TakeHome_Ex04
Po Theodora
5/25/2020
Link to rpubs: https://rpubs.com/theodorapo/take-home_ex-04
1. Introduction
1.1 Overview
Brazil is the world’s fifth-largest country by area and the sixth most populous. Brazil is classified as an upper-middle income economy by the World Bank. As a developing country, Brazil has the largest share of global wealth in Latin America. It is considered an advanced emerging economy. It has the ninth largest GDP in the world by nominal, and eighth by PPP measures. Behind all this impressive figures, the spatial development of Brazil is highly unequal. The GDP per capita of the poorest municipality is R$3190.6. On the other hand, the GDP per capita of the richest municipality is R$314638. Half of the municipalities with GDP per capita less than R$16000 and the top 25% municipalities earn R$26155 and above.
1.2 Objective
In this take-home exercise, we will be determining the factors affecting the unequal development of Brazil at the municipality level by using the data provided. The specific task of the analysis are as follows:
1. Prepare a choropleth map showing the distribution of GDP per capita, 2016 at municipality level.
2. Calibrate an explanatory model to explain factors affecting the GDP per capita at the municipality level by using multiple linear regression method.
3. Prepare a choropleth map showing the distribution of the residual of the GDP per capita.
4. Calibrate an explanatory model to explain factors affecting the GDP per capita at the municipality level by using geographically weighted regression method.
5. Prepare a series of choropleth maps showing the outputs of the geographically weighted regression model.
2. Getting started
2.1 The data
We are provided with the first 2 data sets, and the last data set is retrived from the geobr package in r 1. BRAZIL_CITIES.csv. This data file consists of 81 columns and 5573 rows. Each row representing one municipality.
2. Data_Dictionary.csv. This file provides meta data of each columns in BRAZIL_CITIES.csv.
3. 2016 municipality boundary file
2.2 Importing and Installing packages
packages = c('olsrr', 'corrplot', 'ggpubr', 'sf', 'spdep', 'GWmodel', 'tmap', 'tidyverse', 'geobr', 'readr', 'anchors', 'DT', 'fitdistrplus', 'Orcs')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p,character.only = T)
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## print.stsls spdep
## summary.stsls spdep
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## residuals.gmsar spdep
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## coef.gmsar spdep
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## summary.gmsar spdep
## print.summary.gmsar spdep
## print.lagmess spdep
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## residuals.lagmess spdep
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## coef.lagmess spdep
## fitted.lagmess spdep
## logLik.lagmess spdep
## fitted.SFResult spdep
## print.SFResult spdep
## fitted.ME_res spdep
## print.ME_res spdep
## print.lagImpact spdep
## plot.lagImpact spdep
## summary.lagImpact spdep
## HPDinterval.lagImpact spdep
## print.summary.lagImpact spdep
## print.sarlm spdep
## summary.sarlm spdep
## residuals.sarlm spdep
## deviance.sarlm spdep
## coef.sarlm spdep
## vcov.sarlm spdep
## fitted.sarlm spdep
## logLik.sarlm spdep
## anova.sarlm spdep
## predict.sarlm spdep
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## as.data.frame.sarlm.pred spdep
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## summary.spautolm, summary.stsls, trW, vcov.sarlm, Wald1.sarlm## Welcome to GWmodel version 2.1-4.
## The new version of GWmodel 2.1-4 now is readyLoading required package: tmap
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## ## rgenoud (Version 5.8-3.0, Build Date: 2019-01-22)
## ## See http://sekhon.berkeley.edu/rgenoud for additional documentation.
## ## Please cite software as:
## ## Walter Mebane, Jr. and Jasjeet S. Sekhon. 2011.
## ## ``Genetic Optimization Using Derivatives: The rgenoud package for R.''
## ## Journal of Statistical Software, 42(11): 1-26.
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3.1 Importing Geospatial Data
3.1.1 Import mun data using geobr package
Brazil 2016 municipality boundary
mun <- read_municipality(code_muni= "all", year=2016)## Using year 2016## Loading data for the whole country. This might take a few minutes.##
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|======================================================================| 100%Plot the boundary of Brazil
no_axis <- theme(axis.title=element_blank(),
axis.text=element_blank(),
axis.ticks=element_blank())
ggplot() +
geom_sf(data=mun, fill="#2D3E50", color="#FEBF57", size=.15, show.legend = FALSE) +
labs(subtitle="Brazil", size=8) +
theme_minimal() +
no_axis
Check crs of mun
st_crs(mun)## Coordinate Reference System:
## User input: SIRGAS 2000
## wkt:
## GEOGCRS["SIRGAS 2000",
## DATUM["Sistema de Referencia Geocentrico para las AmericaS 2000",
## ELLIPSOID["GRS 1980",6378137,298.257222101,
## LENGTHUNIT["metre",1]]],
## PRIMEM["Greenwich",0,
## ANGLEUNIT["degree",0.0174532925199433]],
## CS[ellipsoidal,2],
## AXIS["geodetic latitude (Lat)",north,
## ORDER[1],
## ANGLEUNIT["degree",0.0174532925199433]],
## AXIS["geodetic longitude (Lon)",east,
## ORDER[2],
## ANGLEUNIT["degree",0.0174532925199433]],
## USAGE[
## SCOPE["unknown"],
## AREA["Latin America - SIRGAS 2000 by country"],
## BBOX[-59.87,-122.19,32.72,-25.28]],
## ID["EPSG",4674]]
The crs of brazil is set at 4674.
We will check if the geometry in mun is valid
all(st_is_valid(mun))## [1] FALSESince FALSE, we need to make sure geometry is valid
mun <- st_make_valid(mun)Now, check again if geometry is valid
all(st_is_valid(mun))## [1] TRUENext, we will check for any empty geometries
any(is.na(st_dimension(mun)))## [1] FALSE4. Aspatial Data Wrangling
4.1 Importing Aspatial Data
brazil <- read_delim("data/aspatial/BRAZIL_CITIES.csv", delim = ";")## Parsed with column specification:
## cols(
## .default = col_double(),
## CITY = col_character(),
## STATE = col_character(),
## AREA = col_number(),
## REGIAO_TUR = col_character(),
## CATEGORIA_TUR = col_character(),
## RURAL_URBAN = col_character(),
## GVA_MAIN = col_character()
## )## See spec(...) for full column specifications.After importing the data, we will need to check if the data is imported correctly.
We will use glimpse() to check.
glimpse(brazil)## Rows: 5,573
## Columns: 81
## $ CITY <chr> "Abadia De Goiás", "Abadia Dos Dourados", ...
## $ STATE <chr> "GO", "MG", "GO", "MG", "PA", "CE", "BA", ...
## $ CAPITAL <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ IBGE_RES_POP <dbl> 6876, 6704, 15757, 22690, 141100, 10496, 8...
## $ IBGE_RES_POP_BRAS <dbl> 6876, 6704, 15609, 22690, 141040, 10496, 8...
## $ IBGE_RES_POP_ESTR <dbl> 0, 0, 148, 0, 60, 0, 0, 0, 0, 0, 0, 16, 17...
## $ IBGE_DU <dbl> 2137, 2328, 4655, 7694, 31061, 2791, 2572,...
## $ IBGE_DU_URBAN <dbl> 1546, 1481, 3233, 6667, 19057, 1251, 1193,...
## $ IBGE_DU_RURAL <dbl> 591, 847, 1422, 1027, 12004, 1540, 1379, 1...
## $ IBGE_POP <dbl> 5300, 4154, 10656, 18464, 82956, 4538, 372...
## $ IBGE_1 <dbl> 69, 38, 139, 176, 1354, 98, 37, 167, 69, 1...
## $ `IBGE_1-4` <dbl> 318, 207, 650, 856, 5567, 323, 156, 733, 3...
## $ `IBGE_5-9` <dbl> 438, 260, 894, 1233, 7618, 421, 263, 978, ...
## $ `IBGE_10-14` <dbl> 517, 351, 1087, 1539, 8905, 483, 277, 927,...
## $ `IBGE_15-59` <dbl> 3542, 2709, 6896, 11979, 53516, 2631, 2319...
## $ `IBGE_60+` <dbl> 416, 589, 990, 2681, 5996, 582, 673, 803, ...
## $ IBGE_PLANTED_AREA <dbl> 319, 4479, 10307, 1862, 25200, 2598, 895, ...
## $ `IBGE_CROP_PRODUCTION_$` <dbl> 1843, 18017, 33085, 7502, 700872, 5234, 39...
## $ `IDHM Ranking 2010` <dbl> 1689, 2207, 2202, 1994, 3530, 3522, 4086, ...
## $ IDHM <dbl> 0.708, 0.690, 0.690, 0.698, 0.628, 0.628, ...
## $ IDHM_Renda <dbl> 0.687, 0.693, 0.671, 0.720, 0.579, 0.540, ...
## $ IDHM_Longevidade <dbl> 0.830, 0.839, 0.841, 0.848, 0.798, 0.748, ...
## $ IDHM_Educacao <dbl> 0.622, 0.563, 0.579, 0.556, 0.537, 0.612, ...
## $ LONG <dbl> -49.44055, -47.39683, -48.71881, -45.44619...
## $ LAT <dbl> -16.758812, -18.487565, -16.182672, -19.15...
## $ ALT <dbl> 893.60, 753.12, 1017.55, 644.74, 10.12, 40...
## $ PAY_TV <dbl> 360, 77, 227, 1230, 3389, 29, 952, 51, 55,...
## $ FIXED_PHONES <dbl> 842, 296, 720, 1716, 1218, 34, 335, 222, 3...
## $ AREA <dbl> 147.26, 881.06, 1045.13, 1817.07, 1610.65,...
## $ REGIAO_TUR <chr> NA, "Caminhos Do Cerrado", "Região Turísti...
## $ CATEGORIA_TUR <chr> NA, "D", "C", "D", "D", NA, "D", NA, NA, "...
## $ ESTIMATED_POP <dbl> 8583, 6972, 19614, 23223, 156292, 11663, 8...
## $ RURAL_URBAN <chr> "Urbano", "Rural Adjacente", "Rural Adjace...
## $ GVA_AGROPEC <dbl> 6.20, 50524.57, 42.84, 113824.60, 140463.7...
## $ GVA_INDUSTRY <dbl> 27991.25, 25917.70, 16728.30, 31002.62, 58...
## $ GVA_SERVICES <dbl> 74750.32, 62689.23, 138198.58, 172.33, 468...
## $ GVA_PUBLIC <dbl> 36915.04, 28083.79, 63396.20, 86081.41, 48...
## $ ` GVA_TOTAL ` <dbl> 145857.60, 167215.28, 261161.91, 403241.27...
## $ TAXES <dbl> 20554.20, 12873.50, 26822.58, 26994.09, 95...
## $ GDP <dbl> 166.41, 180.09, 287984.49, 430235.36, 1249...
## $ POP_GDP <dbl> 8053, 7037, 18427, 23574, 151934, 11483, 9...
## $ GDP_CAPITA <dbl> 20664.57, 25591.70, 15628.40, 18250.42, 82...
## $ GVA_MAIN <chr> "Demais serviços", "Demais serviços", "Dem...
## $ MUN_EXPENDIT <dbl> 28227691, 17909274, 37513019, NA, NA, NA, ...
## $ COMP_TOT <dbl> 284, 476, 288, 621, 931, 86, 191, 87, 285,...
## $ COMP_A <dbl> 5, 6, 5, 18, 4, 1, 6, 2, 5, 2, 0, 8, 3, 1,...
## $ COMP_B <dbl> 1, 6, 9, 1, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, ...
## $ COMP_C <dbl> 56, 30, 26, 40, 43, 4, 8, 3, 20, 4, 9, 40,...
## $ COMP_D <dbl> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, ...
## $ COMP_E <dbl> 2, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 2, ...
## $ COMP_F <dbl> 29, 34, 7, 20, 27, 6, 4, 0, 10, 2, 0, 25, ...
## $ COMP_G <dbl> 110, 190, 117, 303, 500, 48, 97, 71, 133, ...
## $ COMP_H <dbl> 26, 70, 12, 62, 16, 2, 5, 0, 18, 8, 1, 67,...
## $ COMP_I <dbl> 4, 28, 57, 30, 31, 10, 5, 1, 14, 3, 0, 25,...
## $ COMP_J <dbl> 5, 11, 2, 9, 6, 2, 3, 1, 8, 1, 1, 9, 5, 14...
## $ COMP_K <dbl> 0, 0, 1, 6, 1, 0, 1, 0, 0, 1, 0, 4, 3, 3, ...
## $ COMP_L <dbl> 2, 4, 0, 4, 1, 0, 0, 0, 4, 0, 0, 7, 4, 4, ...
## $ COMP_M <dbl> 10, 15, 7, 28, 22, 2, 5, 0, 11, 4, 2, 26, ...
## $ COMP_N <dbl> 12, 29, 15, 27, 16, 3, 5, 1, 26, 0, 1, 16,...
## $ COMP_O <dbl> 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 6, 2, 4, 2, ...
## $ COMP_P <dbl> 6, 9, 11, 15, 155, 0, 8, 0, 8, 1, 6, 14, 1...
## $ COMP_Q <dbl> 6, 14, 5, 19, 33, 2, 1, 2, 9, 3, 0, 13, 22...
## $ COMP_R <dbl> 1, 6, 1, 9, 15, 0, 2, 0, 4, 0, 0, 4, 6, 6,...
## $ COMP_S <dbl> 5, 19, 8, 27, 56, 4, 38, 4, 12, 3, 4, 23, ...
## $ COMP_T <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ COMP_U <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ HOTELS <dbl> NA, NA, 1, NA, NA, NA, 1, NA, NA, NA, NA, ...
## $ BEDS <dbl> NA, NA, 34, NA, NA, NA, 24, NA, NA, NA, NA...
## $ Pr_Agencies <dbl> NA, NA, 1, 2, 2, NA, NA, 1, 0, 0, 0, 1, 0,...
## $ Pu_Agencies <dbl> NA, NA, 1, 2, 4, NA, NA, 0, 1, 1, 1, 2, 1,...
## $ Pr_Bank <dbl> NA, NA, 1, 2, 2, NA, NA, 1, 0, 0, 0, 1, 0,...
## $ Pu_Bank <dbl> NA, NA, 1, 2, 4, NA, NA, 0, 1, 1, 1, 2, 1,...
## $ Pr_Assets <dbl> NA, NA, 33724584, 44974716, 76181384, NA, ...
## $ Pu_Assets <dbl> NA, NA, 67091904, 371922572, 800078483, NA...
## $ Cars <dbl> 2158, 2227, 2838, 6928, 5277, 553, 896, 61...
## $ Motorcycles <dbl> 1246, 1142, 1426, 2953, 25661, 1674, 696, ...
## $ Wheeled_tractor <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, ...
## $ UBER <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA...
## $ MAC <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA...
## $ `WAL-MART` <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA...
## $ POST_OFFICES <dbl> 1, 1, 3, 4, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, ...head(brazil$LONG)## [1] -49.44055 -47.39683 -48.71881 -45.44619 -48.88440 -39.04755head(brazil$LAT)## [1] -16.758812 -18.487565 -16.182672 -19.155848 -1.723470 -7.356977Convert columns to factor types
brazil$STATE <- factor(brazil$STATE)
brazil$CAPITAL <- factor(brazil$CAPITAL)
brazil$REGIAO_TUR <- factor(brazil$REGIAO_TUR)
brazil$CATEGORIA_TUR <- factor(brazil$CATEGORIA_TUR)
brazil$UBER <- factor(brazil$UBER)Check the summary of brazil
summary(brazil)## CITY STATE CAPITAL IBGE_RES_POP
## Length:5573 MG : 853 0:5546 Min. : 805
## Class :character SP : 645 1: 27 1st Qu.: 5235
## Mode :character RS : 498 Median : 10934
## BA : 418 Mean : 34278
## PR : 399 3rd Qu.: 23424
## SC : 295 Max. :11253503
## (Other):2465 NA's :8
## IBGE_RES_POP_BRAS IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN
## Min. : 805 Min. : 0.0 Min. : 239 Min. : 60
## 1st Qu.: 5230 1st Qu.: 0.0 1st Qu.: 1572 1st Qu.: 874
## Median : 10926 Median : 0.0 Median : 3174 Median : 1846
## Mean : 34200 Mean : 77.5 Mean : 10303 Mean : 8859
## 3rd Qu.: 23390 3rd Qu.: 10.0 3rd Qu.: 6726 3rd Qu.: 4624
## Max. :11133776 Max. :119727.0 Max. :3576148 Max. :3548433
## NA's :8 NA's :8 NA's :10 NA's :10
## IBGE_DU_RURAL IBGE_POP IBGE_1 IBGE_1-4
## Min. : 3 Min. : 174 Min. : 0.0 Min. : 5
## 1st Qu.: 487 1st Qu.: 2801 1st Qu.: 38.0 1st Qu.: 158
## Median : 931 Median : 6170 Median : 92.0 Median : 376
## Mean : 1463 Mean : 27595 Mean : 383.3 Mean : 1544
## 3rd Qu.: 1832 3rd Qu.: 15302 3rd Qu.: 232.0 3rd Qu.: 951
## Max. :33809 Max. :10463636 Max. :129464.0 Max. :514794
## NA's :81 NA's :8 NA's :8 NA's :8
## IBGE_5-9 IBGE_10-14 IBGE_15-59 IBGE_60+
## Min. : 7 Min. : 12 Min. : 94 Min. : 29
## 1st Qu.: 220 1st Qu.: 259 1st Qu.: 1734 1st Qu.: 341
## Median : 516 Median : 588 Median : 3841 Median : 722
## Mean : 2069 Mean : 2381 Mean : 18212 Mean : 3004
## 3rd Qu.: 1300 3rd Qu.: 1478 3rd Qu.: 9628 3rd Qu.: 1724
## Max. :684443 Max. :783702 Max. :7058221 Max. :1293012
## NA's :8 NA's :8 NA's :8 NA's :8
## IBGE_PLANTED_AREA IBGE_CROP_PRODUCTION_$ IDHM Ranking 2010 IDHM
## Min. : 0.0 Min. : 0 Min. : 1 Min. :0.4180
## 1st Qu.: 910.2 1st Qu.: 2326 1st Qu.:1392 1st Qu.:0.5990
## Median : 3471.5 Median : 13846 Median :2783 Median :0.6650
## Mean : 14179.9 Mean : 57384 Mean :2783 Mean :0.6592
## 3rd Qu.: 11194.2 3rd Qu.: 55619 3rd Qu.:4174 3rd Qu.:0.7180
## Max. :1205669.0 Max. :3274885 Max. :5565 Max. :0.8620
## NA's :3 NA's :3 NA's :8 NA's :8
## IDHM_Renda IDHM_Longevidade IDHM_Educacao LONG
## Min. :0.4000 Min. :0.6720 Min. :0.2070 Min. :-72.92
## 1st Qu.:0.5720 1st Qu.:0.7690 1st Qu.:0.4900 1st Qu.:-50.87
## Median :0.6540 Median :0.8080 Median :0.5600 Median :-46.52
## Mean :0.6429 Mean :0.8016 Mean :0.5591 Mean :-46.23
## 3rd Qu.:0.7070 3rd Qu.:0.8360 3rd Qu.:0.6310 3rd Qu.:-41.40
## Max. :0.8910 Max. :0.8940 Max. :0.8250 Max. :-32.44
## NA's :8 NA's :8 NA's :8 NA's :9
## LAT ALT PAY_TV FIXED_PHONES
## Min. :-33.688 Min. : 0.0 Min. : 1 Min. : 3
## 1st Qu.:-22.838 1st Qu.: 169.8 1st Qu.: 88 1st Qu.: 119
## Median :-18.089 Median : 406.5 Median : 247 Median : 327
## Mean :-16.444 Mean : 893.8 Mean : 3094 Mean : 6567
## 3rd Qu.: -8.489 3rd Qu.: 628.9 3rd Qu.: 815 3rd Qu.: 1151
## Max. : 4.585 Max. :874579.0 Max. :2047668 Max. :5543127
## NA's :9 NA's :9 NA's :3 NA's :3
## AREA REGIAO_TUR CATEGORIA_TUR
## Min. : 3.57 Corredores Das Águas: 59 A : 51
## 1st Qu.: 204.44 Vale Do Contestado : 45 B : 168
## Median : 416.59 Amazônia Atlântica : 40 C : 521
## Mean : 1517.44 Araguaia-Tocantins : 39 D :1892
## 3rd Qu.: 1026.57 Cariri : 37 E : 653
## Max. :159533.33 (Other) :3065 NA's:2288
## NA's :3 NA's :2288
## ESTIMATED_POP RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY
## Min. : 786 Length:5573 Min. : 0 Min. : 1
## 1st Qu.: 5454 Class :character 1st Qu.: 4189 1st Qu.: 1726
## Median : 11590 Mode :character Median : 20426 Median : 7424
## Mean : 37432 Mean : 47271 Mean : 175928
## 3rd Qu.: 25296 3rd Qu.: 51227 3rd Qu.: 41022
## Max. :12176866 Max. :1402282 Max. :63306755
## NA's :3 NA's :3 NA's :3
## GVA_SERVICES GVA_PUBLIC GVA_TOTAL TAXES
## Min. : 2 Min. : 7 Min. : 17 Min. : -14159
## 1st Qu.: 10112 1st Qu.: 17267 1st Qu.: 42253 1st Qu.: 1305
## Median : 31211 Median : 35866 Median : 119492 Median : 5100
## Mean : 489451 Mean : 123768 Mean : 832987 Mean : 118864
## 3rd Qu.: 115406 3rd Qu.: 89245 3rd Qu.: 313963 3rd Qu.: 22197
## Max. :464656988 Max. :41902893 Max. :569910503 Max. :117125387
## NA's :3 NA's :3 NA's :3 NA's :3
## GDP POP_GDP GDP_CAPITA GVA_MAIN
## Min. : 15 Min. : 815 Min. : 3191 Length:5573
## 1st Qu.: 43709 1st Qu.: 5483 1st Qu.: 9058 Class :character
## Median : 125153 Median : 11578 Median : 15870 Mode :character
## Mean : 954584 Mean : 36998 Mean : 21126
## 3rd Qu.: 329539 3rd Qu.: 25085 3rd Qu.: 26155
## Max. :687035890 Max. :12038175 Max. :314638
## NA's :3 NA's :3 NA's :3
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B
## Min. :1.421e+06 Min. : 6.0 Min. : 0.00 Min. : 0.000
## 1st Qu.:1.573e+07 1st Qu.: 68.0 1st Qu.: 1.00 1st Qu.: 0.000
## Median :2.746e+07 Median : 162.0 Median : 2.00 Median : 0.000
## Mean :1.043e+08 Mean : 906.8 Mean : 18.25 Mean : 1.852
## 3rd Qu.:5.666e+07 3rd Qu.: 448.0 3rd Qu.: 8.00 3rd Qu.: 2.000
## Max. :4.577e+10 Max. :530446.0 Max. :1948.00 Max. :274.000
## NA's :1492 NA's :3 NA's :3 NA's :3
## COMP_C COMP_D COMP_E COMP_F
## Min. : 0.00 Min. : 0.0000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 3.00 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.: 1.00
## Median : 11.00 Median : 0.0000 Median : 0.000 Median : 4.00
## Mean : 73.44 Mean : 0.4262 Mean : 2.029 Mean : 43.26
## 3rd Qu.: 39.00 3rd Qu.: 0.0000 3rd Qu.: 1.000 3rd Qu.: 15.00
## Max. :31566.00 Max. :332.0000 Max. :657.000 Max. :25222.00
## NA's :3 NA's :3 NA's :3 NA's :3
## COMP_G COMP_H COMP_I COMP_J
## Min. : 1.0 Min. : 0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 32.0 1st Qu.: 1 1st Qu.: 2.00 1st Qu.: 0.00
## Median : 74.5 Median : 7 Median : 7.00 Median : 1.00
## Mean : 348.0 Mean : 41 Mean : 55.88 Mean : 24.74
## 3rd Qu.: 199.0 3rd Qu.: 25 3rd Qu.: 24.00 3rd Qu.: 5.00
## Max. :150633.0 Max. :19515 Max. :29290.00 Max. :38720.00
## NA's :3 NA's :3 NA's :3 NA's :3
## COMP_K COMP_L COMP_M COMP_N
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.0
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 1.00 1st Qu.: 1.0
## Median : 0.00 Median : 0.00 Median : 4.00 Median : 4.0
## Mean : 15.55 Mean : 15.14 Mean : 51.29 Mean : 83.7
## 3rd Qu.: 2.00 3rd Qu.: 3.00 3rd Qu.: 13.00 3rd Qu.: 14.0
## Max. :23738.00 Max. :14003.00 Max. :49181.00 Max. :76757.0
## NA's :3 NA's :3 NA's :3 NA's :3
## COMP_O COMP_P COMP_Q COMP_R
## Min. : 0.000 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 2.000 1st Qu.: 2.00 1st Qu.: 1.00 1st Qu.: 0.00
## Median : 2.000 Median : 6.00 Median : 3.00 Median : 2.00
## Mean : 3.269 Mean : 30.96 Mean : 34.15 Mean : 12.18
## 3rd Qu.: 3.000 3rd Qu.: 17.00 3rd Qu.: 12.00 3rd Qu.: 6.00
## Max. :204.000 Max. :16030.00 Max. :22248.00 Max. :6687.00
## NA's :3 NA's :3 NA's :3 NA's :3
## COMP_S COMP_T COMP_U HOTELS
## Min. : 0.00 Min. :0 Min. : 0.00000 Min. : 1.000
## 1st Qu.: 5.00 1st Qu.:0 1st Qu.: 0.00000 1st Qu.: 1.000
## Median : 12.00 Median :0 Median : 0.00000 Median : 1.000
## Mean : 51.61 Mean :0 Mean : 0.05027 Mean : 3.131
## 3rd Qu.: 31.00 3rd Qu.:0 3rd Qu.: 0.00000 3rd Qu.: 3.000
## Max. :24832.00 Max. :0 Max. :123.00000 Max. :97.000
## NA's :3 NA's :3 NA's :3 NA's :4686
## BEDS Pr_Agencies Pu_Agencies Pr_Bank
## Min. : 2.0 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 40.0 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 0.000
## Median : 82.0 Median : 1.000 Median : 2.000 Median : 1.000
## Mean : 257.5 Mean : 3.383 Mean : 2.829 Mean : 1.312
## 3rd Qu.: 200.0 3rd Qu.: 2.000 3rd Qu.: 2.000 3rd Qu.: 2.000
## Max. :13247.0 Max. :1693.000 Max. :626.000 Max. :83.000
## NA's :4686 NA's :2231 NA's :2231 NA's :2231
## Pu_Bank Pr_Assets Pu_Assets Cars
## Min. :0.00 Min. :0.000e+00 Min. :0.000e+00 Min. : 2
## 1st Qu.:1.00 1st Qu.:0.000e+00 1st Qu.:4.047e+07 1st Qu.: 602
## Median :2.00 Median :3.231e+07 Median :1.339e+08 Median : 1438
## Mean :1.58 Mean :9.180e+09 Mean :6.005e+09 Mean : 9859
## 3rd Qu.:2.00 3rd Qu.:1.148e+08 3rd Qu.:4.970e+08 3rd Qu.: 4086
## Max. :8.00 Max. :1.947e+13 Max. :8.016e+12 Max. :5740995
## NA's :2231 NA's :2231 NA's :2231 NA's :11
## Motorcycles Wheeled_tractor UBER MAC
## Min. : 4 Min. : 0.000 1 : 125 Min. : 1.000
## 1st Qu.: 591 1st Qu.: 0.000 NA's:5448 1st Qu.: 1.000
## Median : 1285 Median : 0.000 Median : 2.000
## Mean : 4879 Mean : 5.754 Mean : 4.277
## 3rd Qu.: 3294 3rd Qu.: 1.000 3rd Qu.: 3.000
## Max. :1134570 Max. :3236.000 Max. :130.000
## NA's :11 NA's :11 NA's :5407
## WAL-MART POST_OFFICES
## Min. : 1.000 Min. : 1.000
## 1st Qu.: 1.000 1st Qu.: 1.000
## Median : 1.000 Median : 1.000
## Mean : 2.059 Mean : 2.081
## 3rd Qu.: 1.750 3rd Qu.: 2.000
## Max. :26.000 Max. :225.000
## NA's :5471 NA's :120
### 4.2 Check for NAs From the summary of brazil, we have identified that there are 9 NAs for LATLONG value
We will now check which are the rows with NA values for LATLONG data
brazil[!complete.cases(brazil$LAT),]## # A tibble: 9 x 81
## CITY STATE CAPITAL IBGE_RES_POP IBGE_RES_POP_BR~ IBGE_RES_POP_ES~ IBGE_DU
## <chr> <fct> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 Baln~ SC 0 NA NA NA NA
## 2 Lago~ RS 0 NA NA NA NA
## 3 Moju~ PA 0 NA NA NA NA
## 4 Para~ MS 0 NA NA NA NA
## 5 Pesc~ SC 0 NA NA NA NA
## 6 Pinh~ RS 0 2130 2130 0 745
## 7 Pint~ RS 0 NA NA NA NA
## 8 Sant~ BA 0 9648 9648 0 2891
## 9 São ~ PE 0 NA NA NA NA
## # ... with 74 more variables: IBGE_DU_URBAN <dbl>, IBGE_DU_RURAL <dbl>,
## # IBGE_POP <dbl>, IBGE_1 <dbl>, `IBGE_1-4` <dbl>, `IBGE_5-9` <dbl>,
## # `IBGE_10-14` <dbl>, `IBGE_15-59` <dbl>, `IBGE_60+` <dbl>,
## # IBGE_PLANTED_AREA <dbl>, `IBGE_CROP_PRODUCTION_$` <dbl>, `IDHM Ranking
## # 2010` <dbl>, IDHM <dbl>, IDHM_Renda <dbl>, IDHM_Longevidade <dbl>,
## # IDHM_Educacao <dbl>, LONG <dbl>, LAT <dbl>, ALT <dbl>, PAY_TV <dbl>,
## # FIXED_PHONES <dbl>, AREA <dbl>, REGIAO_TUR <fct>, CATEGORIA_TUR <fct>,
## # ESTIMATED_POP <dbl>, RURAL_URBAN <chr>, GVA_AGROPEC <dbl>,
## # GVA_INDUSTRY <dbl>, GVA_SERVICES <dbl>, GVA_PUBLIC <dbl>, ` GVA_TOTAL
## # ` <dbl>, TAXES <dbl>, GDP <dbl>, POP_GDP <dbl>, GDP_CAPITA <dbl>,
## # GVA_MAIN <chr>, MUN_EXPENDIT <dbl>, COMP_TOT <dbl>, COMP_A <dbl>,
## # COMP_B <dbl>, COMP_C <dbl>, COMP_D <dbl>, COMP_E <dbl>, COMP_F <dbl>,
## # COMP_G <dbl>, COMP_H <dbl>, COMP_I <dbl>, COMP_J <dbl>, COMP_K <dbl>,
## # COMP_L <dbl>, COMP_M <dbl>, COMP_N <dbl>, COMP_O <dbl>, COMP_P <dbl>,
## # COMP_Q <dbl>, COMP_R <dbl>, COMP_S <dbl>, COMP_T <dbl>, COMP_U <dbl>,
## # HOTELS <dbl>, BEDS <dbl>, Pr_Agencies <dbl>, Pu_Agencies <dbl>,
## # Pr_Bank <dbl>, Pu_Bank <dbl>, Pr_Assets <dbl>, Pu_Assets <dbl>, Cars <dbl>,
## # Motorcycles <dbl>, Wheeled_tractor <dbl>, UBER <fct>, MAC <dbl>,
## # `WAL-MART` <dbl>, POST_OFFICES <dbl>We have identified that the cities that do not have LATLONG are:
1. Balneário Rincão
2. Lagoa Dos Patos
3. Mojuí Dos Campos
4. Paraíso Das Águas
5. Pescaria Brava
6. Pinhal Da Serra
7. Pinto Bandeira
8. Santa Terezinha
9. São Caetano
We will now fill the LATLONG values for the above cities, using https://pt.db-city.com/ to find the values.
