1. Aspatial/Geospatial Data Wrangling

1.1 The data

Aspatial

  1. BRAZILCITIES.csv

Geospatial

  1. mun

1.2 Installing all the relevant packages

Install all the necessary R packages into R and launch thee R packages into R environment.

packages = c('olsrr', 'corrplot', 'ggpubr', 'sf', 'spdep', 'GWmodel', 'tmap', 'tidyverse','geobr','RColorBrewer','fastDummies','patchwork','GISTools')
for (p in packages){
  if(!require(p, character.only = T)){
    install.packages(p)
  }
  library(p,character.only = T)
}

2. Geospatial Data Wrangling

2.1 Bringing geospatial data into R environment

Import Brazil municipality boundary data set from year 2016 and named it as mun. This data set is not imported from the local data folder. The municipality boundary is extract from online package called geobr.

Based on the detials of mun data set, we can see that it is in simple feature format and the coordinates of the data set is in degree format with epsg 4674.

mun <- read_municipality(year = 2016)
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mun
## Simple feature collection with 5572 features and 4 fields
## geometry type:  GEOMETRY
## dimension:      XY
## bbox:           xmin: -73.99045 ymin: -33.75118 xmax: -28.83594 ymax: 5.271841
## epsg (SRID):    4674
## proj4string:    +proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs
## First 10 features:
##    code_muni             name_muni code_state abbrev_state
## 1    1100015 Alta Floresta D'oeste         11           RO
## 2    1100023             Ariquemes         11           RO
## 3    1100031                Cabixi         11           RO
## 4    1100049                Cacoal         11           RO
## 5    1100056            Cerejeiras         11           RO
## 6    1100064     Colorado Do Oeste         11           RO
## 7    1100072            Corumbiara         11           RO
## 8    1100080         Costa Marques         11           RO
## 9    1100098       Espigão D'oeste         11           RO
## 10   1100106         Guajará-Mirim         11           RO
##                              geom
## 1  POLYGON ((-62.19465 -11.827...
## 2  POLYGON ((-62.53648 -9.7322...
## 3  POLYGON ((-60.37075 -13.363...
## 4  POLYGON ((-61.0008 -11.2973...
## 5  POLYGON ((-61.49976 -13.005...
## 6  POLYGON ((-60.50475 -12.966...
## 7  POLYGON ((-61.34273 -12.666...
## 8  POLYGON ((-63.71199 -11.650...
## 9  POLYGON ((-60.94827 -10.988...
## 10 POLYGON ((-65.37724 -10.431...

To use a class() to confirm the mun dat set is in simple feature format.

class(mun)
## [1] "sf"         "data.frame"

2.2 Updating CRS information

However, we need to transform the EPSG:29101 by using st_transform() function. Based on the information provided in the link, we can see that the unit of EPSG:29101 is in metre.
By running the detial of mun, we can see that it chnages its bbox, epsg and proj4string information.

mun <- st_transform(mun,crs=29101)
mun
## Simple feature collection with 5572 features and 4 fields
## geometry type:  GEOMETRY
## dimension:      XY
## bbox:           xmin: 2794590 ymin: 6263816 xmax: 7615330 ymax: 10586410
## epsg (SRID):    29101
## proj4string:    +proj=poly +lat_0=0 +lon_0=-54 +x_0=5000000 +y_0=10000000 +ellps=aust_SA +towgs84=-66.87,4.37,-38.52,0,0,0,0 +units=m +no_defs
## First 10 features:
##    code_muni             name_muni code_state abbrev_state
## 1    1100015 Alta Floresta D'oeste         11           RO
## 2    1100023             Ariquemes         11           RO
## 3    1100031                Cabixi         11           RO
## 4    1100049                Cacoal         11           RO
## 5    1100056            Cerejeiras         11           RO
## 6    1100064     Colorado Do Oeste         11           RO
## 7    1100072            Corumbiara         11           RO
## 8    1100080         Costa Marques         11           RO
## 9    1100098       Espigão D'oeste         11           RO
## 10   1100106         Guajará-Mirim         11           RO
##                              geom
## 1  POLYGON ((4107198 8678957, ...
## 2  POLYGON ((4063462 8912011, ...
## 3  POLYGON ((4310019 8513235, ...
## 4  POLYGON ((4235803 8741535, ...
## 5  POLYGON ((4186577 8549769, ...
## 6  POLYGON ((4294369 8557024, ...
## 7  POLYGON ((4202533 8588007, ...
## 8  POLYGON ((3941253 8693538, ...
## 9  POLYGON ((4240731 8776065, ...
## 10 POLYGON ((3754607 8824106, ...

In order to have a quick idea of how does the Brazil municipality boundary looks like, we can perform a qtm() function to see the layout of Brazil municipality boundary.

qtm(mun)

3. Aspatial Data Wrangling

3.1 Importing Aspatial data

Now we going to import second set of data, this data set is provided in CSV file. As we know that the language of brazil using is in Portuguess. In the Portuguess letter, there are many special character that R markdown cannot can read it in default. However, we can adding an extra code encoding = “latin1” within the read.csv() function in order to read special characters.

br_data <- read.csv("data1/aspatial/BRAZIL_CITIES.csv",encoding="latin1")

Performing a summary() function, to view the detail of summary.

