FOREST FIRES IN BRAZIL

See https://www.kaggle.com/gustavomodelli/forest-fires-in-brazil for a full description of the dataset.

Import packages

import pandas as pd #Handle datasets
import seaborn as sns #Plots
import matplotlib.pyplot as plt  #Plots
import matplotlib

#Set some graphical parameters
rc={'axes.labelsize': 25, 'figure.figsize': (20,10), 
    'axes.titlesize': 25, 'xtick.labelsize': 18, 'ytick.labelsize': 18}
sns.set(rc=rc)

#Path data
path = 'C:/Users/Andreella/Desktop/Doc/GitHub/angeella.github.io/Data'
df = pd.read_csv(path + '/amazon.csv',encoding="ISO-8859-1")

First \(3\) observations:

df.head(n=3)

	year	state	month	date
0	1998	Acre	Janeiro	1998-01-01
1	1999	Acre	Janeiro	1999-01-01
2	2000	Acre	Janeiro	2000-01-01

Some information about the variables:

df.info()

## <class 'pandas.DataFrame'>
## RangeIndex: 6454 entries, 0 to 6453
## Data columns (total 5 columns):
##  #   Column  Non-Null Count  Dtype  
## ---  ------  --------------  -----  
##  0   year    6454 non-null   int64  
##  1   state   6454 non-null   str    
##  2   month   6454 non-null   str    
##  3   number  6454 non-null   float64
##  4   date    6454 non-null   str    
## dtypes: float64(1), int64(1), str(3)
## memory usage: 252.2 KB

We are interested about the number of forest fires in Brazil

df.number.describe()

## count    6454.000000
## mean      108.293163
## std       190.812242
## min         0.000000
## 25%         3.000000
## 50%        24.000000
## 75%       113.000000
## max       998.000000
## Name: number, dtype: float64

To have an simple plot, we take a subset of the dataset:

df1 = df[(df.year > 2010) & (df.year < 2019)]
df1 =df1.loc[(df1.state.str.startswith('M'))]

We do a boxplot about the number of fire by groups, i.e., the states and the years.

sns.boxplot(x = 'year', y = 'number', hue = "state", data = df1)

We do a timeseries plot with error bands:

sns.lineplot(x="year", y="number",hue="state", data=df1)

also we do a grouped violinplots:

sns.violinplot(x="state", y="number", data=df1)

For other plots, please refers to https://seaborn.pydata.org/examples/index.html.

ECONOMIC FREEDOM INDEX

See https://www.kaggle.com/lewisduncan93/the-economic-freedom-index for a full description of the dataset.

Load and preprocess data

dt = pd.read_csv(path + '/economic_freedom_index2019_data.csv',encoding="ISO-8859-1")
dt.columns = dt.columns.str.replace(' ', '')
dt.columns = dt.columns.str.replace('2019', '')
dt.columns = dt.columns.str.replace('%', '')
dt.columns = dt.columns.str.replace('(', '')
dt.columns = dt.columns.str.replace(')', '')
dt = dt.dropna(axis = 0,how='any')

Basic info

dt.info()