Replace NA value in LATLONG
brazil$LONG[brazil$CITY == "Balneário Rincão"] <- -49.2361
brazil$LAT[brazil$CITY == "Balneário Rincão"] <- -28.8344
brazil$LONG[brazil$CITY == "Lagoa Dos Patos"] <- --51.4725
brazil$LAT[brazil$CITY == "Lagoa Dos Patos"] <- -31.0697
brazil$LONG[brazil$CITY == "Mojuí Dos Campos"] <- -54.6431
brazil$LAT[brazil$CITY == "Mojuí Dos Campos"] <- -2.68472
brazil$LONG[brazil$CITY == "Paraíso Das Águas"] <- -53.0102
brazil$LAT[brazil$CITY == "Paraíso Das Águas"] <- -19.0257
brazil$LONG[brazil$CITY == "Pescaria Brava"] <- -48.8956
brazil$LAT[brazil$CITY == "Pescaria Brava"] <- -28.4247
brazil$LONG[brazil$CITY == "Pinhal Da Serra"] <- -51.1733
brazil$LAT[brazil$CITY == "Pinhal Da Serra"] <- -27.8747
brazil$LONG[brazil$CITY == "Pinto Bandeira"] <- -51.4503
brazil$LAT[brazil$CITY == "Pinto Bandeira"] <- -29.0978
brazil$LONG[brazil$CITY == "Santa Terezinha"] <- -39.5184
brazil$LAT[brazil$CITY == "Santa Terezinha"] <- -12.7498
brazil$LONG[brazil$CITY == "São Caetano"] <- -36.1459
brazil$LAT[brazil$CITY == "São Caetano"] <- -8.33Comparing between cities in brazils and mun, we have identified that there are 2 CITIES which exist in brazil, but not in mun. The two cities are Santa Terezinha and São Caetano. Hence, we will remove these two cities for consistency.
brazil <- brazil%>%
filter(CITY!="Santa Terezinha") %>%
filter(CITY!="São Caetano")Check the summary of brazil again
summary(brazil)## CITY STATE CAPITAL IBGE_RES_POP
## Length:5568 MG : 853 0:5541 Min. : 805
## Class :character SP : 645 1: 27 1st Qu.: 5231
## Mode :character RS : 498 Median : 10936
## BA : 417 Mean : 34296
## PR : 399 3rd Qu.: 23513
## SC : 294 Max. :11253503
## (Other):2462 NA's :7
## IBGE_RES_POP_BRAS IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN
## Min. : 805 Min. : 0.00 Min. : 239 Min. : 60
## 1st Qu.: 5223 1st Qu.: 0.00 1st Qu.: 1572 1st Qu.: 874
## Median : 10934 Median : 0.00 Median : 3178 Median : 1850
## Mean : 34218 Mean : 77.56 Mean : 10308 Mean : 8864
## 3rd Qu.: 23397 3rd Qu.: 10.00 3rd Qu.: 6727 3rd Qu.: 4628
## Max. :11133776 Max. :119727.00 Max. :3576148 Max. :3548433
## NA's :7 NA's :7 NA's :9 NA's :9
## IBGE_DU_RURAL IBGE_POP IBGE_1 IBGE_1-4
## Min. : 3.0 Min. : 174 Min. : 0.0 Min. : 5
## 1st Qu.: 486.8 1st Qu.: 2802 1st Qu.: 38.0 1st Qu.: 158
## Median : 931.0 Median : 6177 Median : 92.0 Median : 377
## Mean : 1462.6 Mean : 27612 Mean : 383.5 Mean : 1546
## 3rd Qu.: 1831.2 3rd Qu.: 15306 3rd Qu.: 232.0 3rd Qu.: 952
## Max. :33809.0 Max. :10463636 Max. :129464.0 Max. :514794
## NA's :80 NA's :7 NA's :7 NA's :7
## IBGE_5-9 IBGE_10-14 IBGE_15-59 IBGE_60+
## Min. : 7 Min. : 12 Min. : 94 Min. : 29
## 1st Qu.: 220 1st Qu.: 260 1st Qu.: 1735 1st Qu.: 341
## Median : 516 Median : 589 Median : 3842 Median : 723
## Mean : 2071 Mean : 2383 Mean : 18223 Mean : 3006
## 3rd Qu.: 1301 3rd Qu.: 1479 3rd Qu.: 9633 3rd Qu.: 1725
## Max. :684443 Max. :783702 Max. :7058221 Max. :1293012
## NA's :7 NA's :7 NA's :7 NA's :7
## IBGE_PLANTED_AREA IBGE_CROP_PRODUCTION_$ IDHM Ranking 2010 IDHM
## Min. : 0.0 Min. : 0 Min. : 1 Min. :0.4180
## 1st Qu.: 910.2 1st Qu.: 2328 1st Qu.:1391 1st Qu.:0.5990
## Median : 3471.5 Median : 13846 Median :2782 Median :0.6650
## Mean : 14180.2 Mean : 57389 Mean :2783 Mean :0.6592
## 3rd Qu.: 11173.2 3rd Qu.: 55594 3rd Qu.:4174 3rd Qu.:0.7180
## Max. :1205669.0 Max. :3274885 Max. :5565 Max. :0.8620
## NA's :2 NA's :2 NA's :6 NA's :6
## IDHM_Renda IDHM_Longevidade IDHM_Educacao LONG
## Min. :0.4000 Min. :0.6720 Min. :0.2070 Min. :-72.92
## 1st Qu.:0.5720 1st Qu.:0.7690 1st Qu.:0.4900 1st Qu.:-50.87
## Median :0.6540 Median :0.8080 Median :0.5600 Median :-46.52
## Mean :0.6429 Mean :0.8016 Mean :0.5591 Mean :-46.20
## 3rd Qu.:0.7070 3rd Qu.:0.8360 3rd Qu.:0.6310 3rd Qu.:-41.40
## Max. :0.8910 Max. :0.8940 Max. :0.8250 Max. : 51.47
## NA's :6 NA's :6 NA's :6
## LAT ALT PAY_TV FIXED_PHONES
## Min. :-33.688 Min. : 0.0 Min. : 1.0 Min. : 3
## 1st Qu.:-22.845 1st Qu.: 169.4 1st Qu.: 88.0 1st Qu.: 118
## Median :-18.107 Median : 406.4 Median : 247.0 Median : 328
## Mean :-16.457 Mean : 894.0 Mean : 3095.8 Mean : 6570
## 3rd Qu.: -8.495 3rd Qu.: 628.8 3rd Qu.: 815.5 3rd Qu.: 1151
## Max. : 4.585 Max. :874579.0 Max. :2047668.0 Max. :5543127
## NA's :7 NA's :1 NA's :1
## AREA REGIAO_TUR CATEGORIA_TUR
## Min. : 3.57 Corredores Das Águas: 59 A : 51
## 1st Qu.: 204.44 Vale Do Contestado : 45 B : 168
## Median : 415.86 Amazônia Atlântica : 40 C : 521
## Mean : 1517.07 Araguaia-Tocantins : 39 D :1890
## 3rd Qu.: 1026.57 Cariri : 37 E : 653
## Max. :159533.33 (Other) :3063 NA's:2285
## NA's :2 NA's :2285
## ESTIMATED_POP RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY
## Min. : 786 Length:5568 Min. : 0 Min. : 1
## 1st Qu.: 5452 Class :character 1st Qu.: 4193 1st Qu.: 1725
## Median : 11591 Mode :character Median : 20432 Median : 7428
## Mean : 37447 Mean : 47285 Mean : 176050
## 3rd Qu.: 25301 3rd Qu.: 51227 3rd Qu.: 41240
## Max. :12176866 Max. :1402282 Max. :63306755
## NA's :1 NA's :2 NA's :2
## GVA_SERVICES GVA_PUBLIC GVA_TOTAL TAXES
## Min. : 2 Min. : 7 Min. : 17 Min. : -14159
## 1st Qu.: 10107 1st Qu.: 17254 1st Qu.: 42223 1st Qu.: 1305
## Median : 31214 Median : 35838 Median : 119492 Median : 5108
## Mean : 489787 Mean : 123829 Mean : 833504 Mean : 118947
## 3rd Qu.: 115503 3rd Qu.: 89301 3rd Qu.: 314139 3rd Qu.: 22208
## Max. :464656988 Max. :41902893 Max. :569910503 Max. :117125387
## NA's :2 NA's :2 NA's :2 NA's :2
## GDP POP_GDP GDP_CAPITA GVA_MAIN
## Min. : 15 Min. : 815 Min. : 3191 Length:5568
## 1st Qu.: 43706 1st Qu.: 5480 1st Qu.: 9062 Class :character
## Median : 125153 Median : 11584 Median : 15870 Mode :character
## Mean : 955185 Mean : 37018 Mean : 21132
## 3rd Qu.: 329764 3rd Qu.: 25098 3rd Qu.: 26156
## Max. :687035890 Max. :12038175 Max. :314638
## NA's :2 NA's :2 NA's :2
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B
## Min. :1.421e+06 Min. : 6.0 Min. : 0.00 Min. : 0.000
## 1st Qu.:1.573e+07 1st Qu.: 68.0 1st Qu.: 1.00 1st Qu.: 0.000
## Median :2.748e+07 Median : 162.0 Median : 2.00 Median : 0.000
## Mean :1.044e+08 Mean : 907.3 Mean : 18.27 Mean : 1.853
## 3rd Qu.:5.678e+07 3rd Qu.: 448.8 3rd Qu.: 8.00 3rd Qu.: 2.000
## Max. :4.577e+10 Max. :530446.0 Max. :1948.00 Max. :274.000
## NA's :1491 NA's :2 NA's :2 NA's :2
## COMP_C COMP_D COMP_E COMP_F
## Min. : 0.00 Min. : 0.0000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 3.00 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.: 1.00
## Median : 11.00 Median : 0.0000 Median : 0.000 Median : 4.00
## Mean : 73.49 Mean : 0.4265 Mean : 2.031 Mean : 43.29
## 3rd Qu.: 39.00 3rd Qu.: 0.0000 3rd Qu.: 1.000 3rd Qu.: 15.00
## Max. :31566.00 Max. :332.0000 Max. :657.000 Max. :25222.00
## NA's :2 NA's :2 NA's :2 NA's :2
## COMP_G COMP_H COMP_I COMP_J
## Min. : 1.0 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 32.0 1st Qu.: 1.00 1st Qu.: 2.00 1st Qu.: 0.00
## Median : 75.0 Median : 7.00 Median : 7.00 Median : 1.00
## Mean : 348.2 Mean : 41.02 Mean : 55.91 Mean : 24.76
## 3rd Qu.: 199.8 3rd Qu.: 25.00 3rd Qu.: 24.00 3rd Qu.: 5.00
## Max. :150633.0 Max. :19515.00 Max. :29290.00 Max. :38720.00
## NA's :2 NA's :2 NA's :2 NA's :2
## COMP_K COMP_L COMP_M COMP_N
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 1.00 1st Qu.: 1.00
## Median : 0.00 Median : 0.00 Median : 4.00 Median : 4.00
## Mean : 15.56 Mean : 15.15 Mean : 51.33 Mean : 83.76
## 3rd Qu.: 2.00 3rd Qu.: 3.00 3rd Qu.: 13.00 3rd Qu.: 14.00
## Max. :23738.00 Max. :14003.00 Max. :49181.00 Max. :76757.00
## NA's :2 NA's :2 NA's :2 NA's :2
## COMP_O COMP_P COMP_Q COMP_R
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 2.00 1st Qu.: 2.00 1st Qu.: 1.00 1st Qu.: 0.00
## Median : 2.00 Median : 6.00 Median : 3.00 Median : 2.00
## Mean : 3.27 Mean : 30.98 Mean : 34.17 Mean : 12.19
## 3rd Qu.: 3.00 3rd Qu.: 17.00 3rd Qu.: 12.00 3rd Qu.: 6.00
## Max. :204.00 Max. :16030.00 Max. :22248.00 Max. :6687.00
## NA's :2 NA's :2 NA's :2 NA's :2
## COMP_S COMP_T COMP_U HOTELS
## Min. : 0.00 Min. :0 Min. : 0.00000 Min. : 1.000
## 1st Qu.: 5.00 1st Qu.:0 1st Qu.: 0.00000 1st Qu.: 1.000
## Median : 12.00 Median :0 Median : 0.00000 Median : 1.000
## Mean : 51.64 Mean :0 Mean : 0.05031 Mean : 3.131
## 3rd Qu.: 31.00 3rd Qu.:0 3rd Qu.: 0.00000 3rd Qu.: 3.000
## Max. :24832.00 Max. :0 Max. :123.00000 Max. :97.000
## NA's :2 NA's :2 NA's :2 NA's :4681
## BEDS Pr_Agencies Pu_Agencies Pr_Bank
## Min. : 2.0 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 40.0 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 0.000
## Median : 82.0 Median : 1.000 Median : 2.000 Median : 1.000
## Mean : 257.5 Mean : 3.383 Mean : 2.829 Mean : 1.312
## 3rd Qu.: 200.0 3rd Qu.: 2.000 3rd Qu.: 2.000 3rd Qu.: 2.000
## Max. :13247.0 Max. :1693.000 Max. :626.000 Max. :83.000
## NA's :4681 NA's :2226 NA's :2226 NA's :2226
## Pu_Bank Pr_Assets Pu_Assets Cars
## Min. :0.00 Min. :0.000e+00 Min. :0.000e+00 Min. : 2
## 1st Qu.:1.00 1st Qu.:0.000e+00 1st Qu.:4.047e+07 1st Qu.: 602
## Median :2.00 Median :3.231e+07 Median :1.339e+08 Median : 1440
## Mean :1.58 Mean :9.180e+09 Mean :6.005e+09 Mean : 9864
## 3rd Qu.:2.00 3rd Qu.:1.148e+08 3rd Qu.:4.970e+08 3rd Qu.: 4088
## Max. :8.00 Max. :1.947e+13 Max. :8.016e+12 Max. :5740995
## NA's :2226 NA's :2226 NA's :2226 NA's :9
## Motorcycles Wheeled_tractor UBER MAC
## Min. : 4 Min. : 0.000 1 : 125 Min. : 1.000
## 1st Qu.: 591 1st Qu.: 0.000 NA's:5443 1st Qu.: 1.000
## Median : 1285 Median : 0.000 Median : 2.000
## Mean : 4881 Mean : 5.756 Mean : 4.277
## 3rd Qu.: 3297 3rd Qu.: 1.000 3rd Qu.: 3.000
## Max. :1134570 Max. :3236.000 Max. :130.000
## NA's :9 NA's :9 NA's :5402
## WAL-MART POST_OFFICES
## Min. : 1.000 Min. : 1.000
## 1st Qu.: 1.000 1st Qu.: 1.000
## Median : 1.000 Median : 1.000
## Mean : 2.059 Mean : 2.081
## 3rd Qu.: 1.750 3rd Qu.: 2.000
## Max. :26.000 Max. :225.000
## NA's :5466 NA's :119
We have also identified that there are NA values for GDP_CAPITA, and we will remove these NA values, as it is hard to assign a value to it.
