1. Summary of NDM Data Sample Analysis
Option C: Regression Analysis

2. Contents Regression Analysis per LDZ In-Sample Results
Out-of-Sample Model fit
CWV Contribution
Conclusion

3. 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

4. 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.

5. 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).

6. Regression Analysis Parameters (1 of 2)EA EM NE NO NW SC SE SW WM WS
Intercept
CWV
mean_Temp
mean_Windspeed
mean_WindDirection
-7.55E-07
-1.03E-06
-7.45E-07
-2.85E-07
mean_Humidity
-1.16E-07
mean_Global_Radiation
-5.13E-07
-2.52E-07
-1.15E-06
4.23E-07
6.97E-07
mean_Rainfall
mean_Temp_lag1
-8.53E-06
-8.35E-06
-8.83E-06
mean_Windspeed_lag1
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
WeekEnd
Mon_Fri
WeekEnd_from__Friday
Bank__Hols
School_Hols
-2.35E-06
Mon_Thurs
Slot1_Windspeed
Slot1_Rainfall

7. Regression Analysis Parameters ( of 2)EA EM NE NO NW SC SE SW WM WS
Slot1_GlobalRadiation
2.293E-07
3.061E-07
Slot1_Temp
Slot1_WindDirection
-3.68E-07
2.86E-07
Slot1_Humidity
-3.08E-06
Slot2_Windspeed
9.999E-06
Slot2_Rainfall
Slot2_GlobalRadiation
-3.51E-08
-2.45E-07
-4.49E-07
Slot2_Temp
Slot2_WindDirection
5.639E-07
3.091E-07
-4.25E-07
Slot2_Humidity
3.617E-06
Slot3_Temp
Slot3_Windspeed
-7.84E-06
Slot3_GlobalRadiation
1.357E-08
2.51E-07
Slot3_Rainfall
Slot3_WindDirection
4.538E-07
Slot3_Humidity
3.044E-06
Slot4_Temp
Slot4_WindDirection
3.71E-07
Slot4_Humidity
-1.75E-06
-5.51E-06
-2.28E-06
Slot4_GlobalRadiation
Slot4_Windspeed
Slot4_Rainfall

8. In-Sample MAPE Results

9. In-Sample R2 Results

10. Out-of-Sample MAPE Results

11. Out-of-Sample R2 Results

12. Analysis of Contribution of CWV in Optimised Models

13. 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