summary(br_data)
##            CITY          STATE         CAPITAL          IBGE_RES_POP     
##  Bom Jesus   :   5   MG     : 853   Min.   :0.000000   Min.   :     805  
##  São Domingos:   5   SP     : 645   1st Qu.:0.000000   1st Qu.:    5235  
##  Bonito      :   4   RS     : 498   Median :0.000000   Median :   10934  
##  Planalto    :   4   BA     : 418   Mean   :0.004845   Mean   :   34278  
##  Santa Helena:   4   PR     : 399   3rd Qu.:0.000000   3rd Qu.:   23424  
##  Santa Inês  :   4   SC     : 295   Max.   :1.000000   Max.   :11253503  
##  (Other)     :5547   (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.:-41.41  
##  Max.   :0.8910   Max.   :0.8940   Max.   :0.8250   Max.   :-32.44  
##  NA's   :8        NA's   :8        NA's   :8                        
##       LAT               ALT               PAY_TV         FIXED_PHONES    
##  Min.   :-33.688   Min.   :     0.0   Min.   :      1   Min.   :      3  
##  1st Qu.:-22.843   1st Qu.:   169.8   1st Qu.:     88   1st Qu.:    119  
##  Median :-18.091   Median :   406.5   Median :    247   Median :    327  
##  Mean   :-16.451   Mean   :   893.8   Mean   :   3094   Mean   :   6567  
##  3rd Qu.: -8.490   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   :3         NA's   :3        
##       AREA                          REGIAO_TUR   CATEGORIA_TUR
##  Min.   :     3.57                       :2288    :2288       
##  1st Qu.:   204.44   Corredores Das Águas:  59   A:  51       
##  Median :   416.59   Vale Do Contestado  :  45   B: 168       
##  Mean   :  1517.44   Amazônia Atlântica  :  40   C: 521       
##  3rd Qu.:  1026.57   Araguaia-Tocantins  :  39   D:1892       
##  Max.   :159533.33   Cariri              :  37   E: 653       
##  NA's   :3           (Other)             :3065                
##  ESTIMATED_POP                       RURAL_URBAN    GVA_AGROPEC     
##  Min.   :     786                          :   3   Min.   :      0  
##  1st Qu.:    5454   Intermediário Adjacente: 686   1st Qu.:   4189  
##  Median :   11590   Intermediário Remoto   :  60   Median :  20426  
##  Mean   :   37432   Rural Adjacente        :3040   Mean   :  47271  
##  3rd Qu.:   25296   Rural Remoto           : 323   3rd Qu.:  51227  
##  Max.   :12176866   Sem classificação      :   5   Max.   :1402282  
##  NA's   :3          Urbano                 :1456   NA's   :3        
##   GVA_INDUSTRY       GVA_SERVICES         GVA_PUBLIC         GVA_TOTAL        
##  Min.   :       1   Min.   :        2   Min.   :       7   Min.   :       17  
##  1st Qu.:    1726   1st Qu.:    10112   1st Qu.:   17267   1st Qu.:    42253  
##  Median :    7424   Median :    31211   Median :   35866   Median :   119492  
##  Mean   :  175928   Mean   :   489451   Mean   :  123768   Mean   :   832987  
##  3rd Qu.:   41022   3rd Qu.:   115406   3rd Qu.:   89245   3rd Qu.:   313963  
##  Max.   :63306755   Max.   :464656988   Max.   :41902893   Max.   :569910503  
##  NA's   :3          NA's   :3           NA's   :3          NA's   :3          
##      TAXES                GDP               POP_GDP           GDP_CAPITA    
##  Min.   :   -14159   Min.   :       15   Min.   :     815   Min.   :  3191  
##  1st Qu.:     1305   1st Qu.:    43709   1st Qu.:    5483   1st Qu.:  9058  
##  Median :     5100   Median :   125153   Median :   11578   Median : 15870  
##  Mean   :   118864   Mean   :   954584   Mean   :   36998   Mean   : 21126  
##  3rd Qu.:    22197   3rd Qu.:   329539   3rd Qu.:   25085   3rd Qu.: 26155  
##  Max.   :117125387   Max.   :687035890   Max.   :12038175   Max.   :314638  
##  NA's   :3           NA's   :3           NA's   :3          NA's   :3       
##                                                                                  GVA_MAIN   
##  Administração, defesa, educação e saúde públicas e seguridade social                :2725  
##  Demais serviços                                                                     :1477  
##  Agricultura, inclusive apoio à agricultura e a pós colheita                         : 735  
##  Indústrias de transformação                                                         : 261  
##  Pecuária, inclusive apoio à pecuária                                                : 161  
##  Eletricidade e gás, água, esgoto, atividades de gestão de resíduos e descontaminação:  98  
##  (Other)                                                                             : 116  
##   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   :9.187e+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.   :1.950e+13   Max.   :8.020e+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   Min.   :1      Min.   :  1.000  
##  1st Qu.:    591   1st Qu.:   0.000   1st Qu.:1      1st Qu.:  1.000  
##  Median :   1285   Median :   0.000   Median :1      Median :  2.000  
##  Mean   :   4879   Mean   :   5.754   Mean   :1      Mean   :  4.277  
##  3rd Qu.:   3294   3rd Qu.:   1.000   3rd Qu.:1      3rd Qu.:  3.000  
##  Max.   :1134570   Max.   :3236.000   Max.   :1      Max.   :130.000  
##  NA's   :11        NA's   :11         NA's   :5448   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

Based on the summary results, we can see that there are “LOMG” and “LAT” columns separately. In order to get the coordinates of each Brazil municipality, we need to use st_as_sf() function to combine both columns into a geometry column with a crs 4674.
As we mentioned in the abovce code chunk, we need to convert it into XY coordinates by using st_transform(crs = 29101) function instead of leave it in degree minutes seconds.