brazil <- brazil%>%
filter(!is.na(`GDP_CAPITA`))
summary(brazil)## CITY STATE CAPITAL IBGE_RES_POP
## Length:5566 MG : 853 0:5539 Min. : 805
## Class :character SP : 645 1: 27 1st Qu.: 5231
## Mode :character RS : 497 Median : 10936
## BA : 416 Mean : 34296
## PR : 399 3rd Qu.: 23513
## SC : 294 Max. :11253503
## (Other):2462 NA's :5
## IBGE_RES_POP_BRAS IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN
## Min. : 805 Min. : 0.00 Min. : 239 Min. : 60
## 1st Qu.: 5223 1st Qu.: 0.00 1st Qu.: 1572 1st Qu.: 874
## Median : 10934 Median : 0.00 Median : 3178 Median : 1850
## Mean : 34218 Mean : 77.56 Mean : 10308 Mean : 8864
## 3rd Qu.: 23397 3rd Qu.: 10.00 3rd Qu.: 6727 3rd Qu.: 4628
## Max. :11133776 Max. :119727.00 Max. :3576148 Max. :3548433
## NA's :5 NA's :5 NA's :7 NA's :7
## IBGE_DU_RURAL IBGE_POP IBGE_1 IBGE_1-4
## Min. : 3.0 Min. : 174 Min. : 0.0 Min. : 5
## 1st Qu.: 486.8 1st Qu.: 2802 1st Qu.: 38.0 1st Qu.: 158
## Median : 931.0 Median : 6177 Median : 92.0 Median : 377
## Mean : 1462.6 Mean : 27612 Mean : 383.5 Mean : 1546
## 3rd Qu.: 1831.2 3rd Qu.: 15306 3rd Qu.: 232.0 3rd Qu.: 952
## Max. :33809.0 Max. :10463636 Max. :129464.0 Max. :514794
## NA's :78 NA's :5 NA's :5 NA's :5
## IBGE_5-9 IBGE_10-14 IBGE_15-59 IBGE_60+
## Min. : 7 Min. : 12 Min. : 94 Min. : 29
## 1st Qu.: 220 1st Qu.: 260 1st Qu.: 1735 1st Qu.: 341
## Median : 516 Median : 589 Median : 3842 Median : 723
## Mean : 2071 Mean : 2383 Mean : 18223 Mean : 3006
## 3rd Qu.: 1301 3rd Qu.: 1479 3rd Qu.: 9633 3rd Qu.: 1725
## Max. :684443 Max. :783702 Max. :7058221 Max. :1293012
## NA's :5 NA's :5 NA's :5 NA's :5
## IBGE_PLANTED_AREA IBGE_CROP_PRODUCTION_$ IDHM Ranking 2010 IDHM
## Min. : 0.0 Min. : 0 Min. : 1 Min. :0.4180
## 1st Qu.: 910.2 1st Qu.: 2328 1st Qu.:1391 1st Qu.:0.5990
## Median : 3471.5 Median : 13846 Median :2782 Median :0.6650
## Mean : 14180.2 Mean : 57389 Mean :2782 Mean :0.6592
## 3rd Qu.: 11173.2 3rd Qu.: 55594 3rd Qu.:4173 3rd Qu.:0.7180
## Max. :1205669.0 Max. :3274885 Max. :5565 Max. :0.8620
## NA's :5 NA's :5
## IDHM_Renda IDHM_Longevidade IDHM_Educacao LONG
## Min. :0.4000 Min. :0.6720 Min. :0.2070 Min. :-72.92
## 1st Qu.:0.5720 1st Qu.:0.7690 1st Qu.:0.4900 1st Qu.:-50.87
## Median :0.6540 Median :0.8080 Median :0.5600 Median :-46.53
## Mean :0.6429 Mean :0.8016 Mean :0.5591 Mean :-46.22
## 3rd Qu.:0.7070 3rd Qu.:0.8360 3rd Qu.:0.6310 3rd Qu.:-41.41
## Max. :0.8910 Max. :0.8940 Max. :0.8250 Max. : 51.47
## NA's :5 NA's :5 NA's :5
## LAT ALT PAY_TV FIXED_PHONES
## Min. :-33.688 Min. : 0.0 Min. : 1.0 Min. : 3
## 1st Qu.:-22.843 1st Qu.: 169.4 1st Qu.: 88.0 1st Qu.: 118
## Median :-18.107 Median : 406.5 Median : 247.0 Median : 328
## Mean :-16.455 Mean : 894.2 Mean : 3096.3 Mean : 6572
## 3rd Qu.: -8.491 3rd Qu.: 628.9 3rd Qu.: 815.8 3rd Qu.: 1151
## Max. : 4.585 Max. :874579.0 Max. :2047668.0 Max. :5543127
## NA's :6
## AREA REGIAO_TUR CATEGORIA_TUR
## Min. : 3.57 Corredores Das Águas: 59 A : 51
## 1st Qu.: 204.43 Vale Do Contestado : 45 B : 168
## Median : 415.81 Amazônia Atlântica : 40 C : 521
## Mean : 1515.52 Araguaia-Tocantins : 39 D :1889
## 3rd Qu.: 1026.38 Cariri : 37 E : 653
## Max. :159533.33 (Other) :3062 NA's:2284
## NA's :1 NA's :2284
## ESTIMATED_POP RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY
## Min. : 786 Length:5566 Min. : 0 Min. : 1
## 1st Qu.: 5451 Class :character 1st Qu.: 4193 1st Qu.: 1725
## Median : 11591 Mode :character Median : 20432 Median : 7428
## Mean : 37452 Mean : 47285 Mean : 176050
## 3rd Qu.: 25303 3rd Qu.: 51227 3rd Qu.: 41240
## Max. :12176866 Max. :1402282 Max. :63306755
##
## GVA_SERVICES GVA_PUBLIC GVA_TOTAL TAXES
## Min. : 2 Min. : 7 Min. : 17 Min. : -14159
## 1st Qu.: 10107 1st Qu.: 17254 1st Qu.: 42223 1st Qu.: 1305
## Median : 31214 Median : 35838 Median : 119492 Median : 5108
## Mean : 489787 Mean : 123829 Mean : 833504 Mean : 118947
## 3rd Qu.: 115503 3rd Qu.: 89301 3rd Qu.: 314139 3rd Qu.: 22208
## Max. :464656988 Max. :41902893 Max. :569910503 Max. :117125387
##
## GDP POP_GDP GDP_CAPITA GVA_MAIN
## Min. : 15 Min. : 815 Min. : 3191 Length:5566
## 1st Qu.: 43706 1st Qu.: 5480 1st Qu.: 9062 Class :character
## Median : 125153 Median : 11584 Median : 15870 Mode :character
## Mean : 955185 Mean : 37018 Mean : 21132
## 3rd Qu.: 329764 3rd Qu.: 25098 3rd Qu.: 26156
## Max. :687035890 Max. :12038175 Max. :314638
##
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B
## Min. :1.421e+06 Min. : 6.0 Min. : 0.00 Min. : 0.000
## 1st Qu.:1.573e+07 1st Qu.: 68.0 1st Qu.: 1.00 1st Qu.: 0.000
## Median :2.749e+07 Median : 162.0 Median : 2.00 Median : 0.000
## Mean :1.044e+08 Mean : 907.3 Mean : 18.27 Mean : 1.853
## 3rd Qu.:5.679e+07 3rd Qu.: 448.8 3rd Qu.: 8.00 3rd Qu.: 2.000
## Max. :4.577e+10 Max. :530446.0 Max. :1948.00 Max. :274.000
## NA's :1490
## COMP_C COMP_D COMP_E COMP_F
## Min. : 0.00 Min. : 0.0000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 3.00 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.: 1.00
## Median : 11.00 Median : 0.0000 Median : 0.000 Median : 4.00
## Mean : 73.49 Mean : 0.4265 Mean : 2.031 Mean : 43.29
## 3rd Qu.: 39.00 3rd Qu.: 0.0000 3rd Qu.: 1.000 3rd Qu.: 15.00
## Max. :31566.00 Max. :332.0000 Max. :657.000 Max. :25222.00
##
## COMP_G COMP_H COMP_I COMP_J
## Min. : 1.0 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 32.0 1st Qu.: 1.00 1st Qu.: 2.00 1st Qu.: 0.00
## Median : 75.0 Median : 7.00 Median : 7.00 Median : 1.00
## Mean : 348.2 Mean : 41.02 Mean : 55.91 Mean : 24.76
## 3rd Qu.: 199.8 3rd Qu.: 25.00 3rd Qu.: 24.00 3rd Qu.: 5.00
## Max. :150633.0 Max. :19515.00 Max. :29290.00 Max. :38720.00
##
## COMP_K COMP_L COMP_M COMP_N
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 1.00 1st Qu.: 1.00
## Median : 0.00 Median : 0.00 Median : 4.00 Median : 4.00
## Mean : 15.56 Mean : 15.15 Mean : 51.33 Mean : 83.76
## 3rd Qu.: 2.00 3rd Qu.: 3.00 3rd Qu.: 13.00 3rd Qu.: 14.00
## Max. :23738.00 Max. :14003.00 Max. :49181.00 Max. :76757.00
##
## COMP_O COMP_P COMP_Q COMP_R
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 2.00 1st Qu.: 2.00 1st Qu.: 1.00 1st Qu.: 0.00
## Median : 2.00 Median : 6.00 Median : 3.00 Median : 2.00
## Mean : 3.27 Mean : 30.98 Mean : 34.17 Mean : 12.19
## 3rd Qu.: 3.00 3rd Qu.: 17.00 3rd Qu.: 12.00 3rd Qu.: 6.00
## Max. :204.00 Max. :16030.00 Max. :22248.00 Max. :6687.00
##
## COMP_S COMP_T COMP_U HOTELS
## Min. : 0.00 Min. :0 Min. : 0.00000 Min. : 1.000
## 1st Qu.: 5.00 1st Qu.:0 1st Qu.: 0.00000 1st Qu.: 1.000
## Median : 12.00 Median :0 Median : 0.00000 Median : 1.000
## Mean : 51.64 Mean :0 Mean : 0.05031 Mean : 3.131
## 3rd Qu.: 31.00 3rd Qu.:0 3rd Qu.: 0.00000 3rd Qu.: 3.000
## Max. :24832.00 Max. :0 Max. :123.00000 Max. :97.000
## NA's :4679
## BEDS Pr_Agencies Pu_Agencies Pr_Bank
## Min. : 2.0 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 40.0 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 0.000
## Median : 82.0 Median : 1.000 Median : 2.000 Median : 1.000
## Mean : 257.5 Mean : 3.383 Mean : 2.829 Mean : 1.312
## 3rd Qu.: 200.0 3rd Qu.: 2.000 3rd Qu.: 2.000 3rd Qu.: 2.000
## Max. :13247.0 Max. :1693.000 Max. :626.000 Max. :83.000
## NA's :4679 NA's :2224 NA's :2224 NA's :2224
## Pu_Bank Pr_Assets Pu_Assets Cars
## Min. :0.00 Min. :0.000e+00 Min. :0.000e+00 Min. : 2
## 1st Qu.:1.00 1st Qu.:0.000e+00 1st Qu.:4.047e+07 1st Qu.: 602
## Median :2.00 Median :3.231e+07 Median :1.339e+08 Median : 1440
## Mean :1.58 Mean :9.180e+09 Mean :6.005e+09 Mean : 9866
## 3rd Qu.:2.00 3rd Qu.:1.148e+08 3rd Qu.:4.970e+08 3rd Qu.: 4089
## Max. :8.00 Max. :1.947e+13 Max. :8.016e+12 Max. :5740995
## NA's :2224 NA's :2224 NA's :2224 NA's :8
## Motorcycles Wheeled_tractor UBER MAC
## Min. : 4 Min. : 0.000 1 : 125 Min. : 1.000
## 1st Qu.: 591 1st Qu.: 0.000 NA's:5441 1st Qu.: 1.000
## Median : 1285 Median : 0.000 Median : 2.000
## Mean : 4881 Mean : 5.757 Mean : 4.277
## 3rd Qu.: 3298 3rd Qu.: 1.000 3rd Qu.: 3.000
## Max. :1134570 Max. :3236.000 Max. :130.000
## NA's :8 NA's :8 NA's :5400
## WAL-MART POST_OFFICES
## Min. : 1.000 Min. : 1.000
## 1st Qu.: 1.000 1st Qu.: 1.000
## Median : 1.000 Median : 1.000
## Mean : 2.059 Mean : 2.081
## 3rd Qu.: 1.750 3rd Qu.: 2.000
## Max. :26.000 Max. :225.000
## NA's :5464 NA's :117
There are now no more NA values for GDP_CAPITA
5. Exploratory Data Analysis (EDA)
To help us better understand which variables are needed in calculating GDP_CAPITA, and why we need these variables ### 5.1 EDA using statistical graphics We can plot the distribution of GDP_CAPITA by using histograms
ggplot(data=brazil, aes(x=`GDP_CAPITA`))+
geom_histogram(bins=20, color="black", fill="light blue")
The histogram above shows a right skewed distribution. This suggests that more municipalities have relatively lower GDP per CAPITA. We will normalise the skewed distribution by using log transformation
brazil <- brazil%>%
mutate(`LOG_GDP_CAPITA`=log(GDP_CAPITA))Then, plot the LOG_GDP_CAPITA histogram
ggplot(data=brazil, aes(x=`LOG_GDP_CAPITA`))+
geom_histogram(bins=20, color="black", fill="light blue")
The histogram now is less skewed, and in fact, resembles a normal distribution.
5.2 Renaming of variables first
Next, we will rename the variables as some original names are quite long / difficult to use. This ensures simplicity for us.
names(brazil)[names(brazil) == "IBGE_CROP_PRODUCTION_$"] <- "IBGE_CROP_PRODUCTION"
names(brazil)[names(brazil) == " GVA_TOTAL "] <- "GVA_TOTAL"
names(brazil)[names(brazil) == "IBGE_15-59"] <- "Active_pop"5.3 Check the distribution of GDP per CAPITA
GDP_CAPITA by continent
We draw a boxplot to illustrate the distribution over the different states in brazil
brazil_states <- brazil%>%
group_by(STATE)
ggplot(data=brazil_states, mapping=aes(x=STATE, y=GDP_CAPITA)) + geom_boxplot()+
ggtitle("Distribution of GDP per CAPITA across states in brazil")
There are a few outliners for some states (BA, MS), but with some countries very well spread out, such as AC, RR.
Let’s take a look at the top 10 GDP_CAPITA
We will filter out the top 10 countries with the highest GDP_CAPITA, and identify if the variables that might have possibly resulted in the high GDP value
brazil_gdp_capita <- brazil%>%
arrange(desc(GDP_CAPITA))%>%
top_n(n=10, wt=GDP_CAPITA)
head(brazil_gdp_capita)## # A tibble: 6 x 82
## CITY STATE CAPITAL IBGE_RES_POP IBGE_RES_POP_BR~ IBGE_RES_POP_ES~ IBGE_DU
## <chr> <fct> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 Paul~ SP 0 82146 81967 179 24311
## 2 Selv~ MS 0 6287 6287 0 2003
## 3 São ~ BA 0 33183 33183 0 9503
## 4 Triu~ RS 0 25793 25787 6 8635
## 5 Brej~ SP 0 2573 2565 8 822
## 6 Seba~ SP 0 3031 3031 0 1055
## # ... with 75 more variables: IBGE_DU_URBAN <dbl>, IBGE_DU_RURAL <dbl>,
## # IBGE_POP <dbl>, IBGE_1 <dbl>, `IBGE_1-4` <dbl>, `IBGE_5-9` <dbl>,
## # `IBGE_10-14` <dbl>, Active_pop <dbl>, `IBGE_60+` <dbl>,
## # IBGE_PLANTED_AREA <dbl>, IBGE_CROP_PRODUCTION <dbl>, `IDHM Ranking
## # 2010` <dbl>, IDHM <dbl>, IDHM_Renda <dbl>, IDHM_Longevidade <dbl>,
## # IDHM_Educacao <dbl>, LONG <dbl>, LAT <dbl>, ALT <dbl>, PAY_TV <dbl>,
## # FIXED_PHONES <dbl>, AREA <dbl>, REGIAO_TUR <fct>, CATEGORIA_TUR <fct>,
## # ESTIMATED_POP <dbl>, RURAL_URBAN <chr>, GVA_AGROPEC <dbl>,
## # GVA_INDUSTRY <dbl>, GVA_SERVICES <dbl>, GVA_PUBLIC <dbl>, GVA_TOTAL <dbl>,
## # TAXES <dbl>, GDP <dbl>, POP_GDP <dbl>, GDP_CAPITA <dbl>, GVA_MAIN <chr>,
## # MUN_EXPENDIT <dbl>, COMP_TOT <dbl>, COMP_A <dbl>, COMP_B <dbl>,
## # COMP_C <dbl>, COMP_D <dbl>, COMP_E <dbl>, COMP_F <dbl>, COMP_G <dbl>,
## # COMP_H <dbl>, COMP_I <dbl>, COMP_J <dbl>, COMP_K <dbl>, COMP_L <dbl>,
## # COMP_M <dbl>, COMP_N <dbl>, COMP_O <dbl>, COMP_P <dbl>, COMP_Q <dbl>,
## # COMP_R <dbl>, COMP_S <dbl>, COMP_T <dbl>, COMP_U <dbl>, HOTELS <dbl>,
## # BEDS <dbl>, Pr_Agencies <dbl>, Pu_Agencies <dbl>, Pr_Bank <dbl>,
## # Pu_Bank <dbl>, Pr_Assets <dbl>, Pu_Assets <dbl>, Cars <dbl>,
## # Motorcycles <dbl>, Wheeled_tractor <dbl>, UBER <fct>, MAC <dbl>,
## # `WAL-MART` <dbl>, POST_OFFICES <dbl>, LOG_GDP_CAPITA <dbl>
We are able to identify several variables that are high in value in these countries that have high GDP_CAPITA
For example, IBGE_RES_POP, Active_pop, IBGE_CROP_PRODUCTION, IDHM, PAY_TV, FIXED_PHONES, AREA, GVA_TOTAL, TAXES, GDP, POP_GDP, MUN_EXPENDIT, COMP_TOT, Cars, Motorcycles –> shows correlation between the two variables.
### 5.4 Variables selection Besides the variables that affect GDP_CAPITA in the analysis above, we will consider also the GDP equation, which is C + I + G + (X-M). Simply put, it is the sum of Consumption, Investment, Government expenditures, and Net Exports. We will then identify variables that might have an impact on these components as mentioned, before determining which factors to use.
summary(brazil)## CITY STATE CAPITAL IBGE_RES_POP
## Length:5566 MG : 853 0:5539 Min. : 805
## Class :character SP : 645 1: 27 1st Qu.: 5231
## Mode :character RS : 497 Median : 10936
## BA : 416 Mean : 34296
## PR : 399 3rd Qu.: 23513
## SC : 294 Max. :11253503
## (Other):2462 NA's :5
## IBGE_RES_POP_BRAS IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN
## Min. : 805 Min. : 0.00 Min. : 239 Min. : 60
## 1st Qu.: 5223 1st Qu.: 0.00 1st Qu.: 1572 1st Qu.: 874
## Median : 10934 Median : 0.00 Median : 3178 Median : 1850
## Mean : 34218 Mean : 77.56 Mean : 10308 Mean : 8864
## 3rd Qu.: 23397 3rd Qu.: 10.00 3rd Qu.: 6727 3rd Qu.: 4628
## Max. :11133776 Max. :119727.00 Max. :3576148 Max. :3548433
## NA's :5 NA's :5 NA's :7 NA's :7
## IBGE_DU_RURAL IBGE_POP IBGE_1 IBGE_1-4
## Min. : 3.0 Min. : 174 Min. : 0.0 Min. : 5
## 1st Qu.: 486.8 1st Qu.: 2802 1st Qu.: 38.0 1st Qu.: 158
## Median : 931.0 Median : 6177 Median : 92.0 Median : 377
## Mean : 1462.6 Mean : 27612 Mean : 383.5 Mean : 1546
## 3rd Qu.: 1831.2 3rd Qu.: 15306 3rd Qu.: 232.0 3rd Qu.: 952
## Max. :33809.0 Max. :10463636 Max. :129464.0 Max. :514794
## NA's :78 NA's :5 NA's :5 NA's :5
## IBGE_5-9 IBGE_10-14 Active_pop IBGE_60+
## Min. : 7 Min. : 12 Min. : 94 Min. : 29
## 1st Qu.: 220 1st Qu.: 260 1st Qu.: 1735 1st Qu.: 341
## Median : 516 Median : 589 Median : 3842 Median : 723
## Mean : 2071 Mean : 2383 Mean : 18223 Mean : 3006
## 3rd Qu.: 1301 3rd Qu.: 1479 3rd Qu.: 9633 3rd Qu.: 1725
## Max. :684443 Max. :783702 Max. :7058221 Max. :1293012
## NA's :5 NA's :5 NA's :5 NA's :5
## IBGE_PLANTED_AREA IBGE_CROP_PRODUCTION IDHM Ranking 2010 IDHM
## Min. : 0.0 Min. : 0 Min. : 1 Min. :0.4180
## 1st Qu.: 910.2 1st Qu.: 2328 1st Qu.:1391 1st Qu.:0.5990
## Median : 3471.5 Median : 13846 Median :2782 Median :0.6650
## Mean : 14180.2 Mean : 57389 Mean :2782 Mean :0.6592
## 3rd Qu.: 11173.2 3rd Qu.: 55594 3rd Qu.:4173 3rd Qu.:0.7180
## Max. :1205669.0 Max. :3274885 Max. :5565 Max. :0.8620
## NA's :5 NA's :5
## IDHM_Renda IDHM_Longevidade IDHM_Educacao LONG
## Min. :0.4000 Min. :0.6720 Min. :0.2070 Min. :-72.92
## 1st Qu.:0.5720 1st Qu.:0.7690 1st Qu.:0.4900 1st Qu.:-50.87
## Median :0.6540 Median :0.8080 Median :0.5600 Median :-46.53
## Mean :0.6429 Mean :0.8016 Mean :0.5591 Mean :-46.22
## 3rd Qu.:0.7070 3rd Qu.:0.8360 3rd Qu.:0.6310 3rd Qu.:-41.41
## Max. :0.8910 Max. :0.8940 Max. :0.8250 Max. : 51.47
## NA's :5 NA's :5 NA's :5
## LAT ALT PAY_TV FIXED_PHONES
## Min. :-33.688 Min. : 0.0 Min. : 1.0 Min. : 3
## 1st Qu.:-22.843 1st Qu.: 169.4 1st Qu.: 88.0 1st Qu.: 118
## Median :-18.107 Median : 406.5 Median : 247.0 Median : 328
## Mean :-16.455 Mean : 894.2 Mean : 3096.3 Mean : 6572
## 3rd Qu.: -8.491 3rd Qu.: 628.9 3rd Qu.: 815.8 3rd Qu.: 1151
## Max. : 4.585 Max. :874579.0 Max. :2047668.0 Max. :5543127
## NA's :6
## AREA REGIAO_TUR CATEGORIA_TUR
## Min. : 3.57 Corredores Das Águas: 59 A : 51
## 1st Qu.: 204.43 Vale Do Contestado : 45 B : 168
## Median : 415.81 Amazônia Atlântica : 40 C : 521
## Mean : 1515.52 Araguaia-Tocantins : 39 D :1889
## 3rd Qu.: 1026.38 Cariri : 37 E : 653
## Max. :159533.33 (Other) :3062 NA's:2284
## NA's :1 NA's :2284
## ESTIMATED_POP RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY
## Min. : 786 Length:5566 Min. : 0 Min. : 1
## 1st Qu.: 5451 Class :character 1st Qu.: 4193 1st Qu.: 1725
## Median : 11591 Mode :character Median : 20432 Median : 7428
## Mean : 37452 Mean : 47285 Mean : 176050
## 3rd Qu.: 25303 3rd Qu.: 51227 3rd Qu.: 41240
## Max. :12176866 Max. :1402282 Max. :63306755
##
## GVA_SERVICES GVA_PUBLIC GVA_TOTAL TAXES
## Min. : 2 Min. : 7 Min. : 17 Min. : -14159
## 1st Qu.: 10107 1st Qu.: 17254 1st Qu.: 42223 1st Qu.: 1305
## Median : 31214 Median : 35838 Median : 119492 Median : 5108
## Mean : 489787 Mean : 123829 Mean : 833504 Mean : 118947
## 3rd Qu.: 115503 3rd Qu.: 89301 3rd Qu.: 314139 3rd Qu.: 22208
## Max. :464656988 Max. :41902893 Max. :569910503 Max. :117125387
##
## GDP POP_GDP GDP_CAPITA GVA_MAIN
## Min. : 15 Min. : 815 Min. : 3191 Length:5566
## 1st Qu.: 43706 1st Qu.: 5480 1st Qu.: 9062 Class :character
## Median : 125153 Median : 11584 Median : 15870 Mode :character
## Mean : 955185 Mean : 37018 Mean : 21132
## 3rd Qu.: 329764 3rd Qu.: 25098 3rd Qu.: 26156
## Max. :687035890 Max. :12038175 Max. :314638
##
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B
## Min. :1.421e+06 Min. : 6.0 Min. : 0.00 Min. : 0.000
## 1st Qu.:1.573e+07 1st Qu.: 68.0 1st Qu.: 1.00 1st Qu.: 0.000
## Median :2.749e+07 Median : 162.0 Median : 2.00 Median : 0.000
## Mean :1.044e+08 Mean : 907.3 Mean : 18.27 Mean : 1.853
## 3rd Qu.:5.679e+07 3rd Qu.: 448.8 3rd Qu.: 8.00 3rd Qu.: 2.000
## Max. :4.577e+10 Max. :530446.0 Max. :1948.00 Max. :274.000
## NA's :1490
## COMP_C COMP_D COMP_E COMP_F
## Min. : 0.00 Min. : 0.0000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 3.00 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.: 1.00
## Median : 11.00 Median : 0.0000 Median : 0.000 Median : 4.00
## Mean : 73.49 Mean : 0.4265 Mean : 2.031 Mean : 43.29
## 3rd Qu.: 39.00 3rd Qu.: 0.0000 3rd Qu.: 1.000 3rd Qu.: 15.00
## Max. :31566.00 Max. :332.0000 Max. :657.000 Max. :25222.00
##
## COMP_G COMP_H COMP_I COMP_J
## Min. : 1.0 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 32.0 1st Qu.: 1.00 1st Qu.: 2.00 1st Qu.: 0.00
## Median : 75.0 Median : 7.00 Median : 7.00 Median : 1.00
## Mean : 348.2 Mean : 41.02 Mean : 55.91 Mean : 24.76
## 3rd Qu.: 199.8 3rd Qu.: 25.00 3rd Qu.: 24.00 3rd Qu.: 5.00
## Max. :150633.0 Max. :19515.00 Max. :29290.00 Max. :38720.00
##
## COMP_K COMP_L COMP_M COMP_N
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 1.00 1st Qu.: 1.00
## Median : 0.00 Median : 0.00 Median : 4.00 Median : 4.00
## Mean : 15.56 Mean : 15.15 Mean : 51.33 Mean : 83.76
## 3rd Qu.: 2.00 3rd Qu.: 3.00 3rd Qu.: 13.00 3rd Qu.: 14.00
## Max. :23738.00 Max. :14003.00 Max. :49181.00 Max. :76757.00
##
## COMP_O COMP_P COMP_Q COMP_R
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 2.00 1st Qu.: 2.00 1st Qu.: 1.00 1st Qu.: 0.00
## Median : 2.00 Median : 6.00 Median : 3.00 Median : 2.00
## Mean : 3.27 Mean : 30.98 Mean : 34.17 Mean : 12.19
## 3rd Qu.: 3.00 3rd Qu.: 17.00 3rd Qu.: 12.00 3rd Qu.: 6.00
## Max. :204.00 Max. :16030.00 Max. :22248.00 Max. :6687.00
##
## COMP_S COMP_T COMP_U HOTELS
## Min. : 0.00 Min. :0 Min. : 0.00000 Min. : 1.000
## 1st Qu.: 5.00 1st Qu.:0 1st Qu.: 0.00000 1st Qu.: 1.000
## Median : 12.00 Median :0 Median : 0.00000 Median : 1.000
## Mean : 51.64 Mean :0 Mean : 0.05031 Mean : 3.131
## 3rd Qu.: 31.00 3rd Qu.:0 3rd Qu.: 0.00000 3rd Qu.: 3.000
## Max. :24832.00 Max. :0 Max. :123.00000 Max. :97.000
## NA's :4679
## BEDS Pr_Agencies Pu_Agencies Pr_Bank
## Min. : 2.0 Min. : 0.000 Min. : 0.000 Min. : 0.000
## 1st Qu.: 40.0 1st Qu.: 0.000 1st Qu.: 1.000 1st Qu.: 0.000
## Median : 82.0 Median : 1.000 Median : 2.000 Median : 1.000
## Mean : 257.5 Mean : 3.383 Mean : 2.829 Mean : 1.312
## 3rd Qu.: 200.0 3rd Qu.: 2.000 3rd Qu.: 2.000 3rd Qu.: 2.000
## Max. :13247.0 Max. :1693.000 Max. :626.000 Max. :83.000
## NA's :4679 NA's :2224 NA's :2224 NA's :2224
## Pu_Bank Pr_Assets Pu_Assets Cars
## Min. :0.00 Min. :0.000e+00 Min. :0.000e+00 Min. : 2
## 1st Qu.:1.00 1st Qu.:0.000e+00 1st Qu.:4.047e+07 1st Qu.: 602
## Median :2.00 Median :3.231e+07 Median :1.339e+08 Median : 1440
## Mean :1.58 Mean :9.180e+09 Mean :6.005e+09 Mean : 9866
## 3rd Qu.:2.00 3rd Qu.:1.148e+08 3rd Qu.:4.970e+08 3rd Qu.: 4089
## Max. :8.00 Max. :1.947e+13 Max. :8.016e+12 Max. :5740995
## NA's :2224 NA's :2224 NA's :2224 NA's :8
## Motorcycles Wheeled_tractor UBER MAC
## Min. : 4 Min. : 0.000 1 : 125 Min. : 1.000
## 1st Qu.: 591 1st Qu.: 0.000 NA's:5441 1st Qu.: 1.000
## Median : 1285 Median : 0.000 Median : 2.000
## Mean : 4881 Mean : 5.757 Mean : 4.277
## 3rd Qu.: 3298 3rd Qu.: 1.000 3rd Qu.: 3.000
## Max. :1134570 Max. :3236.000 Max. :130.000
## NA's :8 NA's :8 NA's :5400
## WAL-MART POST_OFFICES LOG_GDP_CAPITA
## Min. : 1.000 Min. : 1.000 Min. : 8.068
## 1st Qu.: 1.000 1st Qu.: 1.000 1st Qu.: 9.112
## Median : 1.000 Median : 1.000 Median : 9.672
## Mean : 2.059 Mean : 2.081 Mean : 9.697
## 3rd Qu.: 1.750 3rd Qu.: 2.000 3rd Qu.:10.172
## Max. :26.000 Max. :225.000 Max. :12.659
## NA's :5464 NA's :117Raw Variables that we will consider using:
IBGE_RES_POP
Active_pop
IBGE_CROP_PRODUCTION
IDHM_Longevidade
IDHM_Educacao
IDHM_Renda
PAY_TV
FIXED_PHONES
AREA
GVA_AGROPEC
GVA_INDUSTRY
GVA_SERVICES
TAXES
GDP
POP_GDP
GDP_CAPITA
MUN_EXPENDIT
COMP_TOT
Cars
Motorcycles
Pr_Assets
Pu_Assets
5.5 DATA CLEANING
By variables
IBGE_RES_POP
We choose IBGE_RES_POP since it is the population of Brazil, which includes residents and foreigners both.
