I am very confused in testing regressions and know that there are many explanations available online, but I am still not getting anything it in my mind. Suppose I have daily data for past 100 days, I run a simple linear regression estimate the parameters. Now there are three things:
1) If I just use the first 75 days of data and rerun the regression, I'll get slightly different parameters and then I can forecast the 76th day value of dependent variable through it and check the error comparing it with the original 76th day dependent variable value. Is this out of sample testing?
2) If the above is out of sample then what is in-sample testing? To be specific what would I use in regression and what to estimate?
3) If I use the original regression and estimate the 101th day dependent value then would it be a forecasting or another form of out of sample testing? Also for every next forecast, how would I know if I need to rerun the model adding more recent data or should I continue with the parameters derived from the first regression.