3.2 Updating CRS information

Currently br_data.sf is in Simple feature format.

br_data.sf <- st_as_sf(br_data,coords = c("LONG", "LAT"),crs=4674) %>%
  st_transform(crs=29101)
head(br_data.sf)
## Simple feature collection with 6 features and 79 fields
## geometry type:  POINT
## dimension:      XY
## bbox:           xmin: 5486142 ymin: 7859088 xmax: 6650626 ymax: 9808703
## epsg (SRID):    29101
## proj4string:    +proj=poly +lat_0=0 +lon_0=-54 +x_0=5000000 +y_0=10000000 +ellps=aust_SA +towgs84=-66.87,4.37,-38.52,0,0,0,0 +units=m +no_defs
##                  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
##   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
##   IBGE_1.4 IBGE_5.9 IBGE_10.14 IBGE_15.59 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
##   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
##   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
##                            REGIAO_TUR CATEGORIA_TUR ESTIMATED_POP
## 1                                                            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                                                           11663
##       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
##      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
##                                                               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
##   MUN_EXPENDIT COMP_TOT COMP_A COMP_B COMP_C COMP_D COMP_E COMP_F COMP_G COMP_H
## 1     28227691      284      5      1     56      0      2     29    110     26
## 2     17909274      476      6      6     30      1      2     34    190     70
## 3     37513019      288      5      9     26      0      2      7    117     12
## 4           NA      621     18      1     40      0      1     20    303     62
## 5           NA      931      4      2     43      0      1     27    500     16
## 6           NA       86      1      0      4      0      0      6     48      2
##   COMP_I COMP_J COMP_K COMP_L COMP_M COMP_N COMP_O COMP_P COMP_Q COMP_R COMP_S
## 1      4      5      0      2     10     12      4      6      6      1      5
## 2     28     11      0      4     15     29      2      9     14      6     19
## 3     57      2      1      0      7     15      3     11      5      1      8
## 4     30      9      6      4     28     27      2     15     19      9     27
## 5     31      6      1      1     22     16      2    155     33     15     56
## 6     10      2      0      0      2      3      2      0      2      0      4
##   COMP_T COMP_U HOTELS BEDS Pr_Agencies Pu_Agencies Pr_Bank Pu_Bank Pr_Assets
## 1      0      0     NA   NA          NA          NA      NA      NA        NA
## 2      0      0     NA   NA          NA          NA      NA      NA        NA
## 3      0      0      1   34           1           1       1       1  33724584
## 4      0      0     NA   NA           2           2       2       2  44974716
## 5      0      0     NA   NA           2           4       2       4  76181384
## 6      0      0     NA   NA          NA          NA      NA      NA        NA
##   Pu_Assets Cars Motorcycles Wheeled_tractor UBER MAC WAL.MART POST_OFFICES
## 1        NA 2158        1246               0   NA  NA       NA            1
## 2        NA 2227        1142               0   NA  NA       NA            1
## 3  67091904 2838        1426               0   NA  NA       NA            3
## 4 371922572 6928        2953               0   NA  NA       NA            4
## 5 800078483 5277       25661               0   NA  NA       NA            2
## 6        NA  553        1674               0   NA  NA       NA            1
##                  geometry
## 1 POINT (5486142 8140850)
## 2 POINT (5697257 7942355)
## 3 POINT (5564741 8202931)
## 4 POINT (5899496 7859088)
## 5 POINT (5569259 9808703)
## 6 POINT (6650626 9158924)

Performing a summary function to chech the changes. As we can see that are missing value within the data. But at this stage we will not going to replace the NA value. As we can see from the both data sets with different number of rows. Which means there are different in number of Brazil municipality boundary. We will be only converting those NA value to ZERO at the later stage.