IBGE_RES_POP has 8 NA values, which could be due to the particular city not having any population. We will remove these NA values as it does not have any impact on GDP_CAPITA. It is also hard to assign a value to these
We have identified that after removing these 8 NAs, the amount of NAs in other variables have decreased too. This could be due to cities having multiple NA values for different variables
brazil <- brazil%>%
filter(!is.na(`IBGE_RES_POP`))
summary(brazil)## CITY STATE CAPITAL IBGE_RES_POP
## Length:5561 MG : 853 0:5534 Min. : 805
## Class :character SP : 645 1: 27 1st Qu.: 5231
## Mode :character RS : 496 Median : 10936
## BA : 416 Mean : 34296
## PR : 399 3rd Qu.: 23513
## SC : 292 Max. :11253503
## (Other):2460
## IBGE_RES_POP_BRAS IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN
## Min. : 805 Min. : 0.00 Min. : 239 Min. : 60
## 1st Qu.: 5223 1st Qu.: 0.00 1st Qu.: 1572 1st Qu.: 874
## Median : 10934 Median : 0.00 Median : 3178 Median : 1850
## Mean : 34218 Mean : 77.56 Mean : 10308 Mean : 8864
## 3rd Qu.: 23397 3rd Qu.: 10.00 3rd Qu.: 6727 3rd Qu.: 4628
## Max. :11133776 Max. :119727.00 Max. :3576148 Max. :3548433
## NA's :2 NA's :2
## IBGE_DU_RURAL IBGE_POP IBGE_1 IBGE_1-4
## Min. : 3.0 Min. : 174 Min. : 0.0 Min. : 5
## 1st Qu.: 486.8 1st Qu.: 2802 1st Qu.: 38.0 1st Qu.: 158
## Median : 931.0 Median : 6177 Median : 92.0 Median : 377
## Mean : 1462.6 Mean : 27612 Mean : 383.5 Mean : 1546
## 3rd Qu.: 1831.2 3rd Qu.: 15306 3rd Qu.: 232.0 3rd Qu.: 952
## Max. :33809.0 Max. :10463636 Max. :129464.0 Max. :514794
## NA's :73
## IBGE_5-9 IBGE_10-14 Active_pop IBGE_60+
## Min. : 7 Min. : 12 Min. : 94 Min. : 29
## 1st Qu.: 220 1st Qu.: 260 1st Qu.: 1735 1st Qu.: 341
## Median : 516 Median : 589 Median : 3842 Median : 723
## Mean : 2071 Mean : 2383 Mean : 18223 Mean : 3006
## 3rd Qu.: 1301 3rd Qu.: 1479 3rd Qu.: 9633 3rd Qu.: 1725
## Max. :684443 Max. :783702 Max. :7058221 Max. :1293012
##
## IBGE_PLANTED_AREA IBGE_CROP_PRODUCTION IDHM Ranking 2010 IDHM
## Min. : 0 Min. : 0 Min. : 1 Min. :0.4180
## 1st Qu.: 911 1st Qu.: 2333 1st Qu.:1391 1st Qu.:0.5990
## Median : 3473 Median : 13845 Median :2782 Median :0.6650
## Mean : 14171 Mean : 57356 Mean :2782 Mean :0.6592
## 3rd Qu.: 11171 3rd Qu.: 55490 3rd Qu.:4173 3rd Qu.:0.7180
## Max. :1205669 Max. :3274885 Max. :5565 Max. :0.8620
##
## IDHM_Renda IDHM_Longevidade IDHM_Educacao LONG
## Min. :0.4000 Min. :0.6720 Min. :0.2070 Min. :-72.92
## 1st Qu.:0.5720 1st Qu.:0.7690 1st Qu.:0.4900 1st Qu.:-50.87
## Median :0.6540 Median :0.8080 Median :0.5600 Median :-46.52
## Mean :0.6429 Mean :0.8016 Mean :0.5591 Mean :-46.21
## 3rd Qu.:0.7070 3rd Qu.:0.8360 3rd Qu.:0.6310 3rd Qu.:-41.41
## Max. :0.8910 Max. :0.8940 Max. :0.8250 Max. : 51.47
##
## LAT ALT PAY_TV FIXED_PHONES
## Min. :-33.688 Min. : 0.0 Min. : 1 Min. : 3
## 1st Qu.:-22.841 1st Qu.: 169.4 1st Qu.: 88 1st Qu.: 118
## Median :-18.097 Median : 406.5 Median : 247 Median : 328
## Mean :-16.450 Mean : 894.2 Mean : 3099 Mean : 6577
## 3rd Qu.: -8.490 3rd Qu.: 628.9 3rd Qu.: 816 3rd Qu.: 1151
## Max. : 4.585 Max. :874579.0 Max. :2047668 Max. :5543127
## NA's :1
## AREA REGIAO_TUR CATEGORIA_TUR
## Min. : 3.57 Corredores Das Águas: 59 A : 51
## 1st Qu.: 204.54 Vale Do Contestado : 45 B : 168
## Median : 415.86 Amazônia Atlântica : 40 C : 521
## Mean : 1515.03 Araguaia-Tocantins : 39 D :1889
## 3rd Qu.: 1025.73 Cariri : 37 E : 648
## Max. :159533.33 (Other) :3057 NA's:2284
## NA's :1 NA's :2284
## ESTIMATED_POP RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY
## Min. : 786 Length:5561 Min. : 0 Min. : 1
## 1st Qu.: 5450 Class :character 1st Qu.: 4193 1st Qu.: 1724
## Median : 11591 Mode :character Median : 20434 Median : 7432
## Mean : 37477 Mean : 47277 Mean : 176171
## 3rd Qu.: 25311 3rd Qu.: 51238 3rd Qu.: 41026
## Max. :12176866 Max. :1402282 Max. :63306755
##
## GVA_SERVICES GVA_PUBLIC GVA_TOTAL TAXES
## Min. : 2 Min. : 7 Min. : 17 Min. : -14159
## 1st Qu.: 10112 1st Qu.: 17252 1st Qu.: 42253 1st Qu.: 1303
## Median : 31216 Median : 35747 Median : 119481 Median : 5108
## Mean : 490191 Mean : 123904 Mean : 834110 Mean : 119046
## 3rd Qu.: 115644 3rd Qu.: 89363 3rd Qu.: 314190 3rd Qu.: 22251
## Max. :464656988 Max. :41902893 Max. :569910503 Max. :117125387
##
## GDP POP_GDP GDP_CAPITA GVA_MAIN
## Min. : 15 Min. : 815 Min. : 3191 Length:5561
## 1st Qu.: 43645 1st Qu.: 5481 1st Qu.: 9062 Class :character
## Median : 125111 Median : 11584 Median : 15866 Mode :character
## Mean : 955869 Mean : 37043 Mean : 21125
## 3rd Qu.: 329780 3rd Qu.: 25114 3rd Qu.: 26157
## Max. :687035890 Max. :12038175 Max. :314638
##
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B
## Min. :1.421e+06 Min. : 6 Min. : 0.00 Min. : 0.000
## 1st Qu.:1.573e+07 1st Qu.: 68 1st Qu.: 1.00 1st Qu.: 0.000
## Median :2.749e+07 Median : 163 Median : 2.00 Median : 0.000
## Mean :1.045e+08 Mean : 908 Mean : 18.28 Mean : 1.854
## 3rd Qu.:5.681e+07 3rd Qu.: 450 3rd Qu.: 8.00 3rd Qu.: 2.000
## Max. :4.577e+10 Max. :530446 Max. :1948.00 Max. :274.000
## NA's :1489
## COMP_C COMP_D COMP_E COMP_F
## Min. : 0.00 Min. : 0.0000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 3.00 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.: 1.00
## Median : 11.00 Median : 0.0000 Median : 0.000 Median : 4.00
## Mean : 73.55 Mean : 0.4267 Mean : 2.032 Mean : 43.31
## 3rd Qu.: 39.00 3rd Qu.: 0.0000 3rd Qu.: 1.000 3rd Qu.: 15.00
## Max. :31566.00 Max. :332.0000 Max. :657.000 Max. :25222.00
##
## COMP_G COMP_H COMP_I COMP_J
## Min. : 1.0 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 32.0 1st Qu.: 1.00 1st Qu.: 2.00 1st Qu.: 0.00
## Median : 75.0 Median : 7.00 Median : 7.00 Median : 1.00
## Mean : 348.5 Mean : 41.05 Mean : 55.96 Mean : 24.78
## 3rd Qu.: 200.0 3rd Qu.: 25.00 3rd Qu.: 24.00 3rd Qu.: 5.00
## Max. :150633.0 Max. :19515.00 Max. :29290.00 Max. :38720.00
##
## COMP_K COMP_L COMP_M COMP_N
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 1.00 1st Qu.: 1.00
## Median : 0.00 Median : 0.00 Median : 4.00 Median : 4.00
## Mean : 15.58 Mean : 15.16 Mean : 51.37 Mean : 83.82
## 3rd Qu.: 2.00 3rd Qu.: 3.00 3rd Qu.: 13.00 3rd Qu.: 14.00
## Max. :23738.00 Max. :14003.00 Max. :49181.00 Max. :76757.00
##
## COMP_O COMP_P COMP_Q COMP_R
## Min. : 1.000 Min. : 0 Min. : 0.0 Min. : 0.0
## 1st Qu.: 2.000 1st Qu.: 2 1st Qu.: 1.0 1st Qu.: 0.0
## Median : 2.000 Median : 6 Median : 3.0 Median : 2.0
## Mean : 3.272 Mean : 31 Mean : 34.2 Mean : 12.2
## 3rd Qu.: 3.000 3rd Qu.: 17 3rd Qu.: 12.0 3rd Qu.: 6.0
## Max. :204.000 Max. :16030 Max. :22248.0 Max. :6687.0
##
## COMP_S COMP_T COMP_U HOTELS
## Min. : 0.00 Min. :0 Min. : 0.00000 Min. : 1.000
## 1st Qu.: 5.00 1st Qu.:0 1st Qu.: 0.00000 1st Qu.: 1.000
## Median : 12.00 Median :0 Median : 0.00000 Median : 1.000
## Mean : 51.68 Mean :0 Mean : 0.05035 Mean : 3.131
## 3rd Qu.: 31.00 3rd Qu.:0 3rd Qu.: 0.00000 3rd Qu.: 3.000
## Max. :24832.00 Max. :0 Max. :123.00000 Max. :97.000
## NA's :4674
## BEDS Pr_Agencies Pu_Agencies Pr_Bank
## Min. : 2.0 Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 40.0 1st Qu.: 0.000 1st Qu.: 1.00 1st Qu.: 0.000
## Median : 82.0 Median : 1.000 Median : 2.00 Median : 1.000
## Mean : 257.5 Mean : 3.384 Mean : 2.83 Mean : 1.312
## 3rd Qu.: 200.0 3rd Qu.: 2.000 3rd Qu.: 2.00 3rd Qu.: 2.000
## Max. :13247.0 Max. :1693.000 Max. :626.00 Max. :83.000
## NA's :4674 NA's :2220 NA's :2220 NA's :2220
## Pu_Bank Pr_Assets Pu_Assets Cars
## Min. :0.00 Min. :0.000e+00 Min. :0.000e+00 Min. : 2
## 1st Qu.:1.00 1st Qu.:0.000e+00 1st Qu.:4.048e+07 1st Qu.: 602
## Median :2.00 Median :3.234e+07 Median :1.339e+08 Median : 1440
## Mean :1.58 Mean :9.183e+09 Mean :6.007e+09 Mean : 9873
## 3rd Qu.:2.00 3rd Qu.:1.149e+08 3rd Qu.:4.976e+08 3rd Qu.: 4095
## Max. :8.00 Max. :1.947e+13 Max. :8.016e+12 Max. :5740995
## NA's :2220 NA's :2220 NA's :2220 NA's :8
## Motorcycles Wheeled_tractor UBER MAC
## Min. : 4 Min. : 0.000 1 : 125 Min. : 1.000
## 1st Qu.: 591 1st Qu.: 0.000 NA's:5436 1st Qu.: 1.000
## Median : 1285 Median : 0.000 Median : 2.000
## Mean : 4885 Mean : 5.761 Mean : 4.277
## 3rd Qu.: 3299 3rd Qu.: 1.000 3rd Qu.: 3.000
## Max. :1134570 Max. :3236.000 Max. :130.000
## NA's :8 NA's :8 NA's :5395
## WAL-MART POST_OFFICES LOG_GDP_CAPITA
## Min. : 1.000 Min. : 1.000 Min. : 8.068
## 1st Qu.: 1.000 1st Qu.: 1.000 1st Qu.: 9.112
## Median : 1.000 Median : 1.000 Median : 9.672
## Mean : 2.059 Mean : 2.081 Mean : 9.697
## 3rd Qu.: 1.750 3rd Qu.: 2.000 3rd Qu.:10.172
## Max. :26.000 Max. :225.000 Max. :12.659
## NA's :5459 NA's :117
IBGE_CROP_PRODUCTION is chosen since it represents the earnings from the production of crops, which these earnings will contribute to the economy. It is also reported online that agriculture is one of the principal bases of Brazil’s economy.
##### IDHM_Longevidade IDHM is the Human Development Index, which is calculated from IDHM_Longevidade, IDHM_Educacao, and IDHM_Renda.
The Human Development Index might contribute to the economy as a higher HDI value suggests that life expectancy (IDHM_Longevidade) is longer, IDHM_Educacao (Education level) is higher, which will raise the nation’s Gross National Income. This could be due to more people being able to work and contribute to the economy.
We will extract these three variables individually and conduct separate analysis on each three.
There is 1 NA value in IDHM_Longevidade. As it is hard to assign a value to this NA, we will drop this NA value
brazil <- brazil%>%
filter(!is.na(IDHM_Longevidade))PAY_TV & FIXED PHONES
PAY_TV and FIXED_PHONES are selected as these as luxury goods, and only a better off person can afford it. A municipality with higher number of PAY_TV and/or FIXED_PHONES may suggest a higher GDP, although it could be due to other factors. We will just include PAY_TV and FIXED_PHONES into our analysis first.
There are no NA values inside PAY_TV and FIXED_PHONES
AREA
A municipality with a bigger area might have more space for economic development, and could result in a change in GDP too.
There is 1 NA value for AREA, and this could be due to the city not being well developed enough for AREA to be calculated. However, it is hard to assign a value to this NA, therefore we will drop this NA value.
brazil <- brazil%>%
filter(!is.na(`AREA`))MUN_EXPENDIT
A municipality with higher MUN_EXPENDIT probably suggests higher expenditure, which might be due to individuals being better off. Expenditure might affect GDP.
However, since there are 1489 NA values in MUN_EXPENDIT, it is a substantial amount of missing values. We will choose not to use this value in this case, as it will remove a large amount of observation.
Cars
Owning a vehicle such as cars or motorcycles is part of private consumption, and it might have an impact on GDP.