## <class 'pandas.DataFrame'>
## Index: 173 entries, 0 to 185
## Data columns (total 34 columns):
##  #   Column                 Non-Null Count  Dtype  
## ---  ------                 --------------  -----  
##  0   CountryID              173 non-null    int64  
##  1   CountryName            173 non-null    str    
##  2   WEBNAME                173 non-null    str    
##  3   Region                 173 non-null    str    
##  4   WorldRank              173 non-null    float64
##  5   RegionRank             173 non-null    float64
##  6   Score                  173 non-null    float64
##  7   PropertyRights         173 non-null    float64
##  8   JudicalEffectiveness   173 non-null    float64
##  9   GovernmentIntegrity    173 non-null    float64
##  10  TaxBurden              173 non-null    float64
##  11  Gov'tSpending          173 non-null    float64
##  12  FiscalHealth           173 non-null    float64
##  13  BusinessFreedom        173 non-null    float64
##  14  LaborFreedom           173 non-null    float64
##  15  MonetaryFreedom        173 non-null    float64
##  16  TradeFreedom           173 non-null    float64
##  17  InvestmentFreedom      173 non-null    float64
##  18  FinancialFreedom       173 non-null    float64
##  19  TariffRate             173 non-null    float64
##  20  IncomeTaxRate          173 non-null    float64
##  21  CorporateTaxRate       173 non-null    float64
##  22  TaxBurdenofGDP         173 non-null    float64
##  23  Gov'tExpenditureofGDP  173 non-null    float64
##  24  Country                173 non-null    str    
##  25  PopulationMillions     173 non-null    str    
##  26  GDPBillions,PPP        173 non-null    str    
##  27  GDPGrowthRate          173 non-null    float64
##  28  5YearGDPGrowthRate     173 non-null    float64
##  29  GDPperCapitaPPP        173 non-null    str    
##  30  Unemployment           173 non-null    str    
##  31  Inflation              173 non-null    float64
##  32  FDIInflowMillions      173 non-null    str    
##  33  PublicDebtofGDP        173 non-null    float64
## dtypes: float64(24), int64(1), str(9)
## memory usage: 47.3 KB

Some plots

Boxplot by group, i.e. region:

sns.boxplot(x = 'Region', y = 'Score', data = dt)

First scatter plot:

plt.scatter(x="PropertyRights", y="Score", data=dt)

We can put directly the linear regression fitting:

sns.lmplot(x="PropertyRights", y="Score", data=dt)

Density plot of the score variable:

sns.distplot(dt.Score, color="r")

Pair plot considering some variables, i.e. Property Rights, Labor Freedom, Government Integrity, Judical Effectiveness, Fiscal Health, Region and Score:

dt1 = dt[['PropertyRights', 'LaborFreedom', 'GovernmentIntegrity', 'JudicalEffectiveness','FiscalHealth', "Score", 'Region']]

matplotlib.rc_file_defaults()
sns.pairplot(dt1, hue="Region")

Linear regression

Import packages

import statsmodels.api as sm
import statsmodels.formula.api as smf
from sklearn.metrics import mean_squared_error
import sklearn

Correlation matrix

corr = dt[['PropertyRights', 'LaborFreedom', 'GovernmentIntegrity', 'JudicalEffectiveness','FiscalHealth', "Score"]].corr()
corr

	PropertyRights	LaborFreedom	GovernmentIntegrity	JudicalEffectiveness	FiscalHealth	Score
PropertyRights	1.000000	0.432746	0.866998	0.826805	0.329969	0.876601
LaborFreedom	0.432746	1.000000	0.413794	0.421694	0.104431	0.512976
GovernmentIntegrity	0.866998	0.413794	1.000000	0.888880	0.292240	0.818174
JudicalEffectiveness	0.826805	0.421694	0.888880	1.000000	0.287380	0.805825
FiscalHealth	0.329969	0.104431	0.292240	0.287380	1.000000	0.559395
Score	0.876601	0.512976	0.818174	0.805825	0.559395	1.000000

Heatmap of the correlation matrix:

sns.heatmap(corr, 
        xticklabels=corr.columns,
        yticklabels=corr.columns)

We split the dataset into training (0.8) and test set (0.2):

import numpy as np
msk = np.random.rand(len(dt)) < 0.8
train = dt[msk]
test = dt[~msk]

Linear regression having as dependent variable the Score and PropertyRights, LaborFreedom and FiscalHealth as explicative variables:

results = smf.ols('Score ~ PropertyRights + LaborFreedom + FiscalHealth', data=train).fit()
results.summary()

