# More cases yield to a lower R-Squared in regression analysis. Is this due to variance?

I've fit a multiple linear regression model on a dataset with approximately 3000 cases. However, due to missing data, the original model only estimated on roughly 1200 cases.
Using data imputation, I managed to estimate the model on all (3000) cases, but doing so, the $R^2$ deteriorates.
Is this caused by the increased variance, which is added to the dataset by imputing the data?

• Details matter. The $R^2$ could have greatly increased, too. Diagnosing this situation requires analyzing the missingness patterns and their relationships to the response variable. The utility of tracking $R^2$ in comparing the results is dubious. – whuber Oct 6 '17 at 19:09
• @whuber Thank you! Okay, but variance could be one of the reasons causing the deterioration in R-squared? If not, which other factors could lead to a deterioration in R-squared? – David Oct 6 '17 at 20:06
• Literally anything could cause a change: your new model need not bear any discernible relationship to the old model, because you have introduced 1800 cases that could be totally different than the original 1200 in terms of how the response is related to the independent variables. All univariate statistics will change: the variances and means of all variables, independent and dependent, will differ. – whuber Oct 6 '17 at 20:45