# Adjusted R square decrease with increase in Sample size in hierarchical regression analysis spss

I collect data in survey (use Likert scale 1-5), after that i did Factor analysis,Extraction Method: Maximum Likelihood, Rotation Method: Oblimin with Kaiser Normalization and did hierarchical regression analysis spss to create a model. Case-1 , Sample size N=176, KMO = 0.669, Adjusted R square = 41.8

Case-2, Sample size = 279, KMO= 0.674. Adjusted R square = 24

I dont know why $R^2$ value suddenly decrease from 0.41 to 0.24 , when sample increase from 176 to 279.

• Because your data was different? You have also added another variable which does not increase adjusted $R^2$ and usually reduces it. Commented Jun 1, 2018 at 13:36
• Hi mdewey we use the same questionnaire in 3 institute , case 1 : we did analysis on 1 institute , case 2: we did on the combine date from 3 institute
– Lam
Commented Jun 1, 2018 at 13:47

Because the data from the other two institutes does not fit the model as well as the data from the first institute. As to why that is the case, you should look at differences among the three institutes.

One other possibility that relates to factor analysis - if you did the factor analysis separately at each institute, check that the signs are equivalent.

One more point - doing FA prior to regression is not always the best way. You might want to look at partial least squares.