OLS Regression Results
Dep. Variable:	Score	R-squared:	0.886
Model:	OLS	Adj. R-squared:	0.883
Method:	Least Squares	F-statistic:	338.4
Date:	Wed, 30 Sep 2026	Prob (F-statistic):	1.72e-61
Time:	11:21:30	Log-Likelihood:	-360.77
No. Observations:	135	AIC:	729.5
Df Residuals:	131	BIC:	741.2
Df Model:	3
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	25.2289	1.444	17.475	0.000	22.373	28.085
PropertyRights	0.3658	0.018	19.932	0.000	0.329	0.402
LaborFreedom	0.1566	0.024	6.416	0.000	0.108	0.205
FiscalHealth	0.1068	0.010	10.487	0.000	0.087	0.127

Omnibus:	3.872	Durbin-Watson:	1.805
Prob(Omnibus):	0.144	Jarque-Bera (JB):	3.514
Skew:	-0.391	Prob(JB):	0.173
Kurtosis:	3.111	Cond. No.	505.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

We predict the score values using the test set:

pred = results.predict(test)
plt.scatter(test.Score, pred,  color='b')

Compute the mean squared error:

mean_squared_error(test.Score, pred)

## 16.08986805570031

We try to use a linear mixed model, considering as random effects the Region variable.

md = smf.mixedlm("Score ~ PropertyRights + LaborFreedom + FiscalHealth", train, groups="Region")
mdf = md.fit()
mdf.summary()

Model:	MixedLM	Dependent Variable:	Score
No. Observations:	135	Method:	REML
No. Groups:	5	Scale:	11.9069
Min. group size:	12	Log-Likelihood:	-369.3327
Max. group size:	37	Converged:	Yes
Mean group size:	27.0

	Coef.	Std.Err.	z	P>\|z\|	[0.025	0.975]
Intercept	24.080	1.640	14.684	0.000	20.866	27.294
PropertyRights	0.384	0.021	18.077	0.000	0.342	0.426
LaborFreedom	0.155	0.024	6.396	0.000	0.107	0.202
FiscalHealth	0.114	0.011	10.708	0.000	0.093	0.135
Region Var	1.360	0.447

See http://www.statsmodels.org/stable/index.html for other commands about the linear (mixed) model. Also, https://www.statsmodels.org/stable/examples/notebooks/generated/mixed_lm_example.html makes a comparison between R lmer and Statsmodels MixedLM.

Principal Component Analysis

Import packages:

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
import numpy as np

Standardize data:

features = ['PropertyRights', 'LaborFreedom', 'GovernmentIntegrity', 'JudicalEffectiveness','FiscalHealth']
# Separating out the features
x = dt.loc[:, features].values
# Separating out the target
y = dt.loc[:,'Score'].values
# Standardizing the features
x = StandardScaler().fit_transform(x)

Perform PCA considering \(2\) principal components:

pca = PCA(4)
projected = pca.fit_transform(x)

print(x.shape)

## (173, 5)

print(projected.shape)

## (173, 4)

Plot the first \(2\) principal components:

plt.scatter(projected[:, 0], projected[:, 1],
            c=y, edgecolor='none', alpha=0.5,
            cmap=plt.get_cmap('seismic', 10))
plt.xlabel('component 1')
plt.ylabel('component 2')
plt.colorbar()

## <matplotlib.colorbar.Colorbar object at 0x00000222FF9B34D0>

plt.plot(np.cumsum(pca.explained_variance_ratio_)) 
plt.xlabel("Number of component") 
plt.ylabel("Variance explained")
plt.xticks(range(4), [1,2,3,4])

## ([<matplotlib.axis.XTick object at 0x00000223109920D0>, <matplotlib.axis.XTick object at 0x00000223109C0550>, <matplotlib.axis.XTick object at 0x00000223109C0CD0>, <matplotlib.axis.XTick object at 0x00000223109C1450>], [Text(0, 0, '1'), Text(1, 0, '2'), Text(2, 0, '3'), Text(3, 0, '4')])