summary(br_data.sf)
##            CITY          STATE         CAPITAL          IBGE_RES_POP     
##  Bom Jesus   :   5   MG     : 853   Min.   :0.000000   Min.   :     805  
##  São Domingos:   5   SP     : 645   1st Qu.:0.000000   1st Qu.:    5235  
##  Bonito      :   4   RS     : 498   Median :0.000000   Median :   10934  
##  Planalto    :   4   BA     : 418   Mean   :0.004845   Mean   :   34278  
##  Santa Helena:   4   PR     : 399   3rd Qu.:0.000000   3rd Qu.:   23424  
##  Santa Inês  :   4   SC     : 295   Max.   :1.000000   Max.   :11253503  
##  (Other)     :5547   (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         ALT          
##  Min.   :0.4000   Min.   :0.6720   Min.   :0.2070   Min.   :     0.0  
##  1st Qu.:0.5720   1st Qu.:0.7690   1st Qu.:0.4900   1st Qu.:   169.8  
##  Median :0.6540   Median :0.8080   Median :0.5600   Median :   406.5  
##  Mean   :0.6429   Mean   :0.8016   Mean   :0.5591   Mean   :   893.8  
##  3rd Qu.:0.7070   3rd Qu.:0.8360   3rd Qu.:0.6310   3rd Qu.:   628.9  
##  Max.   :0.8910   Max.   :0.8940   Max.   :0.8250   Max.   :874579.0  
##  NA's   :8        NA's   :8        NA's   :8        NA's   :9         
##      PAY_TV         FIXED_PHONES          AREA          
##  Min.   :      1   Min.   :      3   Min.   :     3.57  
##  1st Qu.:     88   1st Qu.:    119   1st Qu.:   204.44  
##  Median :    247   Median :    327   Median :   416.59  
##  Mean   :   3094   Mean   :   6567   Mean   :  1517.44  
##  3rd Qu.:    815   3rd Qu.:   1151   3rd Qu.:  1026.57  
##  Max.   :2047668   Max.   :5543127   Max.   :159533.33  
##  NA's   :3         NA's   :3         NA's   :3          
##                 REGIAO_TUR   CATEGORIA_TUR ESTIMATED_POP     
##                      :2288    :2288        Min.   :     786  
##  Corredores Das Águas:  59   A:  51        1st Qu.:    5454  
##  Vale Do Contestado  :  45   B: 168        Median :   11590  
##  Amazônia Atlântica  :  40   C: 521        Mean   :   37432  
##  Araguaia-Tocantins  :  39   D:1892        3rd Qu.:   25296  
##  Cariri              :  37   E: 653        Max.   :12176866  
##  (Other)             :3065                 NA's   :3         
##                   RURAL_URBAN    GVA_AGROPEC       GVA_INDUSTRY     
##                         :   3   Min.   :      0   Min.   :       1  
##  Intermediário Adjacente: 686   1st Qu.:   4189   1st Qu.:    1726  
##  Intermediário Remoto   :  60   Median :  20426   Median :    7424  
##  Rural Adjacente        :3040   Mean   :  47271   Mean   :  175928  
##  Rural Remoto           : 323   3rd Qu.:  51227   3rd Qu.:   41022  
##  Sem classificação      :   5   Max.   :1402282   Max.   :63306755  
##  Urbano                 :1456   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    
##  Min.   :       15   Min.   :     815   Min.   :  3191  
##  1st Qu.:    43709   1st Qu.:    5483   1st Qu.:  9058  
##  Median :   125153   Median :   11578   Median : 15870  
##  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       
##                                                                                  GVA_MAIN   
##  Administração, defesa, educação e saúde públicas e seguridade social                :2725  
##  Demais serviços                                                                     :1477  
##  Agricultura, inclusive apoio à agricultura e a pós colheita                         : 735  
##  Indústrias de transformação                                                         : 261  
##  Pecuária, inclusive apoio à pecuária                                                : 161  
##  Eletricidade e gás, água, esgoto, atividades de gestão de resíduos e descontaminação:  98  
##  (Other)                                                                             : 116  
##   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   :9.187e+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.   :1.950e+13   Max.   :8.020e+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   Min.   :1      Min.   :  1.000  
##  1st Qu.:    591   1st Qu.:   0.000   1st Qu.:1      1st Qu.:  1.000  
##  Median :   1285   Median :   0.000   Median :1      Median :  2.000  
##  Mean   :   4879   Mean   :   5.754   Mean   :1      Mean   :  4.277  
##  3rd Qu.:   3294   3rd Qu.:   1.000   3rd Qu.:1      3rd Qu.:  3.000  
##  Max.   :1134570   Max.   :3236.000   Max.   :1      Max.   :130.000  
##  NA's   :11        NA's   :11         NA's   :5448   NA's   :5407     
##     WAL.MART       POST_OFFICES              geometry   
##  Min.   : 1.000   Min.   :  1.000   POINT        :5573  
##  1st Qu.: 1.000   1st Qu.:  1.000   epsg:29101   :   0  
##  Median : 1.000   Median :  1.000   +proj=poly...:   0  
##  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

We also can use glismps() function to view the variable name of each columns.

