water-consumption-campaign-analytics

Evaluate the effectiveness of water consumption campaign in 12 districts

Problem Definition

• A campaign is running to reduce the water consumption in District 1.
• The city has 11 districts (Campaign only runs at District 1)
• Let's see how effective this campaign is

Data Overview

• The row is the daily water consumption (in liters). There are total 364 rows (364 days) continuously from 01-January.
• The columns are 11 districts
• The campaign ran only in District 1 for the last 28 days (02-Dec to 30-Dec)
• Data samples are shown below

Day	District_1	District_2	District_3	District_4	District_5	District_6	District_7	District_8	District_9	District_10	District_11
01-01	30000.00	25188.97	28538.15	31483.59	30486.67	30892.30	30613.86	27324.14	25658.25	28994.79	27645.36
02-01	31859.96	32538.84	38301.84	28500.64	33390.60	30254.08	24096.06	30740.24	28504.75	32948.60	32895.67
03-01	31516.08	36534.43	24865.96	37001.22	30877.25	26671.67	23436.28	30992.98	27555.64	30934.14	31562.64
04-01	28790.81	19551.51	32441.73	35832.19	40637.68	35049.81	32555.86	28242.00	27142.70	31642.02	27085.91
05-01	27434.27	33289.90	30563.99	36903.76	36365.24	27596.44	19360.99	28404.61	33131.36	29676.91	23879.14

Objective

• Evaluate whether the campaign have any significant impact on the water consumption in District 1? How much?

Hypothesis (select = 5%)

• : Campaign didn't have any impact on District 1 (coefficient of treament in linear equation with consumption = 0)
• : Campaign actually reduce the water consumption in District 1 (coefficient of treament in linear equation is significantly negative)
• One-tailed test valuation

Helper Function

• preproc.py to plot, eda, and decompose time-series into cyclic seasonality features

Example of Data Exploration

DISTRICT 1

DISTRICT 4

Notes:

• There could be a consumption distribution shift after the campaign lauched in District 1
• However, we're still unsure if the change is due to campaign or it's just seasonal effect, or it's just a randomness

Convert time seasonal feature into cyclic features (Fourier Series) with sin and cos:

• Weekly cyclic features as the habit of using water can be repeated with the same weekday
• Yearly cyclic features as the habit of using water can vary depend upon season (i.e: more water used in summer than winter)
• Fourier series are decomposed at level 3

Linear Regression Analysis for consumption of District 1 at day

The objective is to see if is significantly negative than 0, this means the campaign is effective

OLS Regression Analysis for District 1

                                OLS Regression Results                            
    ==============================================================================
    Dep. Variable:             District_1   R-squared:                       0.936
    Model:                            OLS   Adj. R-squared:                  0.932
    Method:                 Least Squares   F-statistic:                     216.1
    Date:                Sun, 24 Oct 2021   Prob (F-statistic):          1.83e-187
    Time:                        10:04:31   Log-Likelihood:                -3102.9
    No. Observations:                 364   AIC:                             6254.
    Df Residuals:                     340   BIC:                             6347.
    Df Model:                          23                                         
    Covariance Type:            nonrobust                                         
    =======================================================================================
                              coef    std err          t      P>|t|      [0.025      0.975]
    ---------------------------------------------------------------------------------------
    Intercept            6353.9583   1368.048      4.645      0.000    3663.054    9044.862
    sin_week_1n          1326.6134    121.505     10.918      0.000    1087.617    1565.610
    cos_week_1n          1052.4853    113.875      9.242      0.000     828.498    1276.473
    sin_week_2n          -338.5787     97.675     -3.466      0.001    -530.703    -146.455
    cos_week_2n           736.4401    103.287      7.130      0.000     533.278     939.602
    sin_week_3n          -385.2357     98.001     -3.931      0.000    -578.001    -192.471
    cos_week_3n          -172.2709     95.951     -1.795      0.073    -361.003      16.461
    sin_year_1n           240.9986    107.444      2.243      0.026      29.659     452.338
    cos_year_1n         -1610.5931    188.649     -8.538      0.000   -1981.659   -1239.527
    sin_year_2n           376.8972    123.336      3.056      0.002     134.300     619.495
    cos_year_2n           605.0006    143.525      4.215      0.000     322.692     887.309
    sin_year_3n           -61.6749    124.646     -0.495      0.621    -306.850     183.500
    cos_year_3n          -457.5879    128.098     -3.572      0.000    -709.551    -205.624
    District_2              0.0176      0.014      1.262      0.208      -0.010       0.045
    District_3              0.0243      0.014      1.793      0.074      -0.002       0.051
    District_4              0.0100      0.014      0.690      0.491      -0.018       0.038
    District_5              0.0318      0.015      2.124      0.034       0.002       0.061
    District_6              0.0666      0.015      4.544      0.000       0.038       0.095
    District_7              0.0483      0.015      3.307      0.001       0.020       0.077
    District_8              0.0548      0.017      3.226      0.001       0.021       0.088
    District_9              0.1075      0.018      5.863      0.000       0.071       0.144
    District_10             0.1373      0.022      6.180      0.000       0.094       0.181
    District_11             0.3010      0.026     11.588      0.000       0.250       0.352
    Treament_District_1 -1192.1777    503.144     -2.369      0.018   -2181.845    -202.510
    ==============================================================================
    Omnibus:                       11.642   Durbin-Watson:                   1.427
    Prob(Omnibus):                  0.003   Jarque-Bera (JB):               17.340
    Skew:                          -0.233   Prob(JB):                     0.000172
    Kurtosis:                       3.962   Cond. No.                     2.06e+06
    ==============================================================================
    
