Summary of NDM Data Sample Analysis

© British Gas Trading Limited 2011

Summary of NDM Data Sample Analysis

Option C: Regression Analysis


Contents

• Regression Analysis per LDZ

• In-Sample Results

• Out-of-Sample Model fit

• CWV Contribution

• Conclusion


Regression Analysis

• Regression Model as follows:

• Dummy variables (Bank Holidays, Easter, Christmas and so forth).

• Weather variables introduced as per DESC meeting on 4th April (e.g. Temperature, Global Radiation, Rainfall and so forth).

• Time intervals used based on office hours and domestic habits.

• Slot 1 from 5am to 8am

• Slot 2 from 9am to 4pm

• Slot 3 from 5pm to 10pm

• Slot 4 from 11pm to 4am


Regression Analysis

• Data normalised by AQ because of erratic level changes observed year on year. Yearly cut-off date is of 1st April due to time span of original files and data deletion process

• Binary permutation of variables used to seek out best regression fit with p≤5% significance level.


Regression Analysis Models used

• A benchmark model was used for each LDZ as the following:

Normalised Consumption = Intercept + a0 * CWV

• Using Binary permutations, a most optimised linear regression model (based on best R2 fit) is chosen. The linear regression is of the form:

Normalised Consumption = Intercept + a0 * CWV + a1 * Temperature + a2* Windspeed +

a3* Solar Radiation + …

• In-Sample data runs from April 2008 to March 2011 whereas Out-of-Sample data spans from April 2011 to March 2012.

• These models were applied to End-User Category 1 only (EUC1).


Regression Analysis Parameters (1 of 2)

Parameters EA EM NE NO NW SC SE SW WM WSIntercept 0.006914 0.006223 0.005724 0.005377 0.006518 0.005753 0.007031 0.007086 0.006198 0.006572

CWV -0.00039 -0.00038 -0.00032 -0.00033 -0.00029 -0.00033 -0.0004 -0.00044 -0.00039 -0.00035mean_Temp -0.00009 0.00011 0.000075 -0.00002 -0.00014 0.000019 -0.00006 0.000024 0.00000351 -0.00005

mean_Windspeed 0.000025 0.000015 0.00006 mean_WindDirection -7.55E-07 -1.03E-06 -7.45E-07 -2.85E-07

mean_Humidity -1.16E-07 0.00000266 0.000012 0.00000427 0.00000174 mean_Global_Radiation -5.13E-07 -2.52E-07 -1.15E-06 4.23E-07 6.97E-07

mean_Rainfall 0.00024 0.000178 0.000179 0.000476 0.000145 mean_Temp_lag1 -0.00001 -8.53E-06 -0.00001 -0.00002 -8.35E-06 -8.83E-06 0.0000034

mean_Windspeed_lag1 0.000022 0.000026 0.000014 0.000041 0.00003 0.000012 0.000014 mean_WindDirection_lag1 4.623E-07 3.49E-07 3.48E-07

mean_Humidity_lag1 -7.05E-07 -2.05E-06 -2.06E-06 -1.87E-06 mean_Global_Radiation_lag1 1.376E-07 -1.47E-07 6.75E-08

mean_Rainfall_lag1 0.000113 -0.00007 0.000096 WeekEnd -0.00005 -0.00014 0.000094 0.000073 0.000071 Mon_Fri -0.00005 -0.00005 0.00000264

WeekEnd_from__Friday 0.000041 Bank__Hols 0.000064 School_Hols 0.000066 0.00007 0.00012 -2.35E-06 Mon_Thurs -0.00009 -0.00013 -0.00003

Slot1_Windspeed Slot1_Rainfall -0.0001 -0.00006


Regression Analysis Parameters ( of 2)

Parameters EA EM NE NO NW SC SE SW WM WS Slot1_GlobalRadiation 2.293E-07 3.061E-07 0.00000351

Slot1_Temp 0.000032 -0.00005 -0.00004 0.000021 Slot1_WindDirection -3.68E-07 2.86E-07

Slot1_Humidity -3.08E-06 Slot2_Windspeed 9.999E-06 -0.00003

Slot2_Rainfall 0.000033 Slot2_GlobalRadiation -3.51E-08 -2.45E-07 -4.49E-07

Slot2_Temp -0.00004 -0.00002 0.000059 -0.00003 Slot2_WindDirection 5.639E-07 3.091E-07 -4.25E-07

Slot2_Humidity 3.617E-06 Slot3_Temp 0.000053 0.000028 0.000029 0.000013 0.000043 0.000022

Slot3_Windspeed -7.84E-06 Slot3_GlobalRadiation 1.357E-08 2.51E-07

Slot3_Rainfall -0.00009 0.000061 Slot3_WindDirection 4.538E-07

Slot3_Humidity 3.044E-06 Slot4_Temp 0.000015 0.000013 0.000021

Slot4_WindDirection 3.71E-07 Slot4_Humidity -1.75E-06 -5.51E-06 -2.28E-06

Slot4_GlobalRadiation Slot4_Windspeed

Slot4_Rainfall 0.000031 0.000072


In-Sample MAPE Results


In-Sample R2 Results


Out-of-Sample MAPE Results


Out-of-Sample R2 Results


Analysis of Contribution of CWV in Optimised Models


Conclusion

• Improvements against Benchmark Results are made using weather and/or calendar effects on top of CWV.

• The significance, or non-significance, level of Weekend/Weekday/Bank Holiday is very much LDZ-specific.

• Global Radiation is a significant variable in all LDZ’s.

• Time Intervals (i.e., Slot 1 to 4) and Monday-to-Thursday dummy variable help explain customer behaviour in some LDZ’s.

• Relative Humidity stands out in almost every LDZ’s.

• CWV heavily contributes in the optimised models obtained.

• No cross-effects utilised in Regression models.

• LDZ SO and NT need further investigations

Summary of NDM Data Sample Analysis

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