glimpse(br_data.sf)
## Observations: 5,573
## Variables: 80
## $ CITY                   <fct> Abadia De Goiás, Abadia Dos Dourados, Abadiâ...
## $ STATE                  <fct> GO, MG, GO, MG, PA, CE, BA, BA, PR, SC, PA, ...
## $ CAPITAL                <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ IBGE_RES_POP           <int> 6876, 6704, 15757, 22690, 141100, 10496, 831...
## $ IBGE_RES_POP_BRAS      <int> 6876, 6704, 15609, 22690, 141040, 10496, 831...
## $ IBGE_RES_POP_ESTR      <int> 0, 0, 148, 0, 60, 0, 0, 0, 0, 0, 0, 16, 17, ...
## $ IBGE_DU                <int> 2137, 2328, 4655, 7694, 31061, 2791, 2572, 4...
## $ IBGE_DU_URBAN          <int> 1546, 1481, 3233, 6667, 19057, 1251, 1193, 2...
## $ IBGE_DU_RURAL          <int> 591, 847, 1422, 1027, 12004, 1540, 1379, 195...
## $ IBGE_POP               <int> 5300, 4154, 10656, 18464, 82956, 4538, 3725,...
## $ IBGE_1                 <int> 69, 38, 139, 176, 1354, 98, 37, 167, 69, 12,...
## $ IBGE_1.4               <int> 318, 207, 650, 856, 5567, 323, 156, 733, 302...
## $ IBGE_5.9               <int> 438, 260, 894, 1233, 7618, 421, 263, 978, 37...
## $ IBGE_10.14             <int> 517, 351, 1087, 1539, 8905, 483, 277, 927, 4...
## $ IBGE_15.59             <int> 3542, 2709, 6896, 11979, 53516, 2631, 2319, ...
## $ IBGE_60.               <int> 416, 589, 990, 2681, 5996, 582, 673, 803, 81...
## $ IBGE_PLANTED_AREA      <int> 319, 4479, 10307, 1862, 25200, 2598, 895, 20...
## $ IBGE_CROP_PRODUCTION_. <int> 1843, 18017, 33085, 7502, 700872, 5234, 3999...
## $ IDHM.Ranking.2010      <int> 1689, 2207, 2202, 1994, 3530, 3522, 4086, 47...
## $ IDHM                   <dbl> 0.708, 0.690, 0.690, 0.698, 0.628, 0.628, 0....
## $ IDHM_Renda             <dbl> 0.687, 0.693, 0.671, 0.720, 0.579, 0.540, 0....
## $ IDHM_Longevidade       <dbl> 0.830, 0.839, 0.841, 0.848, 0.798, 0.748, 0....
## $ IDHM_Educacao          <dbl> 0.622, 0.563, 0.579, 0.556, 0.537, 0.612, 0....
## $ ALT                    <dbl> 893.60, 753.12, 1017.55, 644.74, 10.12, 403....
## $ PAY_TV                 <int> 360, 77, 227, 1230, 3389, 29, 952, 51, 55, 1...
## $ FIXED_PHONES           <int> 842, 296, 720, 1716, 1218, 34, 335, 222, 392...
## $ AREA                   <dbl> 147.26, 881.06, 1045.13, 1817.07, 1610.65, 1...
## $ REGIAO_TUR             <fct> , Caminhos Do Cerrado, Região Turística Do O...
## $ CATEGORIA_TUR          <fct> , D, C, D, D, , D, , , D, E, D, D, D, , E, ,...
## $ ESTIMATED_POP          <int> 8583, 6972, 19614, 23223, 156292, 11663, 876...
## $ RURAL_URBAN            <fct> Urbano, Rural Adjacente, Rural Adjacente, Ur...
## $ GVA_AGROPEC            <dbl> 6.20, 50524.57, 42.84, 113824.60, 140463.72,...
## $ GVA_INDUSTRY           <dbl> 27991.25, 25917.70, 16728.30, 31002.62, 5861...
## $ GVA_SERVICES           <dbl> 74750.32, 62689.23, 138198.58, 172.33, 46812...
## $ GVA_PUBLIC             <dbl> 36915.04, 28083.79, 63396.20, 86081.41, 4868...
## $ GVA_TOTAL              <dbl> 145857.60, 167215.28, 261161.91, 403241.27, ...
## $ TAXES                  <dbl> 20554.20, 12873.50, 26822.58, 26994.09, 9518...
## $ GDP                    <dbl> 166.41, 180.09, 287984.49, 430235.36, 124925...
## $ POP_GDP                <int> 8053, 7037, 18427, 23574, 151934, 11483, 921...
## $ GDP_CAPITA             <dbl> 20664.57, 25591.70, 15628.40, 18250.42, 8222...
## $ GVA_MAIN               <fct> "Demais serviços", "Demais serviços", "Demai...
## $ MUN_EXPENDIT           <dbl> 28227691, 17909274, 37513019, NA, NA, NA, NA...
## $ COMP_TOT               <int> 284, 476, 288, 621, 931, 86, 191, 87, 285, 6...
## $ COMP_A                 <int> 5, 6, 5, 18, 4, 1, 6, 2, 5, 2, 0, 8, 3, 1, 4...
## $ COMP_B                 <int> 1, 6, 9, 1, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0,...
## $ COMP_C                 <int> 56, 30, 26, 40, 43, 4, 8, 3, 20, 4, 9, 40, 3...
## $ COMP_D                 <int> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,...
## $ COMP_E                 <int> 2, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 0,...
## $ COMP_F                 <int> 29, 34, 7, 20, 27, 6, 4, 0, 10, 2, 0, 25, 12...
## $ COMP_G                 <int> 110, 190, 117, 303, 500, 48, 97, 71, 133, 35...
## $ COMP_H                 <int> 26, 70, 12, 62, 16, 2, 5, 0, 18, 8, 1, 67, 3...
## $ COMP_I                 <int> 4, 28, 57, 30, 31, 10, 5, 1, 14, 3, 0, 25, 1...
## $ COMP_J                 <int> 5, 11, 2, 9, 6, 2, 3, 1, 8, 1, 1, 9, 5, 14, ...
## $ COMP_K                 <int> 0, 0, 1, 6, 1, 0, 1, 0, 0, 1, 0, 4, 3, 3, 0,...
## $ COMP_L                 <int> 2, 4, 0, 4, 1, 0, 0, 0, 4, 0, 0, 7, 4, 4, 0,...
## $ COMP_M                 <int> 10, 15, 7, 28, 22, 2, 5, 0, 11, 4, 2, 26, 17...
## $ COMP_N                 <int> 12, 29, 15, 27, 16, 3, 5, 1, 26, 0, 1, 16, 1...
## $ COMP_O                 <int> 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 6, 2, 4, 2, 4,...
## $ COMP_P                 <int> 6, 9, 11, 15, 155, 0, 8, 0, 8, 1, 6, 14, 11,...
## $ COMP_Q                 <int> 6, 14, 5, 19, 33, 2, 1, 2, 9, 3, 0, 13, 22, ...
## $ COMP_R                 <int> 1, 6, 1, 9, 15, 0, 2, 0, 4, 0, 0, 4, 6, 6, 0...
## $ COMP_S                 <int> 5, 19, 8, 27, 56, 4, 38, 4, 12, 3, 4, 23, 38...
## $ COMP_T                 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ COMP_U                 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ HOTELS                 <int> NA, NA, 1, NA, NA, NA, 1, NA, NA, NA, NA, NA...
## $ BEDS                   <int> NA, NA, 34, NA, NA, NA, 24, NA, NA, NA, NA, ...
## $ Pr_Agencies            <int> NA, NA, 1, 2, 2, NA, NA, 1, 0, 0, 0, 1, 0, 2...
## $ Pu_Agencies            <int> NA, NA, 1, 2, 4, NA, NA, 0, 1, 1, 1, 2, 1, 3...
## $ Pr_Bank                <int> NA, NA, 1, 2, 2, NA, NA, 1, 0, 0, 0, 1, 0, 2...
## $ Pu_Bank                <int> NA, NA, 1, 2, 4, NA, NA, 0, 1, 1, 1, 2, 1, 3...
## $ Pr_Assets              <dbl> NA, NA, 33724584, 44974716, 76181384, NA, NA...
## $ Pu_Assets              <dbl> NA, NA, 67091904, 371922572, 800078483, NA, ...
## $ Cars                   <int> 2158, 2227, 2838, 6928, 5277, 553, 896, 613,...
## $ Motorcycles            <int> 1246, 1142, 1426, 2953, 25661, 1674, 696, 15...
## $ Wheeled_tractor        <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0,...
## $ UBER                   <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ MAC                    <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ WAL.MART               <int> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ POST_OFFICES           <int> 1, 1, 3, 4, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,...
## $ geometry               <POINT [m]> POINT (5486142 8140850), POINT (569725...

