From: thomas.e.elam@gmail.com   
      
   On 11/26/2025 1:34 PM, Alan wrote:   
   > On 2025-11-26 08:53, Tom Elam wrote:   
   >> On 11/25/2025 9:12 PM, Alan wrote:   
   >>> On 2025-11-25 17:45, Tom Elam wrote:   
   >>>> On 11/25/2025 3:09 PM, -hh wrote:   
   >>>>> On 11/25/25 14:52, Tom Elam wrote:   
   >>>>>> On 11/17/2025 1:44 PM, -hh wrote:   
   >>>>>>> Yeah, so?  Recall that I eyeballed it & noted the nonlinearity   
   >>>>>>> from the very start without even needing to do any math...because   
   >>>>>>> I understood the basic data apparently much better than you did   
   >>>>>>> (and still do).   
   >>>>>>   
   >>>>>> You have not responded for several days. I'm thinking that calling   
   >>>>>> a simple scatter plot a statistical "work product" has to be   
   >>>>>> embarrassing.   
   >>>>>   
   >>>>> Nope.   
   >>>>>   
   >>>>> You've claimed to have offered just one hour's worth of consulting   
   >>>>> time in total.  What you would get for that is a summary overview   
   >>>>> of what you've missed, as validated by your 'full' spreadsheet.   
   >>>>>   
   >>>>> Of course you'll not like that answer because you want all of the   
   >>>>> work to be also done for that one hour, which is unrealistic &   
   >>>>> disingenuous: the sign of a bad customer who's determined to never   
   >>>>> be satisfied. Thus, you're not worth my time.   
   >>>>>   
   >>>>>   
   >>>>>  > [snipped, without reading]   
   >>>>>   
   >>>>>   
   >>>>> -hh   
   >>>>   
   >>>> OK, I'll take you up on the one hour. $150 for finding out what I   
   >>>> missed. I'm always willing to learn.   
   >>>>   
   >>>> Of course, the advice must be useful as measured by a material model   
   >>>> improvement, not duplicate what I have already done, and not call   
   >>>> for additional data that is not available or does not even exist. If   
   >>>> your advice calls for a statistical model beyond Excel's capability   
   >>>> I can rent something else.   
   >>>>   
   >>>> All I need from you if the work is useful is sufficient info for a   
   >>>> PayPal, Venmo or Zelle transfer.   
   >>>   
   >>> So you'll get to decide afterward if the "work is useful"...   
   >>>   
   >>> ...and then you'll pay?   
   >>>   
   >>> LOL!   
   >>   
   >> Why would I pay up front to a person who has confused a 2 dimension   
   >> data plot with a statistical model?   
   >   
   > Where did he do that exactly?   
   >   
   > Sounds like another one of your lies.   
      
   Hugh called a scatter plot of outside temperature (source: NOAA, daily   
   adjusted for meter read dates, Indianapolis International Airport,   
   2010-2025, see link below) and my total electric (heat pump HVAC) home's   
   kWh billing/day (monthly IPL/AES bills, 2010-2025) a model.   
   Specifically, he called it a univariate model with excessive variance   
   and from other variables not controlled for therefore not meaningful. He   
   also claimed that I did nothing else to try and explain the variance   
   other than the univariate plot that is not even a model in any real sense.   
      
   Quote Hugh:   
      
   "With your present data, I wouldn't bother:  it has too much noise from   
   ~second order variables that you've failed to control for.  One doesn't   
   bother with the likes of a Student t until the data's clean enough to be   
   useful. So the first real step would be to build a better model on the   
   legacy data to replace your trash."   
      
   Note he calls this plot a model.   
      
   Hugh claims above and in the quote that follows I did not start a   
   meaningful model right away. I did, in 2015.   
      
   Quote Hugh:   
      
   "Translation:  a decade in which you were lazy and didn't bother to   
   track down the sources of response variance\.  Instead, you've massaged   
   it to cover up that unresolved noise so that your trend fit looks better."   
      
      
   A model has a null hypothesis that can tested via statistical analysis.   
   If the null hypothesis is kWh is not a statistically significant   
   function of outside temperature the graph alone says reject the null   
   hypothesis. However, you still need to run a regression to test that.   
      
   Why regression, not just ANOVA? Outside temperature should cause kWh to   
   change over time, but kWh consumed by a home cannot change outside   
   temperature at the airport. So there is a one-way causal relationship   
   and regression is a valid tool.   
      
   The 2015 scatter plot was only done to confirm a non-linear relationship   
   of these two variables. Then I ran some trial regressions to confirm the   
   appropriate functional form for a good fit between them, five to be   
   exact. Power, exponential, linear (obviously not a good fit),   
   logarithmic, and polynomial transforms of temperature were all tried.   
   The only one that modeled the data was K = a + b(T) + c(T^2), a   
   quadratic polynomial. That fit has an R^2 of 0.87 (87%) and all three   
   coefficients are have t stats that are significant at the 99+% level.   
   Pretty good for a simple univariate model. But we can do much better   
   with additional variables.   
      
   The day I saw this plot I also had in hand some other variables. In 2015   
   those variables increased R^2 to about 95%. I have been improving the   
   model since. Example: a major increase in independent variable t scores   
   was seen after using ln (natural log) of kWh to reduce   
   heteroscedasticity. This happens when independent variables cause   
   percentage, not linear, changes in the dependent variable   
   (https://en.wikipedia.org/wiki/Homoscedasticity_and_heteroscedasticity).   
   There are other methods, but for my purposes the ln transform suffices.   
      
   I have also found that when the ln transform was made temperature fit   
   was slightly better when I substituted temperature^3 for just   
   temperature in the polynomial.   
      
   Why this result, a polynomial for temperature? The plot tells you that   
   kWh/day increases on both sides of a thermally neutral average   
   temperature of about 68 F. Either side of that and the heat pump runs to   
   either move heat energy into (winter) or out of (summer) the home. At   
   the minimum kWh/day you see use by everything else in the home - lights,   
   clothes dryer, water heater, appliances, etc. These together use about   
   30 kWh a day. Winter total use goes as high as 150-180 kWh/day in   
   January-February. Summer use increases too, but the winter temperature   
   delta is much higher than winter. A polynomial is the only form that   
   models this kWh/day data shape. Saw that from day 1.   
      
   Of course none of these power uses are broken out on our bills. We only   
   get an estimate by doing a statistical analysis.   
      
   I got my November AES bill today, and included that in the model. The   
   result follows. My challenge to Hugh is to improve on these results. My   
   offer for $120 for some ideas stands.   
      
   November 2025 Regression Statistics for ln kWh/day   
   						   
   Multiple R        0.9832					   
   R Square          0.9666					   
   Adjusted R Square 0.9638					   
   Standard Error    0.1048					   
   Observations      191					   
   						   
                             Coefficients Standard Error t Stat   P-value   
   Intercept                   5.7513       0.0460     124.9547  0.0000   
      
   [continued in next message]   
      
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