Due to limited data amount (100 observations) this model is built by full dataset with 2 independent variables. Once the functional form is determined, the data is split into training and test datasets, and refit the model on the training set and test the model on the test set. Can this approach avoid overfitting?
update: Let me put it in another way. The modelers built the model based on 10 years data. Once the model is done. The modelers split the data into training (first 8 years) and test (last 2 years) datasets. They refit the model on the training set, and test on the test set. Once they saw no big differences, they concluded that there is no overfitting. Is there any logical flaw?
Thanks for any suggestion.
Sorry for any confusion. Let me put it in a more specific way.
The target variable is a company size with 10 years monthly data. They have ten independent variables, like DOW, GDP growth, PMI, and so on. Due to limited data amount, the goal is to build a linear regression with 2 or 3 variables. They used the full dataset to get the final model with 2 variables. These 2 variables were selected based on business sense. Basically, they tried different combinations to get the best performance on the full data set. And they were just 2 linear terms, no transformation. Then they refit and model on the training set (first 8 years data) by using the selected 2 variables, and used the refitted model to test on the testing dataset (last 2 years data). They concluded there is no overfit. Without considering the metrics they used, does this process make sense to get the conclusion?