Based on the summary for both data sets, we can see that the name of the Brazil municipality boundaries are not aynchronise in such way that some letters are in Upper case and some letters are in lower case. This case we will not cover all the letters in upper case because all their special character in lower case. Therefore, we will perform funs(tolower) function to the data set.

mun <- mun %>%
  mutate_at(.vars = vars(name_muni), .funs = funs(tolower)) 

funs(tolower) function also applies to br_data.sf dataset.

br_data.sf <- br_data.sf %>%
  mutate_at(.vars = vars(CITY), .funs = funs(tolower)) 

Before, performing the left_join function, we need to convert the br_data.sf data set to data frame in order to combine it with mun data set.

br_data.df <- as.data.frame(br_data.sf)

In this case, we need to assign 2 common columns in order to perform the join. As there are many Brazil municipality city with the same, in order to map it correctly we need to add in an extra common variable which is their State name.

As we know that, in the br_data.df data set we have all the information, one question we have to ask ourselves, then why we need to combine both data set. The reason is we want to filter out those Brazil municipality boundary which not in both data set.

final_br <- left_join(mun, br_data.df , by = c("name_muni" = "CITY","abbrev_state"="STATE"))

After performing the left_join function, we want to check the class of final_br data set. Currently the data set is in Simple feature format.

class(final_br)
## [1] "sf"         "data.frame"

At the same time we also can use summary() function to view the summary of the final_br data set. As we can see in the summary there are 2 columns for geometry. One geometry is for the location point of municipality and the other geometry is for the polygon’s geometry. At the later stage we going to remove the geometry coordinates to make this data set is main for the exact location of municipality.