There are 8 NA values for Cars, and could be due to the cities not having any Cars, but we are unable to correctly assign a value to these cities, hence, we will drop the NA values
brazil <- brazil%>%
filter(!is.na(`Cars`))Motorcycles
There are 9 NA values for Motorcycles, and could be due to the cities not having any motorcycles, but we are unable to correctly assign a value to these cities, hence, we will drop the NA values
brazil <- brazil%>%
filter(!is.na(`Motorcycles`))
summary(brazil)## CITY STATE CAPITAL IBGE_RES_POP
## Length:5552 MG : 852 0:5525 Min. : 805
## Class :character SP : 645 1: 27 1st Qu.: 5236
## Mode :character RS : 496 Median : 10943
## BA : 416 Mean : 34330
## PR : 398 3rd Qu.: 23646
## SC : 292 Max. :11253503
## (Other):2453
## IBGE_RES_POP_BRAS IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN
## Min. : 805 Min. : 0.00 Min. : 239 Min. : 60
## 1st Qu.: 5231 1st Qu.: 0.00 1st Qu.: 1574 1st Qu.: 875
## Median : 10942 Median : 0.00 Median : 3182 Median : 1852
## Mean : 34253 Mean : 77.68 Mean : 10319 Mean : 8875
## 3rd Qu.: 23522 3rd Qu.: 10.00 3rd Qu.: 6728 3rd Qu.: 4628
## Max. :11133776 Max. :119727.00 Max. :3576148 Max. :3548433
## NA's :2 NA's :2
## IBGE_DU_RURAL IBGE_POP IBGE_1 IBGE_1-4
## Min. : 3 Min. : 174 Min. : 0.0 Min. : 5
## 1st Qu.: 487 1st Qu.: 2803 1st Qu.: 38.0 1st Qu.: 158
## Median : 931 Median : 6183 Median : 92.0 Median : 377
## Mean : 1463 Mean : 27642 Mean : 383.9 Mean : 1547
## 3rd Qu.: 1833 3rd Qu.: 15308 3rd Qu.: 232.0 3rd Qu.: 952
## Max. :33809 Max. :10463636 Max. :129464.0 Max. :514794
## NA's :73
## IBGE_5-9 IBGE_10-14 Active_pop IBGE_60+
## Min. : 7 Min. : 12.0 Min. : 94 Min. : 29
## 1st Qu.: 220 1st Qu.: 259.0 1st Qu.: 1735 1st Qu.: 341
## Median : 517 Median : 589.5 Median : 3848 Median : 724
## Mean : 2073 Mean : 2385.3 Mean : 18243 Mean : 3010
## 3rd Qu.: 1301 3rd Qu.: 1479.0 3rd Qu.: 9634 3rd Qu.: 1726
## Max. :684443 Max. :783702.0 Max. :7058221 Max. :1293012
##
## IBGE_PLANTED_AREA IBGE_CROP_PRODUCTION IDHM Ranking 2010 IDHM
## Min. : 0.0 Min. : 0 Min. : 1 Min. :0.4180
## 1st Qu.: 912.8 1st Qu.: 2332 1st Qu.:1389 1st Qu.:0.5990
## Median : 3477.5 Median : 13859 Median :2780 Median :0.6650
## Mean : 14164.2 Mean : 57327 Mean :2781 Mean :0.6593
## 3rd Qu.: 11171.8 3rd Qu.: 55564 3rd Qu.:4172 3rd Qu.:0.7200
## Max. :1205669.0 Max. :3274885 Max. :5565 Max. :0.8620
##
## IDHM_Renda IDHM_Longevidade IDHM_Educacao LONG
## Min. :0.400 Min. :0.6720 Min. :0.2070 Min. :-72.92
## 1st Qu.:0.572 1st Qu.:0.7690 1st Qu.:0.4900 1st Qu.:-50.87
## Median :0.654 Median :0.8080 Median :0.5600 Median :-46.52
## Mean :0.643 Mean :0.8016 Mean :0.5592 Mean :-46.21
## 3rd Qu.:0.707 3rd Qu.:0.8360 3rd Qu.:0.6310 3rd Qu.:-41.41
## Max. :0.891 Max. :0.8940 Max. :0.8250 Max. : 51.47
##
## LAT ALT PAY_TV FIXED_PHONES
## Min. :-33.688 Min. : 0.0 Min. : 1 Min. : 3
## 1st Qu.:-22.843 1st Qu.: 170.1 1st Qu.: 88 1st Qu.: 119
## Median :-18.107 Median : 406.6 Median : 248 Median : 328
## Mean :-16.459 Mean : 895.1 Mean : 3103 Mean : 6587
## 3rd Qu.: -8.508 3rd Qu.: 629.2 3rd Qu.: 817 3rd Qu.: 1156
## Max. : 4.585 Max. :874579.0 Max. :2047668 Max. :5543127
## NA's :1
## AREA REGIAO_TUR CATEGORIA_TUR
## Min. : 3.57 Corredores Das Águas: 59 A : 51
## 1st Qu.: 204.70 Vale Do Contestado : 45 B : 168
## Median : 415.86 Amazônia Atlântica : 40 C : 521
## Mean : 1515.99 Araguaia-Tocantins : 39 D :1888
## 3rd Qu.: 1025.17 Cariri : 37 E : 648
## Max. :159533.33 (Other) :3056 NA's:2276
## NA's :2276
## ESTIMATED_POP RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY
## Min. : 786 Length:5552 Min. : 0 Min. : 1
## 1st Qu.: 5455 Class :character 1st Qu.: 4194 1st Qu.: 1726
## Median : 11602 Mode :character Median : 20440 Median : 7451
## Mean : 37516 Mean : 47279 Mean : 176424
## 3rd Qu.: 25328 3rd Qu.: 51243 3rd Qu.: 41097
## Max. :12176866 Max. :1402282 Max. :63306755
##
## GVA_SERVICES GVA_PUBLIC GVA_TOTAL TAXES
## Min. : 2 Min. : 7 Min. : 17 Min. : -14159
## 1st Qu.: 10110 1st Qu.: 17251 1st Qu.: 42447 1st Qu.: 1302
## Median : 31242 Median : 35778 Median : 119676 Median : 5114
## Mean : 490859 Mean : 124014 Mean : 835285 Mean : 119215
## 3rd Qu.: 115678 3rd Qu.: 89378 3rd Qu.: 314463 3rd Qu.: 22289
## Max. :464656988 Max. :41902893 Max. :569910503 Max. :117125387
##
## GDP POP_GDP GDP_CAPITA GVA_MAIN
## Min. : 15 Min. : 815 Min. : 3191 Length:5552
## 1st Qu.: 43691 1st Qu.: 5492 1st Qu.: 9064 Class :character
## Median : 125473 Median : 11588 Median : 15877 Mode :character
## Mean : 957210 Mean : 37081 Mean : 21136
## 3rd Qu.: 330284 3rd Qu.: 25120 3rd Qu.: 26168
## Max. :687035890 Max. :12038175 Max. :314638
##
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B
## Min. :1.421e+06 Min. : 6.0 Min. : 0.0 Min. : 0.000
## 1st Qu.:1.574e+07 1st Qu.: 68.0 1st Qu.: 1.0 1st Qu.: 0.000
## Median :2.749e+07 Median : 163.0 Median : 2.0 Median : 0.000
## Mean :1.046e+08 Mean : 909.2 Mean : 18.3 Mean : 1.857
## 3rd Qu.:5.680e+07 3rd Qu.: 450.0 3rd Qu.: 8.0 3rd Qu.: 2.000
## Max. :4.577e+10 Max. :530446.0 Max. :1948.0 Max. :274.000
## NA's :1486
## COMP_C COMP_D COMP_E COMP_F
## Min. : 0.00 Min. : 0.0000 Min. : 0.000 Min. : 0.00
## 1st Qu.: 3.00 1st Qu.: 0.0000 1st Qu.: 0.000 1st Qu.: 1.00
## Median : 11.00 Median : 0.0000 Median : 0.000 Median : 4.00
## Mean : 73.65 Mean : 0.4274 Mean : 2.033 Mean : 43.37
## 3rd Qu.: 40.00 3rd Qu.: 0.0000 3rd Qu.: 1.000 3rd Qu.: 15.00
## Max. :31566.00 Max. :332.0000 Max. :657.000 Max. :25222.00
##
## COMP_G COMP_H COMP_I COMP_J
## Min. : 1.0 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.: 32.0 1st Qu.: 1.0 1st Qu.: 2.00 1st Qu.: 0.00
## Median : 75.0 Median : 7.0 Median : 7.00 Median : 1.00
## Mean : 348.9 Mean : 41.1 Mean : 56.03 Mean : 24.82
## 3rd Qu.: 200.2 3rd Qu.: 25.0 3rd Qu.: 24.00 3rd Qu.: 5.00
## Max. :150633.0 Max. :19515.0 Max. :29290.00 Max. :38720.00
##
## COMP_K COMP_L COMP_M COMP_N
## Min. : 0.0 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 0.0 1st Qu.: 0.00 1st Qu.: 1.00 1st Qu.: 1.00
## Median : 0.0 Median : 0.00 Median : 4.00 Median : 4.00
## Mean : 15.6 Mean : 15.19 Mean : 51.45 Mean : 83.95
## 3rd Qu.: 2.0 3rd Qu.: 3.00 3rd Qu.: 13.00 3rd Qu.: 14.00
## Max. :23738.0 Max. :14003.00 Max. :49181.00 Max. :76757.00
##
## COMP_O COMP_P COMP_Q COMP_R
## Min. : 1.000 Min. : 0.00 Min. : 0.00 Min. : 0.00
## 1st Qu.: 2.000 1st Qu.: 2.00 1st Qu.: 1.00 1st Qu.: 0.00
## Median : 2.000 Median : 6.00 Median : 3.00 Median : 2.00
## Mean : 3.272 Mean : 31.03 Mean : 34.25 Mean : 12.21
## 3rd Qu.: 3.000 3rd Qu.: 17.00 3rd Qu.: 12.00 3rd Qu.: 6.00
## Max. :204.000 Max. :16030.00 Max. :22248.00 Max. :6687.00
##
## COMP_S COMP_T COMP_U HOTELS
## Min. : 0.00 Min. :0 Min. : 0.00000 Min. : 1.000
## 1st Qu.: 5.00 1st Qu.:0 1st Qu.: 0.00000 1st Qu.: 1.000
## Median : 13.00 Median :0 Median : 0.00000 Median : 1.000
## Mean : 51.74 Mean :0 Mean : 0.05043 Mean : 3.134
## 3rd Qu.: 31.00 3rd Qu.:0 3rd Qu.: 0.00000 3rd Qu.: 3.000
## Max. :24832.00 Max. :0 Max. :123.00000 Max. :97.000
## NA's :4667
## BEDS Pr_Agencies Pu_Agencies Pr_Bank
## Min. : 2.0 Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 40.0 1st Qu.: 0.000 1st Qu.: 1.00 1st Qu.: 0.000
## Median : 82.0 Median : 1.000 Median : 2.00 Median : 1.000
## Mean : 257.9 Mean : 3.386 Mean : 2.83 Mean : 1.313
## 3rd Qu.: 200.0 3rd Qu.: 2.000 3rd Qu.: 2.00 3rd Qu.: 2.000
## Max. :13247.0 Max. :1693.000 Max. :626.00 Max. :83.000
## NA's :4667 NA's :2214 NA's :2214 NA's :2214
## Pu_Bank Pr_Assets Pu_Assets Cars
## Min. :0.00 Min. :0.000e+00 Min. :0.000e+00 Min. : 2
## 1st Qu.:1.00 1st Qu.:0.000e+00 1st Qu.:4.047e+07 1st Qu.: 602
## Median :2.00 Median :3.231e+07 Median :1.339e+08 Median : 1440
## Mean :1.58 Mean :9.191e+09 Mean :6.012e+09 Mean : 9875
## 3rd Qu.:2.00 3rd Qu.:1.150e+08 3rd Qu.:4.950e+08 3rd Qu.: 4096
## Max. :8.00 Max. :1.947e+13 Max. :8.016e+12 Max. :5740995
## NA's :2214 NA's :2214 NA's :2214
## Motorcycles Wheeled_tractor UBER MAC
## Min. : 4 Min. : 0.000 1 : 125 Min. : 1.000
## 1st Qu.: 591 1st Qu.: 0.000 NA's:5427 1st Qu.: 1.000
## Median : 1286 Median : 0.000 Median : 2.000
## Mean : 4886 Mean : 5.762 Mean : 4.277
## 3rd Qu.: 3300 3rd Qu.: 1.000 3rd Qu.: 3.000
## Max. :1134570 Max. :3236.000 Max. :130.000
## NA's :5386
## WAL-MART POST_OFFICES LOG_GDP_CAPITA
## Min. : 1.000 Min. : 1.000 Min. : 8.068
## 1st Qu.: 1.000 1st Qu.: 1.000 1st Qu.: 9.112
## Median : 1.000 Median : 1.000 Median : 9.673
## Mean : 2.059 Mean : 2.082 Mean : 9.698
## 3rd Qu.: 1.750 3rd Qu.: 2.000 3rd Qu.:10.172
## Max. :26.000 Max. :225.000 Max. :12.659
## NA's :5450 NA's :113Pr_Assets
Pr_Assets and Pu_Assets are selected as assets are equivalent to money, which can count towards interests and investments, and investments is a factor that affects GDP.
As there are 1544 NA values for Pr_Assets, We will choose not to use this value in this case, as it will remove a large amount of observation.
Pu_Assets
There are 1544 NA values for Pu_Assets, We will choose not to use this value in this case, as it will remove a large amount of observation.
After removing all the NA values, we can conduct a correlation matrix
Correlation matrix
We will select our variables first
brazil3 <- brazil%>%
dplyr::select("IBGE_RES_POP", "Active_pop", "IBGE_CROP_PRODUCTION", "IDHM_Longevidade", "IDHM_Educacao", "IDHM_Renda", "PAY_TV", "FIXED_PHONES", "AREA", "GVA_AGROPEC", "GVA_INDUSTRY", "GVA_SERVICES", "TAXES", "GDP", "POP_GDP", "GDP_CAPITA", "COMP_TOT", "Cars", "Motorcycles")
Before doing so, we will double check the NAs in the variables
summary(brazil3)## IBGE_RES_POP Active_pop IBGE_CROP_PRODUCTION IDHM_Longevidade
## Min. : 805 Min. : 94 Min. : 0 Min. :0.6720
## 1st Qu.: 5236 1st Qu.: 1735 1st Qu.: 2332 1st Qu.:0.7690
## Median : 10943 Median : 3848 Median : 13859 Median :0.8080
## Mean : 34330 Mean : 18243 Mean : 57327 Mean :0.8016
## 3rd Qu.: 23646 3rd Qu.: 9634 3rd Qu.: 55564 3rd Qu.:0.8360
## Max. :11253503 Max. :7058221 Max. :3274885 Max. :0.8940
## IDHM_Educacao IDHM_Renda PAY_TV FIXED_PHONES
## Min. :0.2070 Min. :0.400 Min. : 1 Min. : 3
## 1st Qu.:0.4900 1st Qu.:0.572 1st Qu.: 88 1st Qu.: 119
## Median :0.5600 Median :0.654 Median : 248 Median : 328
## Mean :0.5592 Mean :0.643 Mean : 3103 Mean : 6587
## 3rd Qu.:0.6310 3rd Qu.:0.707 3rd Qu.: 817 3rd Qu.: 1156
## Max. :0.8250 Max. :0.891 Max. :2047668 Max. :5543127
## AREA GVA_AGROPEC GVA_INDUSTRY GVA_SERVICES
## Min. : 3.57 Min. : 0 Min. : 1 Min. : 2
## 1st Qu.: 204.70 1st Qu.: 4194 1st Qu.: 1726 1st Qu.: 10110
## Median : 415.86 Median : 20440 Median : 7451 Median : 31242
## Mean : 1515.99 Mean : 47279 Mean : 176424 Mean : 490859
## 3rd Qu.: 1025.17 3rd Qu.: 51243 3rd Qu.: 41097 3rd Qu.: 115678
## Max. :159533.33 Max. :1402282 Max. :63306755 Max. :464656988
## TAXES GDP POP_GDP GDP_CAPITA
## Min. : -14159 Min. : 15 Min. : 815 Min. : 3191
## 1st Qu.: 1302 1st Qu.: 43691 1st Qu.: 5492 1st Qu.: 9064
## Median : 5114 Median : 125473 Median : 11588 Median : 15877
## Mean : 119215 Mean : 957210 Mean : 37081 Mean : 21136
## 3rd Qu.: 22289 3rd Qu.: 330284 3rd Qu.: 25120 3rd Qu.: 26168
## Max. :117125387 Max. :687035890 Max. :12038175 Max. :314638
## COMP_TOT Cars Motorcycles
## Min. : 6.0 Min. : 2 Min. : 4
## 1st Qu.: 68.0 1st Qu.: 602 1st Qu.: 591
## Median : 163.0 Median : 1440 Median : 1286
## Mean : 909.2 Mean : 9875 Mean : 4886
## 3rd Qu.: 450.0 3rd Qu.: 4096 3rd Qu.: 3300
## Max. :530446.0 Max. :5740995 Max. :1134570After confirming there are no NA values, we can now plot the correlation matrix
corrplot(cor(brazil3), diag=FALSE, order="alphabet", tl.pos="td", tl.cex=0.5,number.cex=0.4, method="number", type="upper")
As seen in the correlation plot, many variables are highly correlated. To prevent this, we will derive new variables.
In addition, since IBGE_RES_POP and Active_pop have a correlation value of 1, we conclude that these two variables are rather similar. IBGE_RES_POP and Active_pop are both population of the municipality, but we would choose Active_pop instead since they are the economically active group, which contributes most to the economy, and hence would perhaps have the greatest correlation to GDP_CAPITA. This could be due to the economically active group earning income, spending income, and paying taxes.
5.6 Deriving new variables
Since GDP_CAPITA is taken by GDP divided by population, population affects GDP. For consistency, we will divide several variables by population.
PAY_TV
We will divide PAY_TV by population, to be able to calculate approximate number of pay_tv each individual has
brazil <- brazil %>%
mutate(PAY_TV_p = PAY_TV/POP_GDP)FIXED_PHONES
We will divide FIXED_PHONES by population, to be able to calculate approximate number of fixed_phone each individual has
brazil <- brazil %>%
mutate(FIXED_PHONES_p = FIXED_PHONES/POP_GDP)Cars
We will divide Cars by population, to be able to calculate approximate number of cars each individual has
brazil <- brazil %>%
mutate(Cars_p =Cars/POP_GDP)Motorcycles
We will divide Motorcycles by population, to be able to calculate approximate number of motorcycles each individual has
brazil <- brazil %>%
mutate(Motorcycles_p = Motorcycles/POP_GDP)GVA_AGROPEC
GVA tells us how much value is added or lost from a municipality, which can be used in the calculation of GDP. We divide GVA_AGROPEC by population, to calculate the approximate Gross Added Value of each individual
brazil <- brazil %>%
mutate(GVA_AGROPEC_p = GVA_AGROPEC/POP_GDP)GVA_INDUSTRY
We divide GVA_INDUSTRY by population, to calculate the approximate Gross Added Value of each individual
brazil <- brazil %>%
mutate(GVA_INDUSTRY_p = GVA_INDUSTRY/POP_GDP)GVA_SERVICES
We divide GVA_SERVICES by population, to calculate the approximate Gross Added Value of each individual
brazil <- brazil %>%
mutate(GVA_SERVICES_p = GVA_SERVICES/POP_GDP)We will also derive new variables such as pop_density, as the higher the population density in a city, the higher the possibility of spending in that city, increasing the GDP_CAPITA. We will use population divided by area to calculate pop_density ##### pop_density
brazil <- brazil %>%
mutate(pop_density = POP_GDP/AREA)We will also derive a tax to gdp ratio, which tells us how the government spend the tax money. It is calculated by taking taxes dividing by GDP. A higher ratio suggests higher ability for sustainable economic growth. ##### tax_to_gdp
brazil <- brazil %>%
mutate(tax_to_gdp = TAXES/GDP)5.7 Correlation matrix
Select variables first
brazil4 <- brazil%>%
dplyr::select("Active_pop", "IBGE_CROP_PRODUCTION", "IDHM_Longevidade", "IDHM_Educacao", "IDHM_Renda", "PAY_TV_p", "FIXED_PHONES_p", "GVA_AGROPEC_p", "GVA_INDUSTRY_p", "GVA_SERVICES_p", "tax_to_gdp", "GDP_CAPITA", "COMP_TOT", "Cars_p", "Motorcycles_p", "pop_density")We will, again, double confirm there are no NA values in our data set
summary(brazil4)## Active_pop IBGE_CROP_PRODUCTION IDHM_Longevidade IDHM_Educacao
## Min. : 94 Min. : 0 Min. :0.6720 Min. :0.2070
## 1st Qu.: 1735 1st Qu.: 2332 1st Qu.:0.7690 1st Qu.:0.4900
## Median : 3848 Median : 13859 Median :0.8080 Median :0.5600
## Mean : 18243 Mean : 57327 Mean :0.8016 Mean :0.5592
## 3rd Qu.: 9634 3rd Qu.: 55564 3rd Qu.:0.8360 3rd Qu.:0.6310
## Max. :7058221 Max. :3274885 Max. :0.8940 Max. :0.8250
## IDHM_Renda PAY_TV_p FIXED_PHONES_p GVA_AGROPEC_p
## Min. :0.400 Min. :0.000196 Min. :0.0004817 Min. : 0.0000
## 1st Qu.:0.572 1st Qu.:0.011429 1st Qu.:0.0134803 1st Qu.: 0.3543
## Median :0.654 Median :0.024615 Median :0.0382001 Median : 1.4255
## Mean :0.643 Mean :0.037121 Mean :0.0605970 Mean : 3.7476
## 3rd Qu.:0.707 3rd Qu.:0.048320 3rd Qu.:0.0854910 3rd Qu.: 4.7287
## Max. :0.891 Max. :0.480541 Max. :1.0372617 Max. :121.0575
## GVA_INDUSTRY_p GVA_SERVICES_p tax_to_gdp GDP_CAPITA
## Min. : 0.0001 Min. : 0.00049 Min. : -2.0920 Min. : 3191
## 1st Qu.: 0.2607 1st Qu.: 1.61815 1st Qu.: 0.0297 1st Qu.: 9064
## Median : 0.7919 Median : 3.52467 Median : 0.0527 Median : 15877
## Mean : 3.3100 Mean : 5.61031 Mean : 8.5631 Mean : 21136
## 3rd Qu.: 2.5950 3rd Qu.: 7.73471 3rd Qu.: 0.0973 3rd Qu.: 26168
## Max. :254.9198 Max. :108.80127 Max. :324.6684 Max. :314638
## COMP_TOT Cars_p Motorcycles_p pop_density
## Min. : 6.0 Min. :0.0000529 Min. :0.0001059 Min. : 0.166
## 1st Qu.: 68.0 1st Qu.:0.0627272 1st Qu.:0.0872258 1st Qu.: 11.946
## Median : 163.0 Median :0.1731448 Median :0.1234463 Median : 25.309
## Mean : 909.2 Mean :0.1918811 Mean :0.1340853 Mean : 117.472
## 3rd Qu.: 450.0 3rd Qu.:0.3117910 3rd Qu.:0.1693006 3rd Qu.: 55.477
## Max. :530446.0 Max. :0.6440065 Max. :0.5500341 Max. :13533.497corrplot(cor(brazil4), diag=FALSE, order="alphabet", tl.pos="td", tl.cex=0.5,number.cex=0.5, method="number", type="upper")
corrplot(cor(brazil4), diag=FALSE, order="alphabet", tl.pos="td", tl.cex=0.5,number.cex=0.5, method="square", type="upper")
We chose to order the variables alphabetically for easy identifcation. From the scatterplot, we see that Active_pop is highly correlated to COMP_TOT (correlation value = 0.97). In view of this, we should only include either one in the subsequent model building. As a result, COMP_TOT is excluded in the subsequent model builing.
5.8 Correlation matrix without COMP_TOT
corrplot(cor(brazil4[,c(1:12, 14:16)]), diag=FALSE, order="alphabet", tl.pos="td", tl.cex=0.5,number.cex=0.5, method="number", type="upper")
corrplot(cor(brazil4[,c(1:12,14:16)]), diag=FALSE, order="alphabet", tl.pos="td", tl.cex=0.5,number.cex=0.5, method="square", type="upper")
Having selecting our variables needed, we can now do the modelling.
We will be doing a linear modelling, with the GDP_CAPITA with all the independent variables that we have identified previously.
6. Multiple Linear Regression
6.1 Join the aspatial and geospatial data
Before joining, we have identified that the names of variables in name_muni and CITY in mun and brazil respectively are not consistent. We will hence upper case all the letters for both variables.
mun$name_muni <- toupper(mun$name_muni)
brazil$CITY <- toupper(brazil$CITY)brazil_mun <- right_join(mun, brazil, by=c("name_muni"="CITY", "abbrev_state"="STATE"))## Warning: Column `abbrev_state`/`STATE` joining character vector and factor,
## coercing into character vectorCheck for missing geometries
any(is.na(st_dimension(brazil_mun)))## [1] FALSEqtm(brazil_mun, "GDP_CAPITA", border=NULL, scale=0.6) + tm_legend(main.title="GDP_CAPITA in 2016", main.title.position="centre")
6.2 Building Multiple linear regression
Select variables to use first
brazil6 <- brazil%>%
dplyr::select("Active_pop", "IBGE_CROP_PRODUCTION", "IDHM_Longevidade", "IDHM_Educacao", "IDHM_Renda", "PAY_TV_p", "FIXED_PHONES_p", "GVA_AGROPEC_p", "GVA_INDUSTRY_p", "GVA_SERVICES_p", "tax_to_gdp", "GDP_CAPITA", "Cars_p", "Motorcycles_p", "pop_density")Histogram Plots Distribution of Variables Selected
Before we conduct the linear regression, we will plot histograms of each of the variables, to have an idea of the distribution of the variables.
Active_pop <- ggplot(data=brazil6, aes(x=Active_pop))+
geom_histogram(bins=25, color="black", fill="light blue")
IBGE_CROP_PRODUCTION <- ggplot(data=brazil6, aes(x=IBGE_CROP_PRODUCTION))+
geom_histogram(bins=25, color="black", fill="light blue")
IDHM_Longevidade <- ggplot(data=brazil6, aes(x=IDHM_Longevidade))+
geom_histogram(bins=25, color="black", fill="light blue")
IDHM_Educacao <- ggplot(data=brazil6, aes(x=IDHM_Educacao))+
geom_histogram(bins=25, color="black", fill="light blue")
IDHM_Renda <- ggplot(data=brazil6, aes(x=IDHM_Renda))+
geom_histogram(bins=25, color="black", fill="light blue")
PAY_TV_p <- ggplot(data=brazil6, aes(x=PAY_TV_p))+
geom_histogram(bins=25, color="black", fill="light blue")
FIXED_PHONES_p <- ggplot(data=brazil6, aes(x=FIXED_PHONES_p))+
geom_histogram(bins=25, color="black", fill="light blue")
GVA_AGROPEC_p <- ggplot(data=brazil6, aes(x=GVA_AGROPEC_p))+
geom_histogram(bins=25, color="black", fill="light blue")
GVA_INDUSTRY_p <- ggplot(data=brazil6, aes(x=GVA_INDUSTRY_p))+
geom_histogram(bins=25, color="black", fill="light blue")
GVA_SERVICES_p <- ggplot(data=brazil6, aes(x=GVA_SERVICES_p))+
geom_histogram(bins=25, color="black", fill="light blue")
tax_to_gdp <- ggplot(data=brazil6, aes(x=tax_to_gdp))+
geom_histogram(bins=25, color="black", fill="light blue")
GDP_CAPITA <- ggplot(data=brazil6, aes(x=GDP_CAPITA))+
geom_histogram(bins=25, color="black", fill="light blue")
Cars_p <- ggplot(data=brazil6, aes(x=Cars_p))+
geom_histogram(bins=25, color="black", fill="light blue")
Motorcycles_p <- ggplot(data=brazil6, aes(x=Motorcycles_p))+
geom_histogram(bins=25, color="black", fill="light blue")
pop_density <- ggplot(data=brazil6, aes(x=pop_density))+
geom_histogram(bins=25, color="black", fill="light blue")
ggarrange(Active_pop, IBGE_CROP_PRODUCTION, IDHM_Longevidade, IDHM_Educacao, IDHM_Renda, PAY_TV_p, FIXED_PHONES_p, GVA_AGROPEC_p, GVA_INDUSTRY_p, GVA_SERVICES_p, tax_to_gdp, GDP_CAPITA, Cars_p, Motorcycles_p, pop_density, ncol=3, nrow=6)
We can tell from the data that most of them are skewed, either left or right. Some however, resemble a normal distribution. For eg, IDHM_Longevidade, IDHM_Educacao, IDHM_Renda, or Motorcycles_p (even though it is slightly right skewed)
Specification 1: GDP_CAPITA against all Xs
brazil_lm <- lm(GDP_CAPITA~., data=brazil6)
summary(brazil_lm)##
## Call:
## lm(formula = GDP_CAPITA ~ ., data = brazil6)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31274 -2969 -1027 1068 260244
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.692e+03 3.134e+03 -2.455 0.0141 *
## Active_pop -1.640e-03 1.027e-03 -1.598 0.1102
## IBGE_CROP_PRODUCTION 4.831e-03 8.530e-04 5.664 1.55e-08 ***
## IDHM_Longevidade -1.814e+03 4.676e+03 -0.388 0.6980
## IDHM_Educacao 2.279e+03 2.217e+03 1.028 0.3040
## IDHM_Renda 2.399e+04 3.961e+03 6.057 1.48e-09 ***
## PAY_TV_p 3.089e+03 3.702e+03 0.834 0.4041
## FIXED_PHONES_p 6.257e+03 3.111e+03 2.011 0.0443 *
## GVA_AGROPEC_p 9.139e+02 2.052e+01 44.540 < 2e-16 ***
## GVA_INDUSTRY_p 1.136e+03 1.234e+01 92.086 < 2e-16 ***
## GVA_SERVICES_p 9.654e+02 2.191e+01 44.071 < 2e-16 ***
## tax_to_gdp 1.097e+01 4.404e+00 2.491 0.0128 *
## Cars_p 3.006e+03 1.796e+03 1.674 0.0942 .
## Motorcycles_p -3.573e+03 1.796e+03 -1.989 0.0468 *
## pop_density 4.068e-01 2.155e-01 1.887 0.0592 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8386 on 5537 degrees of freedom
## Multiple R-squared: 0.8304, Adjusted R-squared: 0.8299
## F-statistic: 1936 on 14 and 5537 DF, p-value: < 2.2e-16AIC(brazil_lm)## [1] 116090BIC(brazil_lm)## [1] 116195.9
With reference to the report above, it is clear that not all the independent variables are statistically significant. We will revise the model by removing those variables which are not statistically significant (p > 0.05).
