Energy Efficiency - UCI

Analysis of the energy efficiency dataset from UCI.



In [1]:

    
import numpy as np
import pandas as pd
%pylab inline
pylab.style.use('ggplot')
import seaborn as sns









    



Populating the interactive namespace from numpy and matplotlib



In [2]:

    
data_df = pd.read_csv('energy_efficiency.csv')



In [4]:

    
data_df.head()

Attribute Information

X1 Relative Compactness
X2 Surface Area
X3 Wall Area
X4 Roof Area
X5 Overall Height
X6 Orientation
X7 Glazing Area
X8 Glazing Area Distribution
y1 Heating Load
y2 Cooling Load

Bivariate Analysis - Y1



In [9]:

    
for fname in feature_df:
    pylab.figure()
    sns.jointplot(x=fname, y='Y1', data=data_df)









    





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Feature Correlations with Y1



In [10]:

    
feature_df = data_df.drop(['Y1', 'Y2'], axis=1)



In [11]:

    
y1_corrs = feature_df.corrwith(data_df.Y1)
y1_corrs.plot(kind='bar')









    Out[11]:





<matplotlib.axes._subplots.AxesSubplot at 0x162ef48dc50>

Between Feature Correlations



In [15]:

    
f_corrs = feature_df.corr()
sns.heatmap(f_corrs, annot=True)









    Out[15]:





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The Regression Model



In [17]:

    
import statsmodels.formula.api as sm



In [24]:

    
y1_model = sm.ols(data=data_df, 
                  formula='Y1 ~ X4 + X2 + X7')
y1_result = y1_model.fit()
y1_result.summary()









    Out[24]:





OLS Regression Results

  Dep. Variable:            Y1           R-squared:             0.861


  Model:                    OLS          Adj. R-squared:        0.860


  Method:              Least Squares     F-statistic:           1577.


  Date:              Mon, 07 Aug 2017    Prob (F-statistic):     0.00 


  Time:                  23:16:38        Log-Likelihood:      -2106.9


  No. Observations:          768         AIC:                   4222.


  Df Residuals:              764         BIC:                   4240.


  Df Model:                    3                                     


  Covariance Type:       nonrobust                                   




               coef      std err       t       P>|t|   [0.025     0.975]  


  Intercept     32.5391      1.343     24.229   0.000     29.903     35.175


  X4            -0.2810      0.006    -44.166   0.000     -0.294     -0.269


  X2             0.0515      0.003     15.792   0.000      0.045      0.058


  X7            20.4380      1.022     20.002   0.000     18.432     22.444




  Omnibus:        144.564    Durbin-Watson:         0.535


  Prob(Omnibus):   0.000     Jarque-Bera (JB):    310.656


  Skew:            1.039     Prob(JB):           3.48e-68


  Kurtosis:        5.322     Cond. No.           7.06e+03

Bivariate Analysis - Y2



In [26]:

    
for fname in feature_df:
    pylab.figure()
    sns.jointplot(x=fname, y='Y2', data=data_df)









    





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In [27]:

    
y2_corrs = feature_df.corrwith(data_df.Y2)
y2_corrs.plot(kind='bar')









    Out[27]:





<matplotlib.axes._subplots.AxesSubplot at 0x162f0d540b8>



In [28]:

    
y2_model = sm.ols(data=data_df, 
                  formula='Y2 ~ X4 + X2 + X7')
y2_result = y1_model.fit()
y2_result.summary()









    Out[28]:





OLS Regression Results

  Dep. Variable:            Y1           R-squared:             0.861


  Model:                    OLS          Adj. R-squared:        0.860


  Method:              Least Squares     F-statistic:           1577.


  Date:              Mon, 07 Aug 2017    Prob (F-statistic):     0.00 


  Time:                  23:21:04        Log-Likelihood:      -2106.9


  No. Observations:          768         AIC:                   4222.


  Df Residuals:              764         BIC:                   4240.


  Df Model:                    3                                     


  Covariance Type:       nonrobust                                   




               coef      std err       t       P>|t|   [0.025     0.975]  


  Intercept     32.5391      1.343     24.229   0.000     29.903     35.175


  X4            -0.2810      0.006    -44.166   0.000     -0.294     -0.269


  X2             0.0515      0.003     15.792   0.000      0.045      0.058


  X7            20.4380      1.022     20.002   0.000     18.432     22.444




  Omnibus:        144.564    Durbin-Watson:         0.535


  Prob(Omnibus):   0.000     Jarque-Bera (JB):    310.656


  Skew:            1.039     Prob(JB):           3.48e-68


  Kurtosis:        5.322     Cond. No.           7.06e+03



In [ ]:

	X1	X2	X3	X4	X5	X6	Y1	Y2
0	0.98	514.5	294.0	110.25	7.0	2	15.55	21.33
1	0.98	514.5	294.0	110.25	7.0	3	15.55	21.33
2	0.98	514.5	294.0	110.25	7.0	4	15.55	21.33
3	0.98	514.5	294.0	110.25	7.0	5	15.55	21.33
4	0.90	563.5	318.5	122.50	7.0	2	20.84	28.28

Dep. Variable:	Y1	R-squared:	0.861
Model:	OLS	Adj. R-squared:	0.860
Method:	Least Squares	F-statistic:	1577.
Date:	Mon, 07 Aug 2017	Prob (F-statistic):	0.00
Time:	23:16:38	Log-Likelihood:	-2106.9
No. Observations:	768	AIC:	4222.
Df Residuals:	764	BIC:	4240.
Df Model:	3
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	32.5391	1.343	24.229	0.000	29.903	35.175
X4	-0.2810	0.006	-44.166	0.000	-0.294	-0.269
X2	0.0515	0.003	15.792	0.000	0.045	0.058
X7	20.4380	1.022	20.002	0.000	18.432	22.444

Omnibus:	144.564	Durbin-Watson:	0.535
Prob(Omnibus):	0.000	Jarque-Bera (JB):	310.656
Skew:	1.039	Prob(JB):	3.48e-68
Kurtosis:	5.322	Cond. No.	7.06e+03