summary(final_br)
##    code_muni        name_muni           code_state   abbrev_state      
##  Min.   :1100015   Length:5572        31     : 853   Length:5572       
##  1st Qu.:2512175   Class :character   35     : 645   Class :character  
##  Median :3146354   Mode  :character   43     : 499   Mode  :character  
##  Mean   :3253966                      29     : 417                     
##  3rd Qu.:4119264                      41     : 399                     
##  Max.   :5300108                      42     : 295                     
##                                       (Other):2464                     
##     CAPITAL          IBGE_RES_POP      IBGE_RES_POP_BRAS  IBGE_RES_POP_ESTR 
##  Min.   :0.000000   Min.   :     805   Min.   :     805   Min.   :     0.0  
##  1st Qu.:0.000000   1st Qu.:    5235   1st Qu.:    5230   1st Qu.:     0.0  
##  Median :0.000000   Median :   10934   Median :   10926   Median :     0.0  
##  Mean   :0.004847   Mean   :   34278   Mean   :   34200   Mean   :    77.5  
##  3rd Qu.:0.000000   3rd Qu.:   23424   3rd Qu.:   23390   3rd Qu.:    10.0  
##  Max.   :1.000000   Max.   :11253503   Max.   :11133776   Max.   :119727.0  
##  NA's   :1          NA's   :7          NA's   :7          NA's   :7         
##     IBGE_DU        IBGE_DU_URBAN     IBGE_DU_RURAL      IBGE_POP       
##  Min.   :    239   Min.   :     60   Min.   :    3   Min.   :     174  
##  1st Qu.:   1572   1st Qu.:    874   1st Qu.:  487   1st Qu.:    2801  
##  Median :   3174   Median :   1846   Median :  931   Median :    6170  
##  Mean   :  10303   Mean   :   8859   Mean   : 1463   Mean   :   27595  
##  3rd Qu.:   6726   3rd Qu.:   4624   3rd Qu.: 1832   3rd Qu.:   15302  
##  Max.   :3576148   Max.   :3548433   Max.   :33809   Max.   :10463636  
##  NA's   :9         NA's   :9         NA's   :80      NA's   :7         
##      IBGE_1            IBGE_1.4         IBGE_5.9        IBGE_10.14    
##  Min.   :     0.0   Min.   :     5   Min.   :     7   Min.   :    12  
##  1st Qu.:    38.0   1st Qu.:   158   1st Qu.:   220   1st Qu.:   259  
##  Median :    92.0   Median :   376   Median :   516   Median :   588  
##  Mean   :   383.3   Mean   :  1544   Mean   :  2069   Mean   :  2381  
##  3rd Qu.:   232.0   3rd Qu.:   951   3rd Qu.:  1300   3rd Qu.:  1478  
##  Max.   :129464.0   Max.   :514794   Max.   :684443   Max.   :783702  
##  NA's   :7          NA's   :7        NA's   :7        NA's   :7       
##    IBGE_15.59         IBGE_60.       IBGE_PLANTED_AREA   IBGE_CROP_PRODUCTION_.
##  Min.   :     94   Min.   :     29   Min.   :      0.0   Min.   :      0       
##  1st Qu.:   1734   1st Qu.:    341   1st Qu.:    910.2   1st Qu.:   2326       
##  Median :   3841   Median :    722   Median :   3471.5   Median :  13846       
##  Mean   :  18212   Mean   :   3004   Mean   :  14179.9   Mean   :  57384       
##  3rd Qu.:   9628   3rd Qu.:   1724   3rd Qu.:  11194.2   3rd Qu.:  55619       
##  Max.   :7058221   Max.   :1293012   Max.   :1205669.0   Max.   :3274885       
##  NA's   :7         NA's   :7         NA's   :2           NA's   :2             
##  IDHM.Ranking.2010      IDHM          IDHM_Renda     IDHM_Longevidade
##  Min.   :   1      Min.   :0.4180   Min.   :0.4000   Min.   :0.6720  
##  1st Qu.:1392      1st Qu.:0.5990   1st Qu.:0.5720   1st Qu.:0.7690  
##  Median :2782      Median :0.6650   Median :0.6540   Median :0.8080  
##  Mean   :2783      Mean   :0.6592   Mean   :0.6429   Mean   :0.8016  
##  3rd Qu.:4173      3rd Qu.:0.7180   3rd Qu.:0.7070   3rd Qu.:0.8360  
##  Max.   :5565      Max.   :0.8620   Max.   :0.8910   Max.   :0.8940  
##  NA's   :8         NA's   :8        NA's   :8        NA's   :8       
##  IDHM_Educacao         ALT               PAY_TV         FIXED_PHONES    
##  Min.   :0.2070   Min.   :     0.0   Min.   :      1   Min.   :      3  
##  1st Qu.:0.4900   1st Qu.:   169.7   1st Qu.:     88   1st Qu.:    119  
##  Median :0.5600   Median :   406.5   Median :    247   Median :    327  
##  Mean   :0.5591   Mean   :   894.0   Mean   :   3095   Mean   :   6568  
##  3rd Qu.:0.6310   3rd Qu.:   629.0   3rd Qu.:    815   3rd Qu.:   1151  
##  Max.   :0.8250   Max.   :874579.0   Max.   :2047668   Max.   :5543127  
##  NA's   :8        NA's   :9          NA's   :3         NA's   :3        
##       AREA                          REGIAO_TUR   CATEGORIA_TUR
##  Min.   :     3.57                       :2287       :2287    
##  1st Qu.:   204.44   Corredores Das Águas:  59   A   :  51    
##  Median :   416.59   Vale Do Contestado  :  45   B   : 168    
##  Mean   :  1517.44   Amazônia Atlântica  :  40   C   : 521    
##  3rd Qu.:  1026.57   Araguaia-Tocantins  :  39   D   :1891    
##  Max.   :159533.33   (Other)             :3101   E   : 653    
##  NA's   :2           NA's                :   1   NA's:   1    
##  ESTIMATED_POP                       RURAL_URBAN    GVA_AGROPEC     
##  Min.   :     786   Rural Adjacente        :3040   Min.   :      0  
##  1st Qu.:    5454   Urbano                 :1456   1st Qu.:   4189  
##  Median :   11591   Intermediário Adjacente: 686   Median :  20426  
##  Mean   :   37437   Rural Remoto           : 323   Mean   :  47271  
##  3rd Qu.:   25297   Intermediário Remoto   :  60   3rd Qu.:  51227  
##  Max.   :12176866   (Other)                :   6   Max.   :1402282  
##  NA's   :3          NA's                   :   1   NA's   :2        
##   GVA_INDUSTRY       GVA_SERVICES         GVA_PUBLIC         GVA_TOTAL        
##  Min.   :       1   Min.   :        2   Min.   :       7   Min.   :       17  
##  1st Qu.:    1726   1st Qu.:    10112   1st Qu.:   17267   1st Qu.:    42253  
##  Median :    7424   Median :    31211   Median :   35866   Median :   119492  
##  Mean   :  175928   Mean   :   489451   Mean   :  123768   Mean   :   832987  
##  3rd Qu.:   41022   3rd Qu.:   115406   3rd Qu.:   89245   3rd Qu.:   313963  
##  Max.   :63306755   Max.   :464656988   Max.   :41902893   Max.   :569910503  
##  NA's   :2          NA's   :2           NA's   :2          NA's   :2          
##      TAXES                GDP               POP_GDP           GDP_CAPITA    
##  Min.   :   -14159   Min.   :       15   Min.   :     815   Min.   :  3191  
##  1st Qu.:     1305   1st Qu.:    43709   1st Qu.:    5483   1st Qu.:  9058  
##  Median :     5100   Median :   125153   Median :   11578   Median : 15870  
##  Mean   :   118864   Mean   :   954584   Mean   :   36998   Mean   : 21126  
##  3rd Qu.:    22197   3rd Qu.:   329539   3rd Qu.:   25085   3rd Qu.: 26155  
##  Max.   :117125387   Max.   :687035890   Max.   :12038175   Max.   :314638  
##  NA's   :2           NA's   :2           NA's   :2          NA's   :2       
##                                                                  GVA_MAIN   
##  Administração, defesa, educação e saúde públicas e seguridade social:2725  
##  Demais serviços                                                     :1477  
##  Agricultura, inclusive apoio à agricultura e a pós colheita         : 735  
##  Indústrias de transformação                                         : 261  
##  Pecuária, inclusive apoio à pecuária                                : 161  
##  (Other)                                                             : 212  
##  NA's                                                                :   1  
##   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.:5.672e+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   :1493        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   :   73.44   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   :2          NA's   :2          NA's   :2         NA's   :2         
##      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   :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.   :    0.0  
##  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   :2          NA's   :2          NA's   :2          NA's   :2        
##      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   :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   :   51.61   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   :2          NA's   :2   NA's   :2           NA's   :4685    
##       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   :4685      NA's   :2230       NA's   :2230      NA's   :2230    
##     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   :9.187e+09   Mean   :6.005e+09   Mean   :   9861  
##  3rd Qu.:2.00   3rd Qu.:1.148e+08   3rd Qu.:4.970e+08   3rd Qu.:   4086  
##  Max.   :8.00   Max.   :1.950e+13   Max.   :8.020e+12   Max.   :5740995  
##  NA's   :2230   NA's   :2230        NA's   :2230        NA's   :11       
##   Motorcycles      Wheeled_tractor         UBER           MAC         
##  Min.   :      4   Min.   :   0.000   Min.   :1      Min.   :  1.000  
##  1st Qu.:    591   1st Qu.:   0.000   1st Qu.:1      1st Qu.:  1.000  
##  Median :   1285   Median :   0.000   Median :1      Median :  2.000  
##  Mean   :   4879   Mean   :   5.755   Mean   :1      Mean   :  4.277  
##  3rd Qu.:   3295   3rd Qu.:   1.000   3rd Qu.:1      3rd Qu.:  3.000  
##  Max.   :1134570   Max.   :3236.000   Max.   :1      Max.   :130.000  
##  NA's   :11        NA's   :11         NA's   :5447   NA's   :5406     
##     WAL.MART       POST_OFFICES                geom               geometry   
##  Min.   : 1.000   Min.   :  1.000   MULTIPOLYGON :2773   POINT        :5572  
##  1st Qu.: 1.000   1st Qu.:  1.000   POLYGON      :2799   epsg:29101   :   0  
##  Median : 1.000   Median :  1.000   epsg:29101   :   0   +proj=poly...:   0  
##  Mean   : 2.059   Mean   :  2.081   +proj=poly...:   0                       
##  3rd Qu.: 1.750   3rd Qu.:  2.000                                            
##  Max.   :26.000   Max.   :225.000                                            
##  NA's   :5470     NA's   :119