brazil_lm2 <- lm(GDP_CAPITA~ IBGE_CROP_PRODUCTION + IDHM_Renda + FIXED_PHONES_p + GVA_AGROPEC_p + GVA_INDUSTRY_p + GVA_SERVICES_p + tax_to_gdp + Motorcycles_p, data=brazil6)
summary(brazil_lm2)##
## Call:
## lm(formula = GDP_CAPITA ~ IBGE_CROP_PRODUCTION + IDHM_Renda +
## FIXED_PHONES_p + GVA_AGROPEC_p + GVA_INDUSTRY_p + GVA_SERVICES_p +
## tax_to_gdp + Motorcycles_p, data = brazil6)
##
## Residuals:
## Min 1Q Median 3Q Max
## -31029 -2986 -1077 1048 260099
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.056e+04 1.293e+03 -8.170 3.78e-16 ***
## IBGE_CROP_PRODUCTION 4.437e-03 8.406e-04 5.279 1.35e-07 ***
## IDHM_Renda 2.909e+04 2.297e+03 12.664 < 2e-16 ***
## FIXED_PHONES_p 8.901e+03 2.696e+03 3.302 0.000966 ***
## GVA_AGROPEC_p 9.133e+02 2.031e+01 44.974 < 2e-16 ***
## GVA_INDUSTRY_p 1.136e+03 1.232e+01 92.252 < 2e-16 ***
## GVA_SERVICES_p 9.694e+02 2.168e+01 44.725 < 2e-16 ***
## tax_to_gdp 1.105e+01 4.400e+00 2.510 0.012094 *
## Motorcycles_p -3.852e+03 1.776e+03 -2.169 0.030108 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8389 on 5543 degrees of freedom
## Multiple R-squared: 0.8301, Adjusted R-squared: 0.8298
## F-statistic: 3385 on 8 and 5543 DF, p-value: < 2.2e-16ols_regress(brazil_lm2)## Model Summary
## --------------------------------------------------------------------
## R 0.911 RMSE 8388.797
## R-Squared 0.830 Coef. Var 39.689
## Adj. R-Squared 0.830 MSE 70371919.117
## Pred R-Squared 0.828 MAE 3618.252
## --------------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## -------------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## -------------------------------------------------------------------------------------
## Regression 1.905457e+12 8 238182096351.380 3384.618 0.0000
## Residual 390071547665.115 5543 70371919.117
## Total 2.295528e+12 5551
## -------------------------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------------------------
## (Intercept) -10563.125 1292.878 -8.170 0.000 -13097.672 -8028.578
## IBGE_CROP_PRODUCTION 0.004 0.001 0.032 5.279 0.000 0.003 0.006
## IDHM_Renda 29090.224 2297.138 0.115 12.664 0.000 24586.934 33593.514
## FIXED_PHONES_p 8901.109 2695.720 0.030 3.302 0.001 3616.440 14185.778
## GVA_AGROPEC_p 913.327 20.308 0.287 44.974 0.000 873.516 953.138
## GVA_INDUSTRY_p 1136.382 12.318 0.553 92.252 0.000 1112.233 1160.530
## GVA_SERVICES_p 969.445 21.676 0.330 44.725 0.000 926.952 1011.938
## tax_to_gdp 11.046 4.400 0.014 2.510 0.012 2.419 19.673
## Motorcycles_p -3851.553 1775.544 -0.013 -2.169 0.030 -7332.315 -370.792
## ------------------------------------------------------------------------------------------------------------AIC(brazil_lm2)## [1] 116087.7BIC(brazil_lm2)## [1] 116153.9
Adjusted R2 = 0.8298
AIC = 116087.7
BIC = 116153.9
In order to use this model for the rest of our analysis, we need to check the assumptions of multiple linear regression.
##### 6.2.1 Check for multicolinearity
ols_vif_tol(brazil_lm)## Variables Tolerance VIF
## 1 Active_pop 0.7651375 1.306955
## 2 IBGE_CROP_PRODUCTION 0.7928779 1.261228
## 3 IDHM_Longevidade 0.2900536 3.447638
## 4 IDHM_Educacao 0.2958672 3.379894
## 5 IDHM_Renda 0.1240375 8.062076
## 6 PAY_TV_p 0.5831230 1.714904
## 7 FIXED_PHONES_p 0.2842390 3.518166
## 8 GVA_AGROPEC_p 0.7358332 1.359004
## 9 GVA_INDUSTRY_p 0.8496988 1.176888
## 10 GVA_SERVICES_p 0.5511510 1.814385
## 11 tax_to_gdp 0.9731863 1.027552
## 12 Cars_p 0.2071776 4.826778
## 13 Motorcycles_p 0.8815642 1.134347
## 14 pop_density 0.7243592 1.380531
Since the VIF of the independent variables are less than 10, we can safely conclude that there are no sign of multicollinearity among the independent variables. This suggests that there is a low to moderate correlation between variables, but it is not a significant cause for concern.
6.2.2 Test for Non-Linearity
Test the assumption that linearity and additivity of the relationship between dependent and independent variables
ols_plot_resid_fit(brazil_lm2)
Looking at the residuals vs fitted values plot, the red line is approximately at 0. There is no pattern in the residual plot, suggesting that we can assume a linear relationship between the predictors and outcome variables.
6.2.3 Test for Normality Assumption
ols_plot_resid_hist(brazil_lm2)
The figure reveals that the residual of the multiple linear regression model resemble normal distribution
We will make another test to further verify out testing of assumption
fnorm <- fitdist(residuals(brazil_lm2), distr="norm")
summary(fnorm)## Fitting of the distribution ' norm ' by maximum likelihood
## Parameters :
## estimate Std. Error
## mean 2.674790e-14 114.40902
## sd 8.381995e+03 79.49234
## Loglikelihood: -58033.83 AIC: 116071.7 BIC: 116084.9
## Correlation matrix:
## mean sd
## mean 1 0
## sd 0 1plot(fnorm)
Q-Q plot and P-P plot shows no deviation from normal distribution. From the code chunk below, at the 95% significance level, KS statistic is smaller than the critical value (0.1968861 < 0.3205551). Do not reject null hypothesis. There is insufficient evidence to suspect that the residuals of the multiple linear regression model are not normally distributed. Hence, they are normally distributed.
par(mfrow=c(2,2))
plot(brazil_lm2)
gofstat(fnorm,discrete=FALSE)## Goodness-of-fit statistics
## 1-mle-norm
## Kolmogorov-Smirnov statistic 0.2266629
## Cramer-von Mises statistic 112.2075310
## Anderson-Darling statistic Inf
##
## Goodness-of-fit criteria
## 1-mle-norm
## Akaike's Information Criterion 116071.7
## Bayesian Information Criterion 116084.9KScritvalue <- 1.36/sqrt(length(brazil6))
KScritvalue ## [1] 0.3511505
Looking at the spread location plot, the variances of the residual points increases with the value of the fitted outcome variable, suggesting heteroscedasticity.
As some of our assumptions are not met, we run a 2nd specification: log GDP_CAPITA against all other Xs to correct extreme values, and eliminate heteroscedasticity..
6.3 Multiple Log-Linear Regression
brazil_lglm <- lm(log(GDP_CAPITA)~., data=brazil6)
summary(brazil_lglm)##
## Call:
## lm(formula = log(GDP_CAPITA) ~ ., data = brazil6)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.85604 -0.16554 -0.03425 0.13553 2.75065
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.504e+00 1.025e-01 63.467 < 2e-16 ***
## Active_pop -3.059e-08 3.357e-08 -0.911 0.362
## IBGE_CROP_PRODUCTION 2.670e-07 2.789e-08 9.574 < 2e-16 ***
## IDHM_Longevidade 6.452e-01 1.529e-01 4.219 2.49e-05 ***
## IDHM_Educacao 1.023e-01 7.250e-02 1.411 0.158
## IDHM_Renda 3.494e+00 1.295e-01 26.974 < 2e-16 ***
## PAY_TV_p -1.358e-01 1.211e-01 -1.122 0.262
## FIXED_PHONES_p 5.489e-02 1.017e-01 0.540 0.590
## GVA_AGROPEC_p 2.786e-02 6.710e-04 41.515 < 2e-16 ***
## GVA_INDUSTRY_p 1.880e-02 4.035e-04 46.600 < 2e-16 ***
## GVA_SERVICES_p 2.013e-02 7.164e-04 28.100 < 2e-16 ***
## tax_to_gdp 7.901e-04 1.440e-04 5.487 4.28e-08 ***
## Cars_p 4.289e-01 5.873e-02 7.302 3.24e-13 ***
## Motorcycles_p -6.957e-02 5.875e-02 -1.184 0.236
## pop_density -8.081e-07 7.049e-06 -0.115 0.909
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2742 on 5537 degrees of freedom
## Multiple R-squared: 0.8394, Adjusted R-squared: 0.839
## F-statistic: 2067 on 14 and 5537 DF, p-value: < 2.2e-16AIC(brazil_lglm)## [1] 1407.291BIC(brazil_lglm)## [1] 1513.241
With reference to the report above, it is clear that not all the independent variables are statistically significant. We will revise the model by removing those variables which are not statistically significant.
##### 6.3.1 Selecting statistically significant variables
brazil_lglm2 <- lm(log(GDP_CAPITA)~ IBGE_CROP_PRODUCTION + IDHM_Longevidade + IDHM_Renda + GVA_AGROPEC_p + GVA_INDUSTRY_p + GVA_SERVICES_p + tax_to_gdp + Cars_p, data=brazil6)
summary(brazil_lglm2)##
## Call:
## lm(formula = log(GDP_CAPITA) ~ IBGE_CROP_PRODUCTION + IDHM_Longevidade +
## IDHM_Renda + GVA_AGROPEC_p + GVA_INDUSTRY_p + GVA_SERVICES_p +
## tax_to_gdp + Cars_p, data = brazil6)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.86710 -0.16500 -0.03439 0.13338 2.75733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.512e+00 9.999e-02 65.126 < 2e-16 ***
## IBGE_CROP_PRODUCTION 2.663e-07 2.754e-08 9.671 < 2e-16 ***
## IDHM_Longevidade 6.639e-01 1.522e-01 4.362 1.32e-05 ***
## IDHM_Renda 3.523e+00 1.143e-01 30.807 < 2e-16 ***
## GVA_AGROPEC_p 2.787e-02 6.319e-04 44.104 < 2e-16 ***
## GVA_INDUSTRY_p 1.884e-02 4.022e-04 46.856 < 2e-16 ***
## GVA_SERVICES_p 2.010e-02 6.731e-04 29.859 < 2e-16 ***
## tax_to_gdp 7.833e-04 1.434e-04 5.461 4.93e-08 ***
## Cars_p 4.546e-01 5.691e-02 7.988 1.66e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2742 on 5543 degrees of freedom
## Multiple R-squared: 0.8392, Adjusted R-squared: 0.839
## F-statistic: 3616 on 8 and 5543 DF, p-value: < 2.2e-16ols_regress(brazil_lglm2)## Model Summary
## -------------------------------------------------------------
## R 0.916 RMSE 0.274
## R-Squared 0.839 Coef. Var 2.828
## Adj. R-Squared 0.839 MSE 0.075
## Pred R-Squared 0.836 MAE 0.197
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------
## Regression 2175.562 8 271.945 3616.278 0.0000
## Residual 416.835 5543 0.075
## Total 2592.397 5551
## ------------------------------------------------------------------------
##
## Parameter Estimates
## ----------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ----------------------------------------------------------------------------------------------
## (Intercept) 6.512 0.100 65.126 0.000 6.316 6.708
## IBGE_CROP_PRODUCTION 0.000 0.000 0.058 9.671 0.000 0.000 0.000
## IDHM_Longevidade 0.664 0.152 0.043 4.362 0.000 0.365 0.962
## IDHM_Renda 3.523 0.114 0.416 30.807 0.000 3.298 3.747
## GVA_AGROPEC_p 0.028 0.001 0.261 44.104 0.000 0.027 0.029
## GVA_INDUSTRY_p 0.019 0.000 0.273 46.856 0.000 0.018 0.020
## GVA_SERVICES_p 0.020 0.001 0.204 29.859 0.000 0.019 0.021
## tax_to_gdp 0.001 0.000 0.030 5.461 0.000 0.001 0.001
## Cars_p 0.455 0.057 0.092 7.988 0.000 0.343 0.566
## ----------------------------------------------------------------------------------------------AIC(brazil_lglm2)## [1] 1400.531BIC(brazil_lglm2)## [1] 1466.75
Adjusted R2=0.839
AIC = 1400.531
BIC = 1466.75
6.3.2 Checking assumptions
ols_plot_resid_hist(brazil_lglm2)
fnorm <- fitdist(residuals(brazil_lglm2), distr="norm")
summary(fnorm)## Fitting of the distribution ' norm ' by maximum likelihood
## Parameters :
## estimate Std. Error
## mean -3.231877e-18 0.003677332
## sd 2.740044e-01 0.002600110
## Loglikelihood: -690.2656 AIC: 1384.531 BIC: 1397.775
## Correlation matrix:
## mean sd
## mean 1 0
## sd 0 1plot(fnorm)
par(mfrow=c(2,2))
plot(brazil_lglm2)
gofstat(fnorm,discrete=FALSE)## Goodness-of-fit statistics
## 1-mle-norm
## Kolmogorov-Smirnov statistic 0.06763436
## Cramer-von Mises statistic 10.70174891
## Anderson-Darling statistic Inf
##
## Goodness-of-fit criteria
## 1-mle-norm
## Akaike's Information Criterion 1384.531
## Bayesian Information Criterion 1397.775KScritvalue <- 1.36/sqrt(length(brazil6))
KScritvalue ## [1] 0.3511505
The plots are now more favourable and there is a higher adjusted R2 and lower AIC and BIC values. The significant variables have changed slightly too.
summary(brazil_lglm2)##
## Call:
## lm(formula = log(GDP_CAPITA) ~ IBGE_CROP_PRODUCTION + IDHM_Longevidade +
## IDHM_Renda + GVA_AGROPEC_p + GVA_INDUSTRY_p + GVA_SERVICES_p +
## tax_to_gdp + Cars_p, data = brazil6)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.86710 -0.16500 -0.03439 0.13338 2.75733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.512e+00 9.999e-02 65.126 < 2e-16 ***
## IBGE_CROP_PRODUCTION 2.663e-07 2.754e-08 9.671 < 2e-16 ***
## IDHM_Longevidade 6.639e-01 1.522e-01 4.362 1.32e-05 ***
## IDHM_Renda 3.523e+00 1.143e-01 30.807 < 2e-16 ***
## GVA_AGROPEC_p 2.787e-02 6.319e-04 44.104 < 2e-16 ***
## GVA_INDUSTRY_p 1.884e-02 4.022e-04 46.856 < 2e-16 ***
## GVA_SERVICES_p 2.010e-02 6.731e-04 29.859 < 2e-16 ***
## tax_to_gdp 7.833e-04 1.434e-04 5.461 4.93e-08 ***
## Cars_p 4.546e-01 5.691e-02 7.988 1.66e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2742 on 5543 degrees of freedom
## Multiple R-squared: 0.8392, Adjusted R-squared: 0.839
## F-statistic: 3616 on 8 and 5543 DF, p-value: < 2.2e-16The following equation includes variables that are significant in the log multiple linear regression model.
###### GDP_CAPITA = 6.512 + 2.663e-07 IBGE_CROP_PRODUCTION + 0.6639 IDHM_Longevidade + 3.523 IDHM_Renda + 0.4546 Cars_p + 0.02787 GVA_AGROPEC_p + 0.01884 GVA_INDUSTRY_p + 0.02010 GVA_SERVICES + 7.833e-04 tax_to_gdp
6.4 Testing for Spatial Autocorrelation
We have to visualise the residuals of the multiple linear regression model that we have achieved above
In order to perform spatial autocorrelation test, We will need to convert brazil into a SpatialPointsDataFrame
6.4.1 SpatialPoint
brazil.point.sf <- st_as_sf(brazil, coords=c("LONG", "LAT"), crs=4674)%>%
st_transform(crs=4674)6.4.2 SpatialPolygon
brazil.polygon.sf <- right_join(mun, brazil, by=c("name_muni" = "CITY", "abbrev_state" = "STATE"))## Warning: Column `abbrev_state`/`STATE` joining character vector and factor,
## coercing into character vector6.4.3 Convert to sf
brazil.polygon.sf <- st_as_sf(brazil.polygon.sf, crs=4674) %>%
st_transform(crs=4674)6.4.4 Residuals
Next, we will export the residual of the model and save it as a separate data frame
mlr.output <- as.data.frame(brazil_lglm2$residuals)We will then join this newly created mlr.output data frame with brazil.point.sf object and brazil.polygon.sf object
brazil.point.res.sf <- cbind(brazil.point.sf,
brazil_lglm2$residuals) %>%
rename(`MLR_RES` = `brazil_lglm2.residuals`)
brazil.polygon.res.sf <- cbind(brazil.polygon.sf,
brazil_lglm2$residuals) %>%
rename(`MLR_RES` = `brazil_lglm2.residuals`)We will load the spatial point and spatial polygon point respectively
brazil.point.res.sf## Simple feature collection with 5552 features and 90 fields
## geometry type: POINT
## dimension: XY
## bbox: xmin: -72.9165 ymin: -33.68757 xmax: 51.4725 ymax: 4.58544
## geographic CRS: SIRGAS 2000
## First 10 features:
## CITY STATE CAPITAL IBGE_RES_POP IBGE_RES_POP_BRAS
## 1 ABADIA DE GOIÁS GO 0 6876 6876
## 2 ABADIA DOS DOURADOS MG 0 6704 6704
## 3 ABADIÂNIA GO 0 15757 15609
## 4 ABAETÉ MG 0 22690 22690
## 5 ABAETETUBA PA 0 141100 141040
## 6 ABAIARA CE 0 10496 10496
## 7 ABAÍRA BA 0 8316 8316
## 8 ABARÉ BA 0 17064 17064
## 9 ABATIÁ PR 0 7764 7764
## 10 ABDON BATISTA SC 0 2653 2653
## IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN IBGE_DU_RURAL IBGE_POP IBGE_1
## 1 0 2137 1546 591 5300 69
## 2 0 2328 1481 847 4154 38
## 3 148 4655 3233 1422 10656 139
## 4 0 7694 6667 1027 18464 176
## 5 60 31061 19057 12004 82956 1354
## 6 0 2791 1251 1540 4538 98
## 7 0 2572 1193 1379 3725 37
## 8 0 4332 2379 1953 8994 167
## 9 0 2499 1877 622 5685 69
## 10 0 848 234 614 724 12
## IBGE_1.4 IBGE_5.9 IBGE_10.14 Active_pop IBGE_60. IBGE_PLANTED_AREA
## 1 318 438 517 3542 416 319
## 2 207 260 351 2709 589 4479
## 3 650 894 1087 6896 990 10307
## 4 856 1233 1539 11979 2681 1862
## 5 5567 7618 8905 53516 5996 25200
## 6 323 421 483 2631 582 2598
## 7 156 263 277 2319 673 895
## 8 733 978 927 5386 803 2058
## 9 302 370 483 3650 811 1197
## 10 32 49 63 479 89 5502
## IBGE_CROP_PRODUCTION IDHM.Ranking.2010 IDHM IDHM_Renda IDHM_Longevidade
## 1 1843 1689 0.708 0.687 0.830
## 2 18017 2207 0.690 0.693 0.839
## 3 33085 2202 0.690 0.671 0.841
## 4 7502 1994 0.698 0.720 0.848
## 5 700872 3530 0.628 0.579 0.798
## 6 5234 3522 0.628 0.540 0.748
## 7 3999 4086 0.603 0.577 0.746
## 8 22761 4756 0.575 0.533 0.776
## 9 9943 2258 0.687 0.676 0.804
## 10 26195 2092 0.690 0.660 0.812
## IDHM_Educacao ALT PAY_TV FIXED_PHONES AREA
## 1 0.622 893.60 360 842 147.26
## 2 0.563 753.12 77 296 881.06
## 3 0.579 1017.55 227 720 1045.13
## 4 0.556 644.74 1230 1716 1817.07
## 5 0.537 10.12 3389 1218 1610.65
## 6 0.612 403.11 29 34 180.08
## 7 0.510 674.22 952 335 538.68
## 8 0.460 316.38 51 222 1604.92
## 9 0.596 579.30 55 392 228.72
## 10 0.625 720.98 109 260 237.16
## REGIAO_TUR CATEGORIA_TUR ESTIMATED_POP
## 1 <NA> <NA> 8583
## 2 Caminhos Do Cerrado D 6972
## 3 Região Turística Do Ouro E Cristais C 19614
## 4 Lago De Três Marias D 23223
## 5 Araguaia-Tocantins D 156292
## 6 <NA> <NA> 11663
## 7 Chapada Diamantina D 8767
## 8 <NA> <NA> 19814
## 9 <NA> <NA> 7507
## 10 Vale Do Contestado D 2577
## RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY GVA_SERVICES GVA_PUBLIC GVA_TOTAL
## 1 Urbano 6.20 27991.25 74750.32 36915.04 145857.60
## 2 Rural Adjacente 50524.57 25917.70 62689.23 28083.79 167215.28
## 3 Rural Adjacente 42.84 16728.30 138198.58 63396.20 261161.91
## 4 Urbano 113824.60 31002.62 172.33 86081.41 403241.27
## 5 Urbano 140463.72 58610.00 468128.69 486872.40 1154074.81
## 6 Rural Adjacente 4435.16 5.88 22.81 35989.96 69108.67
## 7 Rural Remoto 12.41 3437.43 17990.74 28463.74 62304.83
## 8 Rural Remoto 9176.40 6.70 36921.84 65.75 118.55
## 9 Rural Adjacente 73340.52 8839.71 42999.37 34103.49 159283.08
## 10 Rural Adjacente 24996.75 3578.87 16011.10 17842.64 62429.36
## TAXES GDP POP_GDP GDP_CAPITA
## 1 20554.20 166.41 8053 20664.57
## 2 12873.50 180.09 7037 25591.70
## 3 26822.58 287984.49 18427 15628.40
## 4 26994.09 430235.36 23574 18250.42
## 5 95180.48 1249255.29 151934 8222.36
## 6 4042.79 73151.46 11483 6370.41
## 7 2019.77 64324.59 9212 6982.70
## 8 6.21 124754.26 19939 6256.80
## 9 5.77 165048.21 7795 21173.60
## 10 2312.65 64742.01 2617 24739.02
## GVA_MAIN
## 1 Demais serviços
## 2 Demais serviços
## 3 Demais serviços
## 4 Demais serviços
## 5 Administração, defesa, educação e saúde públicas e seguridade social
## 6 Administração, defesa, educação e saúde públicas e seguridade social
## 7 Administração, defesa, educação e saúde públicas e seguridade social
## 8 Administração, defesa, educação e saúde públicas e seguridade social
## 9 Agricultura, inclusive apoio à agricultura e a pós colheita
## 10 Administração, defesa, educação e saúde públicas e seguridade social
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B COMP_C COMP_D COMP_E COMP_F COMP_G
## 1 28227691 284 5 1 56 0 2 29 110
## 2 17909274 476 6 6 30 1 2 34 190
## 3 37513019 288 5 9 26 0 2 7 117
## 4 NA 621 18 1 40 0 1 20 303
## 5 NA 931 4 2 43 0 1 27 500
## 6 NA 86 1 0 4 0 0 6 48
## 7 NA 191 6 0 8 0 1 4 97
## 8 NA 87 2 0 3 0 0 0 71
## 9 NA 285 5 0 20 0 1 10 133
## 10 19506956 69 2 0 4 0 0 2 35
## COMP_H COMP_I COMP_J COMP_K COMP_L COMP_M COMP_N COMP_O COMP_P COMP_Q COMP_R
## 1 26 4 5 0 2 10 12 4 6 6 1
## 2 70 28 11 0 4 15 29 2 9 14 6
## 3 12 57 2 1 0 7 15 3 11 5 1
## 4 62 30 9 6 4 28 27 2 15 19 9
## 5 16 31 6 1 1 22 16 2 155 33 15
## 6 2 10 2 0 0 2 3 2 0 2 0
## 7 5 5 3 1 0 5 5 2 8 1 2
## 8 0 1 1 0 0 0 1 2 0 2 0
## 9 18 14 8 0 4 11 26 2 8 9 4
## 10 8 3 1 1 0 4 0 2 1 3 0
## COMP_S COMP_T COMP_U HOTELS BEDS Pr_Agencies Pu_Agencies Pr_Bank Pu_Bank
## 1 5 0 0 NA NA NA NA NA NA
## 2 19 0 0 NA NA NA NA NA NA
## 3 8 0 0 1 34 1 1 1 1
## 4 27 0 0 NA NA 2 2 2 2
## 5 56 0 0 NA NA 2 4 2 4
## 6 4 0 0 NA NA NA NA NA NA
## 7 38 0 0 1 24 NA NA NA NA
## 8 4 0 0 NA NA 1 0 1 0
## 9 12 0 0 NA NA 0 1 0 1
## 10 3 0 0 NA NA 0 1 0 1
## Pr_Assets Pu_Assets Cars Motorcycles Wheeled_tractor UBER MAC WAL.MART
## 1 NA NA 2158 1246 0 <NA> NA NA
## 2 NA NA 2227 1142 0 <NA> NA NA
## 3 33724584 67091904 2838 1426 0 <NA> NA NA
## 4 44974716 371922572 6928 2953 0 <NA> NA NA
## 5 76181384 800078483 5277 25661 0 <NA> NA NA
## 6 NA NA 553 1674 0 <NA> NA NA
## 7 NA NA 896 696 0 <NA> NA NA
## 8 21823314 0 613 1532 0 <NA> NA NA
## 9 0 45976288 2168 912 0 <NA> NA NA
## 10 0 42909056 976 345 2 <NA> NA NA
## POST_OFFICES LOG_GDP_CAPITA PAY_TV_p FIXED_PHONES_p Cars_p
## 1 1 9.936176 0.044703837 0.104557308 0.26797467
## 2 1 10.150023 0.010942163 0.042063379 0.31647009
## 3 3 9.656845 0.012318880 0.039073099 0.15401313
## 4 4 9.811943 0.052176126 0.072792059 0.29388309
## 5 2 9.014613 0.022305738 0.008016639 0.03473219
## 6 1 8.759419 0.002525472 0.002960899 0.04815815
## 7 1 8.851191 0.103343465 0.036365610 0.09726444
## 8 1 8.741424 0.002557801 0.011133959 0.03074377
## 9 1 9.960510 0.007055805 0.050288647 0.27812700
## 10 1 10.116137 0.041650745 0.099350401 0.37294612
## Motorcycles_p GVA_AGROPEC_p GVA_INDUSTRY_p GVA_SERVICES_p pop_density
## 1 0.15472495 0.0007698994 3.4758785546 9.282294797 54.68559
## 2 0.16228506 7.1798451044 3.6830609635 8.908516413 7.98697
## 3 0.07738644 0.0023248494 0.9078146199 7.499787269 17.63130
## 4 0.12526512 4.8283956902 1.3151191991 0.007310172 12.97363
## 5 0.16889570 0.9245048508 0.3857596061 3.081131873 94.33086
## 6 0.14578072 0.3862370461 0.0005120613 0.001986415 63.76610
## 7 0.07555363 0.0013471559 0.3731469822 1.952967868 17.10106
## 8 0.07683434 0.4602236822 0.0003360249 1.851739806 12.42367
## 9 0.11699808 9.4086619628 1.1340230917 5.516275818 34.08097
## 10 0.13183034 9.5516813145 1.3675468093 6.118112342 11.03474
## tax_to_gdp MLR_RES geometry
## 1 1.235154e+02 -0.01765106 POINT (-49.44055 -16.75881)
## 2 7.148370e+01 -0.01299481 POINT (-47.39683 -18.48756)
## 3 9.313897e-02 -0.02357896 POINT (-48.71881 -16.18267)
## 4 6.274261e-02 -0.09409796 POINT (-45.44619 -19.15585)
## 5 7.618978e-02 -0.36386803 POINT (-48.8844 -1.72347)
## 6 5.526602e-02 -0.18516124 POINT (-39.04755 -7.356977)
## 7 3.139966e-02 -0.27987653 POINT (-41.66161 -13.25353)
## 8 4.977786e-05 -0.23302640 POINT (-39.11659 -8.723418)
## 9 3.495948e-05 0.01027696 POINT (-50.31253 -23.30049)
## 10 3.572101e-02 0.14900808 POINT (-51.02527 -27.60899)brazil.polygon.res.sf## Simple feature collection with 5552 features and 94 fields
