# Multiple Regression Model determination suggestions? (Time-series** or Cross-section)

What I have to model is the trend that occurs after a transient event (water pump failure, water pump repair etc.) where pump flow goes to 0 in order to forecast the pump flow after a planned event in the future. The most important things to capture are the area under the curve (Total water filtered) and then the peak water filtration.

One way for me to describe the trend after these transient events is that the rate starts from 0, increases sharply to about the pre-transient event rate value, then continues to ramp up to a peak (since more water has built up around the pump since it was not pumping for some time) then trends back down and stabilizes at the pre-transient event rate. To describe this in numbers : Pre-transient event - Rate = 60 1:00 - Rate = 0 2:00 - Rate = 20 3:00 - Rate = 40 4:00 - Rate = 60 5:00 - Rate = 75 6:00 - Rate = 85 7:00 - Rate = 92.5 8:00 - Rate = 97.5 9:00 - Rate =~ 92.5 10:00- Rate =~ 87 11:00 - Rate =~ 85 ... 20:00 - Rate =~ 60 (Pre-transient rate) 21:00 - Rate =~ 60 ...

Data I have: ~20 Filters ~3-4 individual filter events (repair, replacement etc) basically this mentioned trend 3-4 times. ~hourly data for the life of the water filter

1 Dependant variable ( Water Pump Rate )

7-10 Independant variables ( pump rate before transient event, number of hours it takes to replace filter, temperatures, pressures, etc.)

1 common event that leads to a similar trend - Can be a filter replacement - Filter repair - Filter

All data is captured on a hourly basis of which the trend usually takes 15-20 hours to ramp up and return to it's pre-trasient position.

I want advice on my approach listed below please. I am trying to best model the trend in order to predict the total water that is pumped during this post-transient event period, and also the length of time that this pump-flow period lasts (can be deduced if I can get the trend properly) for forecasting future events.

My approach: 1) Since the pump rate data is noisy, smooth pre or post regression model creation with Sovitzky-Golay (retains peak and total pump volume). 2) Put all data into Matlab 3) Determine multiple linear regression equation with all variable combinations. 4) Use 5 comparisons to determine best model (SSE, adjusted R^2, Akaikes Information Criterion, Correlated AIC, Schwarz Bayesian info criterion) 5) Attempt to optimize by adding polynomials of these variables (^2,^3 maximum), or logs of variables. 6) Since independent variables (such as the temperatures/pressures) follow linear or otherwise predictable trends after a transient period, determine equations to fit these variables based on their values before the event and the length of time to repair. 7) Use these values in the model for forecasting the water pump rates going forward 100 hours into the future (4-5 days)

I have just began to learn more about time-series and where this is a recurring event after each transient and often based on the pump rate before the transient and the length of time of the transient, I may be able to model it that way as well. I think that would be less reliable but could provide type-curves for this event.

SORRY IN ADVANCE FOR LENGTH OF THIS POST. If anyone would better understand it with help of a spreadsheet of sample data, please don't hesitate to ask. @irishstat

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Welcome to the site. I deleted your signature as the site adds it automatically. –  Peter Flom Oct 10 '12 at 15:23
I would suggest editing your title. I think this is much more a time series problem than a multiple regression one. I am not a time series expert, but we do have some on the site (e.g. @IrishStat) –  Peter Flom Oct 10 '12 at 15:24
possible duplicate of Multiple regression method –  Peter Flom Oct 10 '12 at 15:35
Thanks for your comments. I have edited the title and removed my old post that did not ask the proper question. –  Pat Keough Oct 10 '12 at 15:52
I don't see a way to message individuals on the site. Can @Irishstat let me know if this can be modeled with time-series analysis? moreso than multiple regression? –  Pat Keough Oct 11 '12 at 18:09