Approach for estimating expected time required (Regression analysis) I am analyzing data from a factorial experiment with between subject factor Purifier (two types A and B) and within subject factor time (measured at level baseline, 1 hr, 24 hr, 48 hours). I have come to conclusion that both purifiers shows improvement in the assessment variable (water quality) over time. It is also observed that the amount of improvement observed with two the purifiers are significantly different. Now I want to estimate the Expected minimum time for which we should keep water in the purifier to bring it at acceptable quality (standard values are provided).  
I am confused how to deal with this issue. I think that regression will be good approach(?), but I am not sure if:  


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*time should be response or predictor variable.

*What type of regression should I use?

*Using a regression model, can I interpolate 'time' values (because in the data used to fit the model, I have only 4 levels / values of time)?

*Will treating time as ordinal be good option?

 A: The questions you should ask yourself are:


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*How do I want to phrase my research question in terms of the three parameters, purifier type, time and water quality?

*What knowledge about the system do I have that I want to use when building my modeling scheme?
It seems that you have two separate water purification behaviors, one for each purifier type.
So your model tries to characterize the purification power of each type of purifier over time, with possibly other covariates (you didn't specifically mention such covariates, but I assume there are more than just the ones you mentioned).
Therefore I would set up a regression where water quality is the response, and time is the predictor. Water quality is clearly related to the amount of time that had passed, so I would use time quantitavely and not as a nominal variable. The type of regression in time depends on the expected development over time of the response variable, for example, the particular quantity you measure as "water quality" might decay exponentially rather than grow linearly with time.
You may want to use other known physical traits of the system. For example, if you have experiments that start with different quality levels at t=0, you need to find a way to compare the results of these experiments. You may do so by using the initial quality as an additional predictor, or by normalizing so that these experiments can be compared on the same scale.
Finally, the purification-power parameter you extract from the regressions in time can be used as a response in a secondary model. This secondary model can be used to predict purification power in ”blocks” (i.e. combinations of factors) that were missing missing from your experimental design due to the ubiquitous problem of limited experimentation resources.