## geometry type: GEOMETRY
## dimension: XY
## bbox: xmin: -73.99045 ymin: -33.75118 xmax: -28.83594 ymax: 5.271841
## geographic CRS: SIRGAS 2000
## First 10 features:
## code_muni name_muni code_state abbrev_state CAPITAL IBGE_RES_POP
## 1 5200050 ABADIA DE GOIÁS 52 GO 0 6876
## 2 3100104 ABADIA DOS DOURADOS 31 MG 0 6704
## 3 5200100 ABADIÂNIA 52 GO 0 15757
## 4 3100203 ABAETÉ 31 MG 0 22690
## 5 1500107 ABAETETUBA 15 PA 0 141100
## 6 2300101 ABAIARA 23 CE 0 10496
## 7 2900108 ABAÍRA 29 BA 0 8316
## 8 2900207 ABARÉ 29 BA 0 17064
## 9 4100103 ABATIÁ 41 PR 0 7764
## 10 4200051 ABDON BATISTA 42 SC 0 2653
## IBGE_RES_POP_BRAS IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN IBGE_DU_RURAL
## 1 6876 0 2137 1546 591
## 2 6704 0 2328 1481 847
## 3 15609 148 4655 3233 1422
## 4 22690 0 7694 6667 1027
## 5 141040 60 31061 19057 12004
## 6 10496 0 2791 1251 1540
## 7 8316 0 2572 1193 1379
## 8 17064 0 4332 2379 1953
## 9 7764 0 2499 1877 622
## 10 2653 0 848 234 614
## IBGE_POP IBGE_1 IBGE_1.4 IBGE_5.9 IBGE_10.14 Active_pop IBGE_60.
## 1 5300 69 318 438 517 3542 416
## 2 4154 38 207 260 351 2709 589
## 3 10656 139 650 894 1087 6896 990
## 4 18464 176 856 1233 1539 11979 2681
## 5 82956 1354 5567 7618 8905 53516 5996
## 6 4538 98 323 421 483 2631 582
## 7 3725 37 156 263 277 2319 673
## 8 8994 167 733 978 927 5386 803
## 9 5685 69 302 370 483 3650 811
## 10 724 12 32 49 63 479 89
## IBGE_PLANTED_AREA IBGE_CROP_PRODUCTION IDHM.Ranking.2010 IDHM IDHM_Renda
## 1 319 1843 1689 0.708 0.687
## 2 4479 18017 2207 0.690 0.693
## 3 10307 33085 2202 0.690 0.671
## 4 1862 7502 1994 0.698 0.720
## 5 25200 700872 3530 0.628 0.579
## 6 2598 5234 3522 0.628 0.540
## 7 895 3999 4086 0.603 0.577
## 8 2058 22761 4756 0.575 0.533
## 9 1197 9943 2258 0.687 0.676
## 10 5502 26195 2092 0.690 0.660
## IDHM_Longevidade IDHM_Educacao LONG LAT ALT PAY_TV
## 1 0.830 0.622 -49.44055 -16.758812 893.60 360
## 2 0.839 0.563 -47.39683 -18.487565 753.12 77
## 3 0.841 0.579 -48.71881 -16.182672 1017.55 227
## 4 0.848 0.556 -45.44619 -19.155848 644.74 1230
## 5 0.798 0.537 -48.88440 -1.723470 10.12 3389
## 6 0.748 0.612 -39.04755 -7.356977 403.11 29
## 7 0.746 0.510 -41.66161 -13.253532 674.22 952
## 8 0.776 0.460 -39.11659 -8.723418 316.38 51
## 9 0.804 0.596 -50.31253 -23.300494 579.30 55
## 10 0.812 0.625 -51.02527 -27.608987 720.98 109
## FIXED_PHONES AREA REGIAO_TUR CATEGORIA_TUR
## 1 842 147.26 <NA> <NA>
## 2 296 881.06 Caminhos Do Cerrado D
## 3 720 1045.13 Região Turística Do Ouro E Cristais C
## 4 1716 1817.07 Lago De Três Marias D
## 5 1218 1610.65 Araguaia-Tocantins D
## 6 34 180.08 <NA> <NA>
## 7 335 538.68 Chapada Diamantina D
## 8 222 1604.92 <NA> <NA>
## 9 392 228.72 <NA> <NA>
## 10 260 237.16 Vale Do Contestado D
## ESTIMATED_POP RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY GVA_SERVICES
## 1 8583 Urbano 6.20 27991.25 74750.32
## 2 6972 Rural Adjacente 50524.57 25917.70 62689.23
## 3 19614 Rural Adjacente 42.84 16728.30 138198.58
## 4 23223 Urbano 113824.60 31002.62 172.33
## 5 156292 Urbano 140463.72 58610.00 468128.69
## 6 11663 Rural Adjacente 4435.16 5.88 22.81
## 7 8767 Rural Remoto 12.41 3437.43 17990.74
## 8 19814 Rural Remoto 9176.40 6.70 36921.84
## 9 7507 Rural Adjacente 73340.52 8839.71 42999.37
## 10 2577 Rural Adjacente 24996.75 3578.87 16011.10
## GVA_PUBLIC GVA_TOTAL TAXES GDP POP_GDP GDP_CAPITA
## 1 36915.04 145857.60 20554.20 166.41 8053 20664.57
## 2 28083.79 167215.28 12873.50 180.09 7037 25591.70
## 3 63396.20 261161.91 26822.58 287984.49 18427 15628.40
## 4 86081.41 403241.27 26994.09 430235.36 23574 18250.42
## 5 486872.40 1154074.81 95180.48 1249255.29 151934 8222.36
## 6 35989.96 69108.67 4042.79 73151.46 11483 6370.41
## 7 28463.74 62304.83 2019.77 64324.59 9212 6982.70
## 8 65.75 118.55 6.21 124754.26 19939 6256.80
## 9 34103.49 159283.08 5.77 165048.21 7795 21173.60
## 10 17842.64 62429.36 2312.65 64742.01 2617 24739.02
## GVA_MAIN
## 1 Demais serviços
## 2 Demais serviços
## 3 Demais serviços
## 4 Demais serviços
## 5 Administração, defesa, educação e saúde públicas e seguridade social
## 6 Administração, defesa, educação e saúde públicas e seguridade social
## 7 Administração, defesa, educação e saúde públicas e seguridade social
## 8 Administração, defesa, educação e saúde públicas e seguridade social
## 9 Agricultura, inclusive apoio à agricultura e a pós colheita
## 10 Administração, defesa, educação e saúde públicas e seguridade social
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B COMP_C COMP_D COMP_E COMP_F COMP_G
## 1 28227691 284 5 1 56 0 2 29 110
## 2 17909274 476 6 6 30 1 2 34 190
## 3 37513019 288 5 9 26 0 2 7 117
## 4 NA 621 18 1 40 0 1 20 303
## 5 NA 931 4 2 43 0 1 27 500
## 6 NA 86 1 0 4 0 0 6 48
## 7 NA 191 6 0 8 0 1 4 97
## 8 NA 87 2 0 3 0 0 0 71
## 9 NA 285 5 0 20 0 1 10 133
## 10 19506956 69 2 0 4 0 0 2 35
## COMP_H COMP_I COMP_J COMP_K COMP_L COMP_M COMP_N COMP_O COMP_P COMP_Q COMP_R
## 1 26 4 5 0 2 10 12 4 6 6 1
## 2 70 28 11 0 4 15 29 2 9 14 6
## 3 12 57 2 1 0 7 15 3 11 5 1
## 4 62 30 9 6 4 28 27 2 15 19 9
## 5 16 31 6 1 1 22 16 2 155 33 15
## 6 2 10 2 0 0 2 3 2 0 2 0
## 7 5 5 3 1 0 5 5 2 8 1 2
## 8 0 1 1 0 0 0 1 2 0 2 0
## 9 18 14 8 0 4 11 26 2 8 9 4
## 10 8 3 1 1 0 4 0 2 1 3 0
## COMP_S COMP_T COMP_U HOTELS BEDS Pr_Agencies Pu_Agencies Pr_Bank Pu_Bank
## 1 5 0 0 NA NA NA NA NA NA
## 2 19 0 0 NA NA NA NA NA NA
## 3 8 0 0 1 34 1 1 1 1
## 4 27 0 0 NA NA 2 2 2 2
## 5 56 0 0 NA NA 2 4 2 4
## 6 4 0 0 NA NA NA NA NA NA
## 7 38 0 0 1 24 NA NA NA NA
## 8 4 0 0 NA NA 1 0 1 0
## 9 12 0 0 NA NA 0 1 0 1
## 10 3 0 0 NA NA 0 1 0 1
## Pr_Assets Pu_Assets Cars Motorcycles Wheeled_tractor UBER MAC WAL.MART
## 1 NA NA 2158 1246 0 <NA> NA NA
## 2 NA NA 2227 1142 0 <NA> NA NA
## 3 33724584 67091904 2838 1426 0 <NA> NA NA
## 4 44974716 371922572 6928 2953 0 <NA> NA NA
## 5 76181384 800078483 5277 25661 0 <NA> NA NA
## 6 NA NA 553 1674 0 <NA> NA NA
## 7 NA NA 896 696 0 <NA> NA NA
## 8 21823314 0 613 1532 0 <NA> NA NA
## 9 0 45976288 2168 912 0 <NA> NA NA
## 10 0 42909056 976 345 2 <NA> NA NA
## POST_OFFICES LOG_GDP_CAPITA PAY_TV_p FIXED_PHONES_p Cars_p
## 1 1 9.936176 0.044703837 0.104557308 0.26797467
## 2 1 10.150023 0.010942163 0.042063379 0.31647009
## 3 3 9.656845 0.012318880 0.039073099 0.15401313
## 4 4 9.811943 0.052176126 0.072792059 0.29388309
## 5 2 9.014613 0.022305738 0.008016639 0.03473219
## 6 1 8.759419 0.002525472 0.002960899 0.04815815
## 7 1 8.851191 0.103343465 0.036365610 0.09726444
## 8 1 8.741424 0.002557801 0.011133959 0.03074377
## 9 1 9.960510 0.007055805 0.050288647 0.27812700
## 10 1 10.116137 0.041650745 0.099350401 0.37294612
## Motorcycles_p GVA_AGROPEC_p GVA_INDUSTRY_p GVA_SERVICES_p pop_density
## 1 0.15472495 0.0007698994 3.4758785546 9.282294797 54.68559
## 2 0.16228506 7.1798451044 3.6830609635 8.908516413 7.98697
## 3 0.07738644 0.0023248494 0.9078146199 7.499787269 17.63130
## 4 0.12526512 4.8283956902 1.3151191991 0.007310172 12.97363
## 5 0.16889570 0.9245048508 0.3857596061 3.081131873 94.33086
## 6 0.14578072 0.3862370461 0.0005120613 0.001986415 63.76610
## 7 0.07555363 0.0013471559 0.3731469822 1.952967868 17.10106
## 8 0.07683434 0.4602236822 0.0003360249 1.851739806 12.42367
## 9 0.11699808 9.4086619628 1.1340230917 5.516275818 34.08097
## 10 0.13183034 9.5516813145 1.3675468093 6.118112342 11.03474
## tax_to_gdp MLR_RES geom
## 1 1.235154e+02 -0.01765106 MULTIPOLYGON (((-49.4444 -1...
## 2 7.148370e+01 -0.01299481 POLYGON ((-47.4384 -18.1657...
## 3 9.313897e-02 -0.02357896 MULTIPOLYGON (((-48.84178 -...
## 4 6.274261e-02 -0.09409796 POLYGON ((-45.16777 -18.890...
## 5 7.618978e-02 -0.36386803 MULTIPOLYGON (((-48.83139 -...
## 6 5.526602e-02 -0.18516124 MULTIPOLYGON (((-39.01733 -...
## 7 3.139966e-02 -0.27987653 MULTIPOLYGON (((-41.64722 -...
## 8 4.977786e-05 -0.23302640 MULTIPOLYGON (((-39.35855 -...
## 9 3.495948e-05 0.01027696 POLYGON ((-50.22465 -23.226...
## 10 3.572101e-02 0.14900808 MULTIPOLYGON (((-51.03724 -...Next, we will convert brazil.point.res.sf simple feature object into a SpatialPointDataFrame by using as_Spatial()
brazil.point.sp <- as_Spatial(brazil.point.res.sf)
brazil.point.sp## class : SpatialPointsDataFrame
## features : 5552
## extent : -72.9165, 51.4725, -33.68757, 4.58544 (xmin, xmax, ymin, ymax)## Warning in proj4string(x): CRS object has comment, which is lost in output## crs : +proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs
## variables : 90
## names : CITY, STATE, CAPITAL, IBGE_RES_POP, IBGE_RES_POP_BRAS, IBGE_RES_POP_ESTR, IBGE_DU, IBGE_DU_URBAN, IBGE_DU_RURAL, IBGE_POP, IBGE_1, IBGE_1.4, IBGE_5.9, IBGE_10.14, Active_pop, ...
## min values : ABADIA DE GOIÁS, AC, 0, 805, 805, 0, 239, 60, 3, 174, 0, 5, 7, 12, 94, ...
## max values : ZORTÉA, TO, 1, 11253503, 11133776, 119727, 3576148, 3548433, 33809, 10463636, 129464, 514794, 684443, 783702, 7058221, ...6.5 Series of Choropleth maps
6.5.1 GDP_CAPITA
brazil.polygon.res.sf <- st_make_valid(brazil.polygon.res.sf)
qtm(brazil.polygon.res.sf, "GDP_CAPITA", borders=NULL, scale=0.7)+
tm_legend(main.title="GDP_CAPITA",
main.title.position="centre")
6.5.2 Residuals
brazil.polygon.res.sf <- st_make_valid(brazil.polygon.res.sf)
qtm(brazil.polygon.res.sf, "MLR_RES", borders=NULL,scale = 0.7) + tm_legend(
main.title = "Residuals",
main.title.position = "centre")## Variable(s) "MLR_RES" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
6.5.3 Plot point symbol map of residuals
tm_shape(mun)+
tm_polygons()+
tm_shape(brazil.point.res.sf)+
tm_dots(col="MLR_RES", alpha=0.6, style="quantile")## Variable(s) "MLR_RES" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
The figure above reveal that there is sign of spatial autocorrelation.
We will now perform Moran’s I test, to further confirm our observation
The hypothesis test is as follow:
H0: Residual for regression model is randomly distributed
H1: Residual for regression model is not randomly distributed
Confidence interval: 0.95
6.6 Determine the upper limit for distance band
The code chunk below will tell us the upper limit for distance band
coords <- coordinates(brazil.point.sp)
k <- knn2nb(knearneigh(coords))
kdists <- unlist(nbdists(k, coords, longlat=FALSE))
summary(kdists)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00548 0.08484 0.12164 0.17221 0.18149 88.21169
The output above tells us that the maximum distance is 88.2119. Using this as the upper threshold, this gives us certainty that all units will have at least one neighbour.
Computing Global Moran’s Test I
wm_knn6 <- knn2nb(knearneigh(coordinates(brazil.point.sp), k=6))wm_knn6## Neighbour list object:
## Number of regions: 5552
## Number of nonzero links: 33312
## Percentage nonzero weights: 0.1080692
## Average number of links: 6
## Non-symmetric neighbours listWe will now need to convert the output neighbour lists into spatial weights
wm_lw <- nb2listw(wm_knn6, style="W")
summary(wm_lw)## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 5552
## Number of nonzero links: 33312
## Percentage nonzero weights: 0.1080692
## Average number of links: 6
## Non-symmetric neighbours list
## Link number distribution:
##
## 6
## 5552
## 5552 least connected regions:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 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## 5552 most connected regions:
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##
## Weights style: W
## Weights constants summary:
## n nn S0 S1 S2
## W 5552 30824704 5552 1670.611 22701.22
Use lm.morantest() to perform Moran’s I test
lm.morantest(brazil_lglm2, wm_lw)##
## Global Moran I for regression residuals
##
## data:
## model: lm(formula = log(GDP_CAPITA) ~ IBGE_CROP_PRODUCTION +
## IDHM_Longevidade + IDHM_Renda + GVA_AGROPEC_p + GVA_INDUSTRY_p +
## GVA_SERVICES_p + tax_to_gdp + Cars_p, data = brazil6)
## weights: wm_lw
##
## Moran I statistic standard deviate = 26.248, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Observed Moran I Expectation Variance
## 1.922521e-01 -5.926404e-04 5.397861e-05
Since pvalue < 2.2e-16, which is less than alpha value (0.05), reject null hypothesis. There is sufficient evidence to conclude that the residuals are not randomly distributed. In fact, from analysis previously, we can now safely conclude that the residuals are normally distributed.
Since the observed Moran I = 0.1929323, which is greater than 0, we can infer that the residuals resemble cluster distribution.
7. Building Models using GWmodel
7.1 CV approach and Gaussian Kernel
We will be using the CV approach for Gaussian Kernel, with the Adaptive Bandwidth ##### 7.1.1 Computing Adaptive Bandwidth GWR Model We will now set adaptive = TRUE since we are calculating the adaptive bandwidth
dmat <- gw.dist(dp.locat=coordinates(brazil.point.sp))bw.adaptive <- bw.gwr(log(GDP_CAPITA)~ IBGE_CROP_PRODUCTION + IDHM_Longevidade + IDHM_Renda + GVA_AGROPEC_p + GVA_INDUSTRY_p + GVA_SERVICES_p + tax_to_gdp + Cars_p, data=brazil.point.sp, approach = "CV", kernel="gaussian", adaptive = TRUE, longlat=FALSE, dMat=dmat)## Take a cup of tea and have a break, it will take a few minutes.
## -----A kind suggestion from GWmodel development group
## Adaptive bandwidth: 3438 CV score: 412.7773
## Adaptive bandwidth: 2133 CV score: 403.4622
## Adaptive bandwidth: 1324 CV score: 391.1685
## Adaptive bandwidth: 827 CV score: 389.4456
## Adaptive bandwidth: 516 CV score: 401.3057
## Adaptive bandwidth: 1015 CV score: 388.4169
## Adaptive bandwidth: 1135 CV score: 388.8933
## Adaptive bandwidth: 944 CV score: 388.7654
## Adaptive bandwidth: 1062 CV score: 388.389
## Adaptive bandwidth: 1088 CV score: 388.5388
## Adaptive bandwidth: 1043 CV score: 388.2676
## Adaptive bandwidth: 1034 CV score: 388.2838
## Adaptive bandwidth: 1051 CV score: 388.3163
## Adaptive bandwidth: 1040 CV score: 388.2508
## Adaptive bandwidth: 1036 CV score: 388.2812
## Adaptive bandwidth: 1040 CV score: 388.2508
The result shows that 1040 is the recommended data points to be used.
