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Topic: Extrapolation of a Point on a 3-D Surface
Replies: 0

 Kevin Ellis Posts: 62 Registered: 11/29/10
Extrapolation of a Point on a 3-D Surface
Posted: Apr 8, 2013 10:26 PM

Hello,

I have been trying to extrapolate electricity usage based on information received from a utility company. I have attempted to use smoothing functions and the built-in function "fit" in the statistics toolbox to fit a variety of curves. I have even been trying to make different ARIMA time series models.The "goodness of fit" is always an issue though and the extrapolated values never match (I use historical data to check the accuracy of the model). On a whim, I began to think that I might be able to create a surface and try to extrapolate that way. I have the following data:

Dates =
15-Oct-2009
12-Nov-2009
14-Dec-2009
15-Jan-2010
16-Feb-2010
17-Mar-2010
16-Apr-2010
17-May-2010
16-Jun-2010
15-Jul-2010
13-Aug-2010
15-Sep-2010
14-Oct-2010

EnergyUsage =
4640
4400
5920
5600
5280
4640
5280
5360
5680
7040
7440
7280

Cost =
530.91
504.46
667.1
649.12
573.45
536.91
616.13
624.98
661.13
814.26
828.19
811.05
596.44

Now, it is difficult to see, but the size (or length) of the Dates and Cost is 13 and the EnergyUsage is 12. So all I am trying to do is extrapolate/determine that 13th point for Energy Usage (10/14/2010 paid 596.44 for electricity). Thus, I was wondering if there was a way to extrapolate that single value for the energy usage using "fit" or "nlnfit" or something else with the surface?

I thought it may be easier because I am including another variable, Cost, which would help "ground" the model. Previously, I had been using the date and energy usage to fit the curve and extrapolate the 13th value which typically was off of the actual. By the way, the actual energy usage is 5280. If I can somehow fit a model to get me within a reasonable range (thinking +/- 5-7%) that would be great. I understand also if trying to fit or extrapolate a surface is unreasonable, but any help would be much appreciated.

Sorry for the long request.

Kevin