Libraries

import warnings
warnings.filterwarnings("ignore", message="numpy.ufunc size changed")

import numpy as np
import pandas as pd
pd.set_option("display.max.columns", None)
pd.set_option("display.max_colwidth", None)

import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
plt.style.use("ggplot")

from sklearn.model_selection import train_test_split
from sklearn.preprocessing import MinMaxScaler
from sklearn.linear_model import (LinearRegression, 
                                  Ridge, 
                                  Lasso)
from sklearn.metrics import (r2_score, 
                             mean_absolute_error, 
                             mean_squared_error)

The Dataset

The dataset is the Appliances Energy Prediction data. The data set is at 10 min for about 4.5 months. The house temperature and humidity conditions were monitored with a ZigBee wireless sensor network. Each wireless node transmitted the temperature and humidity conditions around 3.3 min. Then, the wireless data was averaged for 10 minutes periods. The energy data was logged every 10 minutes with m-bus energy meters. Weather from the nearest airport weather station (Chievres Airport, Belgium) was downloaded from a public data set from Reliable Prognosis (rp5.ru), and merged together with the experimental data sets using the date and time column. Two random variables have been included in the data set for testing the regression models and to filter out non predictive attributes (parameters).

energy = pd.read_csv("datasets/energydata_complete.csv")
energy.head()

	date	Appliances	lights	T1	RH_1	T2	RH_2	T3	RH_3	T4	RH_4	T5	RH_5	T6	RH_6	T7	RH_7	T8	RH_8	T9	RH_9	T_out	Press_mm_hg	RH_out	Windspeed	Visibility	Tdewpoint	rv1	rv2
0	2016-01-11 17:00:00	60	30	19.89	47.596667	19.2	44.790000	19.79	44.730000	19.000000	45.566667	17.166667	55.20	7.026667	84.256667	17.200000	41.626667	18.2	48.900000	17.033333	45.53	6.600000	733.5	92.0	7.000000	63.000000	5.3	13.275433	13.275433
1	2016-01-11 17:10:00	60	30	19.89	46.693333	19.2	44.722500	19.79	44.790000	19.000000	45.992500	17.166667	55.20	6.833333	84.063333	17.200000	41.560000	18.2	48.863333	17.066667	45.56	6.483333	733.6	92.0	6.666667	59.166667	5.2	18.606195	18.606195
2	2016-01-11 17:20:00	50	30	19.89	46.300000	19.2	44.626667	19.79	44.933333	18.926667	45.890000	17.166667	55.09	6.560000	83.156667	17.200000	41.433333	18.2	48.730000	17.000000	45.50	6.366667	733.7	92.0	6.333333	55.333333	5.1	28.642668	28.642668
3	2016-01-11 17:30:00	50	40	19.89	46.066667	19.2	44.590000	19.79	45.000000	18.890000	45.723333	17.166667	55.09	6.433333	83.423333	17.133333	41.290000	18.1	48.590000	17.000000	45.40	6.250000	733.8	92.0	6.000000	51.500000	5.0	45.410389	45.410389
4	2016-01-11 17:40:00	60	40	19.89	46.333333	19.2	44.530000	19.79	45.000000	18.890000	45.530000	17.200000	55.09	6.366667	84.893333	17.200000	41.230000	18.1	48.590000	17.000000	45.40	6.133333	733.9	92.0	5.666667	47.666667	4.9	10.084097	10.084097

Dataset Description

The attribute information can be seen below.