    Notes:
    [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
    [2] The condition number is large, 2.06e+06. This might indicate that there are
    strong multicollinearity or other numerical problems.

• Regression result shows that p-value of treatment coefficient (-1192.1777) = 0.005 < 0.05 / 2 for district 1
• This means we can reject the null hypothesis. The coefficient of treament effect is negatively significant and different from 0
• the daily water consumption at District 1 is predicted to be lower by 1192 litres (compared with the usual day), thanks to this campaign
• Also, p-value of variable cos_week_3n, sin_year_3n and consumption of district 2 to 4 > 0.05, so this means those variables are not statistically significantly different from 0. So we can remove this from function
• The consumption of district 5 - 11 signficantly impacts the consumption at district 1

The water consumption model of District 1 is, therefore, explicitly represented by:

Metrics and Plots:

• Adjusted R squared = 0.932
  
• RMSE = 2020.5
  
• MAE = 1723.7
  
• MAPE = 0.056
  

DISTRICT 1 CONSUMPTION

• So we conclude the campaign at District 1 has the great impact to the consumption at District. The campaign can effectively reduce the water consumption by 880 litres, on average
• But do the campaign in District 1 also impacts other Districts ???

Evaluate if the campaign in District 1 also impact other districts. Now we replace the fitting function with each district from 2 to 11

We can have the p-value summary of each coefficients for each district regression analysis as follows:

Output	Coeff. Treament District 1	Coeff. District 1	Coeff. District 2	Coeff. District 3	Coeff. District 4	Coeff. District 5	Coeff. District 6	Coeff. District 7	Coeff. District 8	Coeff. District 9	Coeff. District 10	Coeff. District 11
District 1	0.005		0.516	0.238	0.260	0.016	0.000	0.000	0.000	0.000	0.000	0.000
District 2	0.252	0.516		0.374	0.860	0.463	0.403	0.448	0.562	0.046	0.138	0.961
District 3	0.909	0.238	0.374		0.914	0.430	0.772	0.985	0.154	0.328	0.977	0.748
District 4	0.335	0.260	0.860	0.914		0.753	0.617	0.831	0.783	0.215	0.311	0.241
District 5	0.568	0.016	0.463	0.430	0.753		0.490	0.553	0.863	0.427	0.700	0.350
District 6	0.363	0.000	0.403	0.772	0.617	0.490		0.087	0.413	0.978	0.498	0.242
District 7	0.773	0.000	0.448	0.985	0.831	0.553	0.087		0.249	0.675	0.126	0.422
District 8	0.730	0.000	0.562	0.154	0.763	0.863	0.413	0.249		0.886	0.433	0.380
District 9	0.876	0.000	0.046	0.328	0.215	0.427	0.978	0.675	0.886		0.787	0.447
District 10	0.988	0.000	0.138	0.977	0.311	0.700	0.498	0.126	0.433	0.787		0.409
District 11	0.985	0.000	0.961	0.748	0.241	0.350	0.242	0.422	0.380	0.447	0.409

• The campaign does not significantly affect other districts. However
• It's interesting to see some pairs of district are correlated in water consumption:
  • District 1 with: district 5 - 11
  • District 2 with: district 9
  • District 6 with: district 7

Conclusions and Future Work

• The campaign have significant impact on the water consumption in District 1.
• Daily water consumption at District 1 is predicted to be lower by 1192 litres thanks to the campaign effect, compared with the usual day
• In the next steps, we could evaluate post-campaign effect on district 1, if the effect is just instantly one-off or it really changes the water usage behavior
• If campaign at district 1 has long-term effects, we could design the same campaigns for other districts