Constructing the adaptive bandwidth gwr model
gwr.adaptive <- gwr.basic(log(GDP_CAPITA)~ IBGE_CROP_PRODUCTION + IDHM_Longevidade + IDHM_Renda + GVA_AGROPEC_p + GVA_INDUSTRY_p + GVA_SERVICES_p + tax_to_gdp + Cars_p, data=brazil.point.sp, bw=bw.adaptive, kernel="gaussian", longlat=FALSE)## Warning in proj4string(data): CRS object has comment, which is lost in outputDisplay the model output
gwr.adaptive## ***********************************************************************
## * Package GWmodel *
## ***********************************************************************
## Program starts at: 2020-05-31 22:53:50
## Call:
## gwr.basic(formula = log(GDP_CAPITA) ~ IBGE_CROP_PRODUCTION +
## IDHM_Longevidade + IDHM_Renda + GVA_AGROPEC_p + GVA_INDUSTRY_p +
## GVA_SERVICES_p + tax_to_gdp + Cars_p, data = brazil.point.sp,
## bw = bw.adaptive, kernel = "gaussian", longlat = FALSE)
##
## Dependent (y) variable: GDP_CAPITA
## Independent variables: IBGE_CROP_PRODUCTION IDHM_Longevidade IDHM_Renda GVA_AGROPEC_p GVA_INDUSTRY_p GVA_SERVICES_p tax_to_gdp Cars_p
## Number of data points: 5552
## ***********************************************************************
## * Results of Global Regression *
## ***********************************************************************
##
## Call:
## lm(formula = formula, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.86710 -0.16500 -0.03439 0.13338 2.75733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.512e+00 9.999e-02 65.126 < 2e-16 ***
## IBGE_CROP_PRODUCTION 2.663e-07 2.754e-08 9.671 < 2e-16 ***
## IDHM_Longevidade 6.639e-01 1.522e-01 4.362 1.32e-05 ***
## IDHM_Renda 3.523e+00 1.143e-01 30.807 < 2e-16 ***
## GVA_AGROPEC_p 2.787e-02 6.319e-04 44.104 < 2e-16 ***
## GVA_INDUSTRY_p 1.884e-02 4.022e-04 46.856 < 2e-16 ***
## GVA_SERVICES_p 2.010e-02 6.731e-04 29.859 < 2e-16 ***
## tax_to_gdp 7.833e-04 1.434e-04 5.461 4.93e-08 ***
## Cars_p 4.546e-01 5.691e-02 7.988 1.66e-15 ***
##
## ---Significance stars
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Residual standard error: 0.2742 on 5543 degrees of freedom
## Multiple R-squared: 0.8392
## Adjusted R-squared: 0.839
## F-statistic: 3616 on 8 and 5543 DF, p-value: < 2.2e-16
## ***Extra Diagnostic information
## Residual sum of squares: 416.8353
## Sigma(hat): 0.2740538
## AIC: 1400.531
## AICc: 1400.571
## ***********************************************************************
## * Results of Geographically Weighted Regression *
## ***********************************************************************
##
## *********************Model calibration information*********************
## Kernel function: gaussian
## Fixed bandwidth: 1040
## Regression points: the same locations as observations are used.
## Distance metric: Euclidean distance metric is used.
##
## ****************Summary of GWR coefficient estimates:******************
## Min. 1st Qu. Median 3rd Qu. Max.
## Intercept 6.5115e+00 6.5117e+00 6.5117e+00 6.5117e+00 6.5120
## IBGE_CROP_PRODUCTION 2.6631e-07 2.6633e-07 2.6634e-07 2.6634e-07 0.0000
## IDHM_Longevidade 6.6336e-01 6.6382e-01 6.6384e-01 6.6386e-01 0.6640
## IDHM_Renda 3.5225e+00 3.5226e+00 3.5226e+00 3.5226e+00 3.5226
## GVA_AGROPEC_p 2.7871e-02 2.7871e-02 2.7871e-02 2.7872e-02 0.0279
## GVA_INDUSTRY_p 1.8844e-02 1.8845e-02 1.8845e-02 1.8845e-02 0.0188
## GVA_SERVICES_p 2.0096e-02 2.0096e-02 2.0096e-02 2.0097e-02 0.0201
## tax_to_gdp 7.8329e-04 7.8332e-04 7.8333e-04 7.8335e-04 0.0008
## Cars_p 4.5454e-01 4.5461e-01 4.5464e-01 4.5465e-01 0.4548
## ************************Diagnostic information*************************
## Number of data points: 5552
## Effective number of parameters (2trace(S) - trace(S'S)): 9.001199
## Effective degrees of freedom (n-2trace(S) + trace(S'S)): 5542.999
## AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 1400.526
## AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 1389.485
## Residual sum of squares: 416.8318
## R-square value: 0.8392099
## Adjusted R-square value: 0.8389487
##
## ***********************************************************************
## Program stops at: 2020-05-31 22:54:38
The adjusted R2 is 0.8389487, and pvalue < 2.2e-16
7.5 Analysing the adjusted r2 values
We will now analyse the r2 values of the CV Kernel adaptive bandwidth approach.
We will compare based on adjusted R2 value. The higher the Adjusted R2 value, the better the method.
This is because the adjusted R2 value calculates the correlation of the variables. In other words, it takes into account all the variables in the model.
A higher adjusted R2 would mean that the higher the percentage of variation in GDP_CAPITA can be explained in the regression model.
Adjusted r2 = 0.8389487
The adjusted r2 value above is rather high, which means that our model is good. There is high correlation between our variables and GDP_CAPITA.
8. Visualising GWR Output
In addition to regression residuals, the output feature class table includes fields for observed and predicted y values, condition number, local R2, residuals, and explanatory variable coefficients and standard errors.
We would now attempt to visualise the GWR Output using the AIC approach and Guassian kernel, fixed method, as identified above.
8.1 Converting SDF into sf data.frame
To visualise the SDF, we need to first convert it into sf data.frame
brazil.sf.adaptive <- st_as_sf(gwr.adaptive$SDF) %>%
st_transform(crs=4674)gwr.adaptive.output <- as.data.frame(gwr.adaptive$SDF)
brazil.sf.adaptive <- cbind(brazil.polygon.res.sf, as.matrix(gwr.adaptive.output))brazil.sf.adaptive## Simple feature collection with 5552 features and 129 fields
## geometry type: GEOMETRY
## dimension: XY
## bbox: xmin: -73.99045 ymin: -33.75118 xmax: -28.83594 ymax: 5.271841
## geographic CRS: SIRGAS 2000
## First 10 features:
## code_muni name_muni code_state abbrev_state CAPITAL IBGE_RES_POP
## 1 5200050 ABADIA DE GOIÁS 52 GO 0 6876
## 2 3100104 ABADIA DOS DOURADOS 31 MG 0 6704
## 3 5200100 ABADIÂNIA 52 GO 0 15757
## 4 3100203 ABAETÉ 31 MG 0 22690
## 5 1500107 ABAETETUBA 15 PA 0 141100
## 6 2300101 ABAIARA 23 CE 0 10496
## 7 2900108 ABAÍRA 29 BA 0 8316
## 8 2900207 ABARÉ 29 BA 0 17064
## 9 4100103 ABATIÁ 41 PR 0 7764
## 10 4200051 ABDON BATISTA 42 SC 0 2653
## IBGE_RES_POP_BRAS IBGE_RES_POP_ESTR IBGE_DU IBGE_DU_URBAN IBGE_DU_RURAL
## 1 6876 0 2137 1546 591
## 2 6704 0 2328 1481 847
## 3 15609 148 4655 3233 1422
## 4 22690 0 7694 6667 1027
## 5 141040 60 31061 19057 12004
## 6 10496 0 2791 1251 1540
## 7 8316 0 2572 1193 1379
## 8 17064 0 4332 2379 1953
## 9 7764 0 2499 1877 622
## 10 2653 0 848 234 614
## IBGE_POP IBGE_1 IBGE_1.4 IBGE_5.9 IBGE_10.14 Active_pop IBGE_60.
## 1 5300 69 318 438 517 3542 416
## 2 4154 38 207 260 351 2709 589
## 3 10656 139 650 894 1087 6896 990
## 4 18464 176 856 1233 1539 11979 2681
## 5 82956 1354 5567 7618 8905 53516 5996
## 6 4538 98 323 421 483 2631 582
## 7 3725 37 156 263 277 2319 673
## 8 8994 167 733 978 927 5386 803
## 9 5685 69 302 370 483 3650 811
## 10 724 12 32 49 63 479 89
## IBGE_PLANTED_AREA IBGE_CROP_PRODUCTION IDHM.Ranking.2010 IDHM IDHM_Renda
## 1 319 1843 1689 0.708 0.687
## 2 4479 18017 2207 0.690 0.693
## 3 10307 33085 2202 0.690 0.671
## 4 1862 7502 1994 0.698 0.720
## 5 25200 700872 3530 0.628 0.579
## 6 2598 5234 3522 0.628 0.540
## 7 895 3999 4086 0.603 0.577
## 8 2058 22761 4756 0.575 0.533
## 9 1197 9943 2258 0.687 0.676
## 10 5502 26195 2092 0.690 0.660
## IDHM_Longevidade IDHM_Educacao LONG LAT ALT PAY_TV
## 1 0.830 0.622 -49.44055 -16.758812 893.60 360
## 2 0.839 0.563 -47.39683 -18.487565 753.12 77
## 3 0.841 0.579 -48.71881 -16.182672 1017.55 227
## 4 0.848 0.556 -45.44619 -19.155848 644.74 1230
## 5 0.798 0.537 -48.88440 -1.723470 10.12 3389
## 6 0.748 0.612 -39.04755 -7.356977 403.11 29
## 7 0.746 0.510 -41.66161 -13.253532 674.22 952
## 8 0.776 0.460 -39.11659 -8.723418 316.38 51
## 9 0.804 0.596 -50.31253 -23.300494 579.30 55
## 10 0.812 0.625 -51.02527 -27.608987 720.98 109
## FIXED_PHONES AREA REGIAO_TUR CATEGORIA_TUR
## 1 842 147.26 <NA> <NA>
## 2 296 881.06 Caminhos Do Cerrado D
## 3 720 1045.13 Região Turística Do Ouro E Cristais C
## 4 1716 1817.07 Lago De Três Marias D
## 5 1218 1610.65 Araguaia-Tocantins D
## 6 34 180.08 <NA> <NA>
## 7 335 538.68 Chapada Diamantina D
## 8 222 1604.92 <NA> <NA>
## 9 392 228.72 <NA> <NA>
## 10 260 237.16 Vale Do Contestado D
## ESTIMATED_POP RURAL_URBAN GVA_AGROPEC GVA_INDUSTRY GVA_SERVICES
## 1 8583 Urbano 6.20 27991.25 74750.32
## 2 6972 Rural Adjacente 50524.57 25917.70 62689.23
## 3 19614 Rural Adjacente 42.84 16728.30 138198.58
## 4 23223 Urbano 113824.60 31002.62 172.33
## 5 156292 Urbano 140463.72 58610.00 468128.69
## 6 11663 Rural Adjacente 4435.16 5.88 22.81
## 7 8767 Rural Remoto 12.41 3437.43 17990.74
## 8 19814 Rural Remoto 9176.40 6.70 36921.84
## 9 7507 Rural Adjacente 73340.52 8839.71 42999.37
## 10 2577 Rural Adjacente 24996.75 3578.87 16011.10
## GVA_PUBLIC GVA_TOTAL TAXES GDP POP_GDP GDP_CAPITA
## 1 36915.04 145857.60 20554.20 166.41 8053 20664.57
## 2 28083.79 167215.28 12873.50 180.09 7037 25591.70
## 3 63396.20 261161.91 26822.58 287984.49 18427 15628.40
## 4 86081.41 403241.27 26994.09 430235.36 23574 18250.42
## 5 486872.40 1154074.81 95180.48 1249255.29 151934 8222.36
## 6 35989.96 69108.67 4042.79 73151.46 11483 6370.41
## 7 28463.74 62304.83 2019.77 64324.59 9212 6982.70
## 8 65.75 118.55 6.21 124754.26 19939 6256.80
## 9 34103.49 159283.08 5.77 165048.21 7795 21173.60
## 10 17842.64 62429.36 2312.65 64742.01 2617 24739.02
## GVA_MAIN
## 1 Demais serviços
## 2 Demais serviços
## 3 Demais serviços
## 4 Demais serviços
## 5 Administração, defesa, educação e saúde públicas e seguridade social
## 6 Administração, defesa, educação e saúde públicas e seguridade social
## 7 Administração, defesa, educação e saúde públicas e seguridade social
## 8 Administração, defesa, educação e saúde públicas e seguridade social
## 9 Agricultura, inclusive apoio à agricultura e a pós colheita
## 10 Administração, defesa, educação e saúde públicas e seguridade social
## MUN_EXPENDIT COMP_TOT COMP_A COMP_B COMP_C COMP_D COMP_E COMP_F COMP_G
## 1 28227691 284 5 1 56 0 2 29 110
## 2 17909274 476 6 6 30 1 2 34 190
## 3 37513019 288 5 9 26 0 2 7 117
## 4 NA 621 18 1 40 0 1 20 303
## 5 NA 931 4 2 43 0 1 27 500
## 6 NA 86 1 0 4 0 0 6 48
## 7 NA 191 6 0 8 0 1 4 97
## 8 NA 87 2 0 3 0 0 0 71
## 9 NA 285 5 0 20 0 1 10 133
## 10 19506956 69 2 0 4 0 0 2 35
## COMP_H COMP_I COMP_J COMP_K COMP_L COMP_M COMP_N COMP_O COMP_P COMP_Q COMP_R
## 1 26 4 5 0 2 10 12 4 6 6 1
## 2 70 28 11 0 4 15 29 2 9 14 6
## 3 12 57 2 1 0 7 15 3 11 5 1
## 4 62 30 9 6 4 28 27 2 15 19 9
## 5 16 31 6 1 1 22 16 2 155 33 15
## 6 2 10 2 0 0 2 3 2 0 2 0
## 7 5 5 3 1 0 5 5 2 8 1 2
## 8 0 1 1 0 0 0 1 2 0 2 0
## 9 18 14 8 0 4 11 26 2 8 9 4
## 10 8 3 1 1 0 4 0 2 1 3 0
## COMP_S COMP_T COMP_U HOTELS BEDS Pr_Agencies Pu_Agencies Pr_Bank Pu_Bank
## 1 5 0 0 NA NA NA NA NA NA
## 2 19 0 0 NA NA NA NA NA NA
## 3 8 0 0 1 34 1 1 1 1
## 4 27 0 0 NA NA 2 2 2 2
## 5 56 0 0 NA NA 2 4 2 4
## 6 4 0 0 NA NA NA NA NA NA
## 7 38 0 0 1 24 NA NA NA NA
## 8 4 0 0 NA NA 1 0 1 0
## 9 12 0 0 NA NA 0 1 0 1
## 10 3 0 0 NA NA 0 1 0 1
## Pr_Assets Pu_Assets Cars Motorcycles Wheeled_tractor UBER MAC WAL.MART
## 1 NA NA 2158 1246 0 <NA> NA NA
## 2 NA NA 2227 1142 0 <NA> NA NA
## 3 33724584 67091904 2838 1426 0 <NA> NA NA
## 4 44974716 371922572 6928 2953 0 <NA> NA NA
## 5 76181384 800078483 5277 25661 0 <NA> NA NA
## 6 NA NA 553 1674 0 <NA> NA NA
## 7 NA NA 896 696 0 <NA> NA NA
## 8 21823314 0 613 1532 0 <NA> NA NA
## 9 0 45976288 2168 912 0 <NA> NA NA
## 10 0 42909056 976 345 2 <NA> NA NA
## POST_OFFICES LOG_GDP_CAPITA PAY_TV_p FIXED_PHONES_p Cars_p
## 1 1 9.936176 0.044703837 0.104557308 0.26797467
## 2 1 10.150023 0.010942163 0.042063379 0.31647009
## 3 3 9.656845 0.012318880 0.039073099 0.15401313
## 4 4 9.811943 0.052176126 0.072792059 0.29388309
## 5 2 9.014613 0.022305738 0.008016639 0.03473219
## 6 1 8.759419 0.002525472 0.002960899 0.04815815
## 7 1 8.851191 0.103343465 0.036365610 0.09726444
## 8 1 8.741424 0.002557801 0.011133959 0.03074377
## 9 1 9.960510 0.007055805 0.050288647 0.27812700
## 10 1 10.116137 0.041650745 0.099350401 0.37294612
## Motorcycles_p GVA_AGROPEC_p GVA_INDUSTRY_p GVA_SERVICES_p pop_density
## 1 0.15472495 0.0007698994 3.4758785546 9.282294797 54.68559
## 2 0.16228506 7.1798451044 3.6830609635 8.908516413 7.98697
## 3 0.07738644 0.0023248494 0.9078146199 7.499787269 17.63130
## 4 0.12526512 4.8283956902 1.3151191991 0.007310172 12.97363
## 5 0.16889570 0.9245048508 0.3857596061 3.081131873 94.33086
## 6 0.14578072 0.3862370461 0.0005120613 0.001986415 63.76610
## 7 0.07555363 0.0013471559 0.3731469822 1.952967868 17.10106
## 8 0.07683434 0.4602236822 0.0003360249 1.851739806 12.42367
## 9 0.11699808 9.4086619628 1.1340230917 5.516275818 34.08097
## 10 0.13183034 9.5516813145 1.3675468093 6.118112342 11.03474
## tax_to_gdp MLR_RES Intercept IBGE_CROP_PRODUCTION.1 IDHM_Longevidade.1
## 1 1.235154e+02 -0.01765106 6.511676 2.663345e-07 0.6638586
## 2 7.148370e+01 -0.01299481 6.511691 2.663372e-07 0.6638425
## 3 9.313897e-02 -0.02357896 6.511676 2.663346e-07 0.6638579
## 4 6.274261e-02 -0.09409796 6.511700 2.663390e-07 0.6638312
## 5 7.618978e-02 -0.36386803 6.511606 2.663236e-07 0.6639198
## 6 5.526602e-02 -0.18516124 6.511662 2.663345e-07 0.6638534
## 7 3.139966e-02 -0.27987653 6.511683 2.663372e-07 0.6638398
## 8 4.977786e-05 -0.23302640 6.511669 2.663355e-07 0.6638480
## 9 3.495948e-05 0.01027696 6.511705 2.663389e-07 0.6638347
## 10 3.572101e-02 0.14900808 6.511724 2.663416e-07 0.6638195
## IDHM_Renda.1 GVA_AGROPEC_p.1 GVA_INDUSTRY_p.1 GVA_SERVICES_p.1 tax_to_gdp.1
## 1 3.522576 0.02787146 0.01884477 0.02009643 0.0007833277
## 2 3.522571 0.02787146 0.01884477 0.02009643 0.0007833274
## 3 3.522578 0.02787150 0.01884479 0.02009645 0.0007833297
## 4 3.522568 0.02787149 0.01884479 0.02009644 0.0007833289
## 5 3.522619 0.02787192 0.01884504 0.02009665 0.0007833549
## 6 3.522600 0.02787199 0.01884510 0.02009669 0.0007833583
## 7 3.522584 0.02787175 0.01884495 0.02009658 0.0007833444
## 8 3.522596 0.02787195 0.01884508 0.02009667 0.0007833558
## 9 3.522558 0.02787125 0.01884464 0.02009632 0.0007833150
## 10 3.522546 0.02787111 0.01884455 0.02009625 0.0007833065
## Cars_p.1 y yhat residual CV_Score Stud_residual
## 1 0.4546260 9.936176 9.953826 -0.01764977 0 -0.06448664
## 2 0.4546347 10.150023 10.163017 -0.01299326 0 -0.04741797
## 3 0.4546249 9.656845 9.680424 -0.02357919 0 -0.08602561
## 4 0.4546396 9.811943 9.906040 -0.09409690 0 -0.34328575
## 5 0.4545740 9.014613 9.378475 -0.36386277 0 -1.33036648
## 6 0.4546067 8.759419 8.944573 -0.18515435 0 -0.67536221
## 7 0.4546239 8.851191 9.131064 -0.27987286 0 -1.02086747
## 8 0.4546114 8.741424 8.974444 -0.23301998 0 -0.85005300
## 9 0.4546478 9.960510 9.950234 0.01027673 0 0.03748658
## 10 0.4546620 10.116137 9.967132 0.14900468 0 0.54374552
## Intercept_SE IBGE_CROP_PRODUCTION_SE IDHM_Longevidade_SE IDHM_Renda_SE
## 1 0.09998539 2.753994e-08 0.1522088 0.1143442
## 2 0.09998539 2.753994e-08 0.1522088 0.1143442
## 3 0.09998539 2.753994e-08 0.1522088 0.1143442
## 4 0.09998539 2.753994e-08 0.1522088 0.1143442
## 5 0.09998539 2.753994e-08 0.1522088 0.1143442
## 6 0.09998539 2.753994e-08 0.1522088 0.1143442
## 7 0.09998539 2.753994e-08 0.1522088 0.1143442
## 8 0.09998539 2.753994e-08 0.1522088 0.1143442
## 9 0.09998539 2.753994e-08 0.1522088 0.1143442
## 10 0.09998539 2.753994e-08 0.1522088 0.1143442
## GVA_AGROPEC_p_SE GVA_INDUSTRY_p_SE GVA_SERVICES_p_SE tax_to_gdp_SE
## 1 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 2 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 3 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 4 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 5 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 6 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 7 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 8 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 9 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## 10 0.0006319413 0.0004021848 0.0006730499 0.0001434313
## Cars_p_SE Intercept_TV IBGE_CROP_PRODUCTION_TV IDHM_Longevidade_TV
## 1 0.05691429 65.12628 9.670845 4.361500
## 2 0.05691429 65.12642 9.670943 4.361394
## 3 0.05691429 65.12627 9.670847 4.361495
## 4 0.05691429 65.12651 9.671009 4.361320
## 5 0.05691429 65.12558 9.670448 4.361902
## 6 0.05691429 65.12614 9.670843 4.361466
## 7 0.05691429 65.12634 9.670941 4.361376
## 8 0.05691429 65.12620 9.670879 4.361430
## 9 0.05691429 65.12657 9.671003 4.361343
## 10 0.05691429 65.12675 9.671103 4.361243
## IDHM_Renda_TV GVA_AGROPEC_p_TV GVA_INDUSTRY_p_TV GVA_SERVICES_p_TV
## 1 30.80678 44.10451 46.85598 29.85875
## 2 30.80673 44.10451 46.85599 29.85875
## 3 30.80679 44.10457 46.85604 29.85878
## 4 30.80671 44.10456 46.85604 29.85877
## 5 30.80716 44.10523 46.85667 29.85908
## 6 30.80698 44.10534 46.85682 29.85914
## 7 30.80684 44.10497 46.85646 29.85897
## 8 30.80695 44.10528 46.85676 29.85911
## 9 30.80662 44.10418 46.85566 29.85859
## 10 30.80651 44.10395 46.85544 29.85849
## tax_to_gdp_TV Cars_p_TV Local_R2 coords.x1 coords.x2
## 1 5.461343 7.987906 0.8392090 -49.44055 -16.758812
## 2 5.461341 7.988060 0.8392090 -47.39683 -18.487565
## 3 5.461357 7.987887 0.8392090 -48.71881 -16.182672
## 4 5.461351 7.988146 0.8392091 -45.44619 -19.155848
## 5 5.461533 7.986993 0.8392100 -48.88440 -1.723470
## 6 5.461556 7.987566 0.8392102 -39.04755 -7.356977
## 7 5.461459 7.987869 0.8392097 -41.66161 -13.253532
## 8 5.461538 7.987649 0.8392101 -39.11659 -8.723418
## 9 5.461255 7.988289 0.8392085 -50.31253 -23.300494
## 10 5.461195 7.988538 0.8392082 -51.02527 -27.608987
## geom
## 1 MULTIPOLYGON (((-49.4444 -1...
## 2 POLYGON ((-47.4384 -18.1657...
## 3 MULTIPOLYGON (((-48.84178 -...
## 4 POLYGON ((-45.16777 -18.890...
## 5 MULTIPOLYGON (((-48.83139 -...
## 6 MULTIPOLYGON (((-39.01733 -...
## 7 MULTIPOLYGON (((-41.64722 -...
## 8 MULTIPOLYGON (((-39.35855 -...
## 9 POLYGON ((-50.22465 -23.226...
## 10 MULTIPOLYGON (((-51.03724 -...summary(gwr.adaptive$SDF$yhat)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.498 9.163 9.678 9.698 10.097 15.499
The maximum value is 15.499
Remove code_muni from brazil.sf.fixed2 data frame
brazil.sf.adaptive <- subset(brazil.sf.adaptive, select= -code_muni)8.2 Local R2
The code chunks below are used to plot a choropleth to visualise local R2
qtm(brazil.sf.adaptive, "Local_R2", border=NULL)
The range of local R2 values are in the range of 0.83, which is relatively high.
It can be seen that the upper parts of brazil are darker shaded, which suggests that the relationship between GDP_CAPITA and the independent variables are stronger, since the variables are more correlated.
8.3 Intercept
The code chunks below are used to plot an choropleth map to visualise intercept of the regression model
qtm(brazil.sf.adaptive, "Intercept", border=NULL)
We can see that there is a varying range of intercept value around 6.5, and since intercept value > 0, we can conclude that the slope is positive.
8.4 Residuals
Residual is the difference between the observed GDP_CAPITA and the predicted GDP_CAPITA. Residual will be 0 if there is no difference bewteen observed and predicted values of GDP_CAPITA.
qtm(brazil.sf.adaptive,"residual", border=NULL)## Variable(s) "residual" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
8.5 Y hat plot
The code chunk below allow us to visualise the y hat of the regression model.
Y-hat represents the predicted equation for a line of best fit in a linear regression model. The value of y hat helps us to differentiate between the predicted data and the observed data of GDP_CAPITA.
qtm(brazil.sf.adaptive, "yhat", border=NULL)
Overall, our regression model is able to perform well in explaining the factors that are affecting GDP_CAPITA in Brazil.