Attribute Information:

Attribute	Description	Units
Date	time	year-month-day hour:minute:second
Appliances	energy use	in Wh
lights	energy use of light fixtures in the house	in Wh
T1	Temperature in kitchen area	in Celsius
RH_1	Humidity in kitchen area	in %
T2	Temperature in living room area	in Celsius
RH_2	Humidity in living room area	in %
T3	Temperature in laundry room area
RH_3	Humidity in laundry room area	in %
T4	Temperature in office room	in Celsius
RH_4	Humidity in office room	in %
T5	Temperature in bathroom	in Celsius
RH_5	Humidity in bathroom	in %
T6	Temperature outside the building (north side)	in Celsius
RH_6	Humidity outside the building (north side)	in %
T7	Temperature in ironing room	in Celsius
RH_7	Humidity in ironing room	in %
T8	Temperature in teenager room 2	in Celsius
RH_8	Humidity in teenager room 2	in %
T9	Temperature in parents room	in Celsius
RH_9	Humidity in parents room	in %
To	Temperature outside (from Chievres weather station)	in Celsius
Pressure	(from Chievres weather station)	in mm Hg
RH_out	Humidity outside (from Chievres weather station)	in %
Wind speed	(from Chievres weather station)	in m/s
Visibility	(from Chievres weather station)	in km
Tdewpoint	(from Chievres weather station)	Â °C
rv1	Random variable 1	nondimensional
rv2	Random variable 2	nondimensional

energy.describe()

	Appliances	lights	T1	RH_1	T2	RH_2	T3	RH_3	T4	RH_4	T5	RH_5	T6	RH_6	T7	RH_7	T8	RH_8	T9	RH_9	T_out	Press_mm_hg	RH_out	Windspeed	Visibility	Tdewpoint	rv1	rv2
count	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000	19735.000000
mean	97.694958	3.801875	21.686571	40.259739	20.341219	40.420420	22.267611	39.242500	20.855335	39.026904	19.592106	50.949283	7.910939	54.609083	20.267106	35.388200	22.029107	42.936165	19.485828	41.552401	7.411665	755.522602	79.750418	4.039752	38.330834	3.760707	24.988033	24.988033
std	102.524891	7.935988	1.606066	3.979299	2.192974	4.069813	2.006111	3.254576	2.042884	4.341321	1.844623	9.022034	6.090347	31.149806	2.109993	5.114208	1.956162	5.224361	2.014712	4.151497	5.317409	7.399441	14.901088	2.451221	11.794719	4.194648	14.496634	14.496634
min	10.000000	0.000000	16.790000	27.023333	16.100000	20.463333	17.200000	28.766667	15.100000	27.660000	15.330000	29.815000	-6.065000	1.000000	15.390000	23.200000	16.306667	29.600000	14.890000	29.166667	-5.000000	729.300000	24.000000	0.000000	1.000000	-6.600000	0.005322	0.005322
25%	50.000000	0.000000	20.760000	37.333333	18.790000	37.900000	20.790000	36.900000	19.530000	35.530000	18.277500	45.400000	3.626667	30.025000	18.700000	31.500000	20.790000	39.066667	18.000000	38.500000	3.666667	750.933333	70.333333	2.000000	29.000000	0.900000	12.497889	12.497889
50%	60.000000	0.000000	21.600000	39.656667	20.000000	40.500000	22.100000	38.530000	20.666667	38.400000	19.390000	49.090000	7.300000	55.290000	20.033333	34.863333	22.100000	42.375000	19.390000	40.900000	6.916667	756.100000	83.666667	3.666667	40.000000	3.433333	24.897653	24.897653
75%	100.000000	0.000000	22.600000	43.066667	21.500000	43.260000	23.290000	41.760000	22.100000	42.156667	20.619643	53.663333	11.256000	83.226667	21.600000	39.000000	23.390000	46.536000	20.600000	44.338095	10.408333	760.933333	91.666667	5.500000	40.000000	6.566667	37.583769	37.583769
max	1080.000000	70.000000	26.260000	63.360000	29.856667	56.026667	29.236000	50.163333	26.200000	51.090000	25.795000	96.321667	28.290000	99.900000	26.000000	51.400000	27.230000	58.780000	24.500000	53.326667	26.100000	772.300000	100.000000	14.000000	66.000000	15.500000	49.996530	49.996530

