Thank you txnelson, for your kind input!
I circle back to my data and checked the 5-decimal R-square from manual run and that from the script run: NO, they are different even using the 5-decimal!
I am so (and even more) bewildered now, because:
1. I have multiple data sets (>20), some of them show same R-square from both the manual run and script run (which can verify that the script work well); but some of them show different R-square values from manual run and script run (the difference can be 0.967 versus 0.964); my understanding is if the script is a ROBUST script, isn't it supposed to work well for any data sets? why would there be bias (some data sets work fine for the script while other not)? Something is not right......
2. An example: manual run results (SSE: 0.16159206664151, SST: 4.4432420157201, R-square: 0.96363194575722); script run results (SSE: 0.16159206664151, SST: 4.4432420157201, R-square: 0.96660472225036). Please note that the SST and SSE are respectively identical in the manual run and script run, and because R-square=1-SSE/SST, so the R-square then is suppose to be identical, why on earth are they different? I computerized and confirmed the manual run has the correct R-square (~0.964), so does that mean the script has an issue? Should I check to see if my script is wrong?
I am so so puzzled now......
Your input is very welcome!