. There is a lot of confusion about the subject. I found both papers considering the significance of terms only in the model that these terms entered the equation and papers only considering the last model. It was really confusion to determine which approach is more appropriate. Thank you for your response! – Bensa Jun 22 '16 at 9:16