energy.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 19735 entries, 0 to 19734
Data columns (total 29 columns):
 #   Column       Non-Null Count  Dtype  
---  ------       --------------  -----  
 0   date         19735 non-null  object 
 1   Appliances   19735 non-null  int64  
 2   lights       19735 non-null  int64  
 3   T1           19735 non-null  float64
 4   RH_1         19735 non-null  float64
 5   T2           19735 non-null  float64
 6   RH_2         19735 non-null  float64
 7   T3           19735 non-null  float64
 8   RH_3         19735 non-null  float64
 9   T4           19735 non-null  float64
 10  RH_4         19735 non-null  float64
 11  T5           19735 non-null  float64
 12  RH_5         19735 non-null  float64
 13  T6           19735 non-null  float64
 14  RH_6         19735 non-null  float64
 15  T7           19735 non-null  float64
 16  RH_7         19735 non-null  float64
 17  T8           19735 non-null  float64
 18  RH_8         19735 non-null  float64
 19  T9           19735 non-null  float64
 20  RH_9         19735 non-null  float64
 21  T_out        19735 non-null  float64
 22  Press_mm_hg  19735 non-null  float64
 23  RH_out       19735 non-null  float64
 24  Windspeed    19735 non-null  float64
 25  Visibility   19735 non-null  float64
 26  Tdewpoint    19735 non-null  float64
 27  rv1          19735 non-null  float64
 28  rv2          19735 non-null  float64
dtypes: float64(26), int64(2), object(1)
memory usage: 4.4+ MB

There are no missing values in the dataset.

scaler = MinMaxScaler()
normalised_df = pd.DataFrame(scaler.fit_transform(energy.drop(columns=['date', 'lights'])), 
                             columns=energy.drop(columns=['date', 'lights']).columns)
features_df = normalised_df.drop(columns=['Appliances'])
energy_target = normalised_df.Appliances
X_train, X_test, y_train, y_test = train_test_split(features_df, energy_target, test_size=.3, random_state=42)

From the dataset, fit a linear model on the relationship between the temperature in the living room in Celsius (x = T2) and the temperature outside the building (y = T6).

lin_reg = LinearRegression()
lin_reg.fit(X_train[['T2']], X_train.T6)
T6_pred = lin_reg.predict(X_test[['T2']])
print(f'r^2 score: {round(r2_score(X_test.T6, T6_pred), 2)}')

r^2 score: 0.64

print(f'MAE: {round(mean_absolute_error(X_test.T6, T6_pred), 2)}')

MAE: 0.08

print(f'Residual Sum of Squares: {round(np.sum(np.square(X_test.T6 - T6_pred)), 2)}')

Residual Sum of Squares: 274.9

print(f'Root Mean Squared Error: {round(np.sqrt(mean_squared_error(X_test.T6, T6_pred)), 3)}')

Root Mean Squared Error: 0.215

T7             1.0
T1             1.0
T2             1.0
T9             1.0
RH_8           1.0
RH_out         1.0
Tdewpoint      1.0
Visibility     1.0
Windspeed      1.0
Press_mm_hg    1.0
T_out          1.0
RH_9           1.0
T8             1.0
RH_7           1.0
Appliances     1.0
RH_6           1.0
T6             1.0
RH_5           1.0
RH_4           1.0
RH_3           1.0
T3             1.0
RH_2           1.0
RH_1           1.0
rv1            1.0
rv2            1.0
T5             1.0
T4             1.0
dtype: float64

energy.drop(columns=['date', 'lights']).max().sort_values()

Windspeed        14.000000
Tdewpoint        15.500000
T9               24.500000
T5               25.795000
T7               26.000000
T_out            26.100000
T4               26.200000
T1               26.260000
T8               27.230000
T6               28.290000
T3               29.236000
T2               29.856667
rv1              49.996530
rv2              49.996530
RH_3             50.163333
RH_4             51.090000
RH_7             51.400000
RH_9             53.326667
RH_2             56.026667
RH_8             58.780000
RH_1             63.360000
Visibility       66.000000
RH_5             96.321667
RH_6             99.900000
RH_out          100.000000
Press_mm_hg     772.300000
Appliances     1080.000000
dtype: float64

energy.drop(columns=['date', 'lights']).min().sort_values()

Tdewpoint       -6.600000
T6              -6.065000
T_out           -5.000000
Windspeed        0.000000
rv2              0.005322
rv1              0.005322
Visibility       1.000000
RH_6             1.000000
Appliances      10.000000
T9              14.890000
T4              15.100000
T5              15.330000
T7              15.390000
T2              16.100000
T8              16.306667
T1              16.790000
T3              17.200000
RH_2            20.463333
RH_7            23.200000
RH_out          24.000000
RH_1            27.023333
RH_4            27.660000
RH_3            28.766667
RH_9            29.166667
RH_8            29.600000
RH_5            29.815000
Press_mm_hg    729.300000
dtype: float64

def get_weights_df(model, feat, col_name):
    #this function returns the weight of every feature
    weights = pd.Series(model.coef_, feat.columns).sort_values()
    weights_df = pd.DataFrame(weights).reset_index()
    weights_df.columns = ['Features', col_name]
    weights_df[col_name].round(3)
    return weights_df

ridge_reg = Ridge(alpha=0.4)
ridge_reg.fit(X_train, y_train)

Ridge(alpha=0.4)

lasso_reg = Lasso(alpha=0.001)
lasso_reg.fit(X_train, y_train)

Lasso(alpha=0.001)

model = LinearRegression()
model.fit(X_train, y_train)

LinearRegression()

linear_model_weights = get_weights_df(model, X_train, 'Linear_Model_Weight')
ridge_weights_df = get_weights_df(ridge_reg, X_train, 'Ridge_Weight')
lasso_weights_df = get_weights_df(lasso_reg, X_train, 'Lasso_weight')

final_weights = pd.merge(linear_model_weights, ridge_weights_df, on='Features')
final_weights = pd.merge(final_weights, lasso_weights_df, on='Features')

final_weights.sort_values("Linear_Model_Weight", ascending=False)

	Features	Linear_Model_Weight	Ridge_Weight	Lasso_weight
25	RH_1	0.553547	0.519525	0.017880
24	T3	0.290627	0.288087	0.000000
23	T6	0.236425	0.217292	0.000000
22	Tdewpoint	0.117758	0.083128	0.000000
21	T8	0.101995	0.101028	0.000000
20	RH_3	0.096048	0.095135	0.000000
19	RH_6	0.038049	0.035519	-0.000000
18	Windspeed	0.029183	0.030268	0.002912
17	T4	0.028981	0.027384	-0.000000
16	RH_4	0.026386	0.024579	0.000000
15	RH_5	0.016006	0.016152	0.000000
14	Visibility	0.012307	0.012076	0.000000
13	T7	0.010319	0.010098	-0.000000
12	Press_mm_hg	0.006839	0.006584	-0.000000
11	rv2	0.000770	0.000748	-0.000000
10	rv1	0.000770	0.000748	-0.000000
9	T1	-0.003281	-0.018406	0.000000
8	T5	-0.015657	-0.019853	-0.000000
7	RH_9	-0.039800	-0.041367	-0.000000
6	RH_7	-0.044614	-0.045977	-0.000000
5	RH_out	-0.077671	-0.054724	-0.049557
4	RH_8	-0.157595	-0.156830	-0.000110
3	T9	-0.189941	-0.188916	-0.000000
2	T2	-0.236178	-0.201397	0.000000
1	T_out	-0.321860	-0.262172	0.000000
0	RH_2	-0.456698	-0.411071	-0.000000

y_pred_lg = model.predict(X_test)
y_pred_r = ridge_reg.predict(X_test)
y_pred_l = lasso_reg.predict(X_test)

print(f'Root Mean Squared Error: {round(np.sqrt(mean_squared_error(y_test, y_pred_r)), 3)}')

Root Mean Squared Error: 0.088

print(f'Root Mean Squared Error: {round(np.sqrt(mean_squared_error(y_test, y_pred_l)), 3)}')

Root Mean Squared Error: 0.094