As we mentioned, in the above, now we going to combine the data set again to make another data set purely for the location of Brazil municipality boundary.

br_data <- br_data %>%
  mutate_at(.vars = vars(CITY), .funs = funs(tolower)) 

We will perform the left_join() function again.

mun_map <- left_join(mun, br_data , by = c("name_muni" = "CITY","abbrev_state"="STATE"))

Since we got all the common Brazil municipality boundares, now we going to remove all the irrelevant columns and only keep those columns which related to Brazil municipality boundary and we will named it as mun_map.

mun_map <- dplyr::select(mun_map,1:4)

4. Exploratory Data Analysis (EDA)

4.1 Choropleth map (GDP per capita, 2016)

Now we going to use tmap() function to show the GDP per Capita. As we mentioned before, in this data set there are 2 geometries, one is in point the other one is in polygon. When we use tm_fill it will use the polygon geometry instead of the point geometry.

tm_shape (final_br) +
  tm_fill (col= "GDP_CAPITA", 
               style = "quantile",palette = "Blues",legend.hist = TRUE) +
  tm_borders(alpha = 0.2)+
  tm_layout(main.title = "BRAZIL GDP CAPITA",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 1,
          legend.text.size = 0.8,
          legend.position = c("left","bottom"),
          legend.bg.alpha = 1,
          legend.outside = TRUE,
          legend.hist.width = 1,
          outer.bg.color = "lightblue") +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom")) 

Based on the choropleth map of distribution of GDP per capita, 2016 at municipality level. We can see that those municipality with higher level GDP_CAPITA is tend to located at the bottom and centre of brazil. Those area with lower GDP_CAPITA is tend to located at the left-top and mid-right of brazil. At the same time, we can see from the histogram that lowest and second lowest GDP per CAPITA range have the highest number of municipalities compare to the rest.

Based on the choropleth map we can identify that, there are 2 missing municipalities that without any GPD. In order to get a most accurate analysis we need to exclude this 2 municipalities, as we cannot by assuming it to be zero when we going to use GDP per capita as our depentent variable.

final_br <- final_br[-c(4607,4608),]

Since all the missing GDP per capita has been removed, now we can convert those columns with missing values.

final_br[is.na(final_br)] <- 0

4.2 Histogram plot and Boxplot for distribution of GDp per Capita

Now can use ggplot to plot 2 plots on the same output by using a package called “Patchwork”.

plt1 <- ggplot(data=final_br, aes(x=`GDP_CAPITA`)) +
  geom_histogram(bins=20, color="black", fill="light blue")+
  scale_x_continuous(labels = function(x) format(x, big.mark = ",", scientific = FALSE)) +
  theme_classic()

plt2 <- ggplot(data=final_br,aes(x = "", y = GDP_CAPITA ))+
    geom_boxplot(fill = "lightblue", color = "black") + 
  scale_y_continuous(labels = function(x) format(x, big.mark = ",", scientific = FALSE)) +
  coord_flip() +
  theme_classic() +
  xlab("") +
  theme(axis.text.y=element_blank(),
        axis.ticks.y=element_blank())

plt2 + plt1 +plot_layout(nrow = 2, heights = c(1,2))

Based on the histogram and boxplot we can see the distribution of GDP_CAPTIA.

4.3 Drawing Statistical Point Map

tmap_mode("plot")

Not only that, we also can use tmap to plot an interactive map. However, in this case we will change the map from tmap_mode(“view”) to tmap_mode(“plot”) first. The purpose of plotting the map is to see the location the municipality point. As we mentioned beofore, in this plot both tm_polygons and tm_dots will be using the data from the same set of data, as in this data set there are 2 geometries.

tm_shape(final_br)+
  tm_polygons(alpha = 0.7) +
tm_shape(final_br) +  
  tm_dots(alpha = 0.6, col = "red")

tmap_mode("plot")

5. Data Preparation of Multi-linear Regression

5.1 Converting into Dummy Variables

Now we going to remove the geometry column which referring to the municipalitity polygons and only left one geometry column which is for the municipality point.

final_br.point <- final_br %>%
 st_set_geometry(NULL)
summary(final_br.point)
##    code_muni        name_muni           code_state   abbrev_state      
##  Min.   :1100015   Length:5570        31     : 853   Length:5570       
##  1st Qu.:2512126   Class :character   35     : 645   Class :character  
##  Median :3146280   Mode  :character   43     : 497   Mode  :character  
##  Mean   :3253591                      29     : 417                     
##  3rd Qu.:4119190                      41     : 399                     
##  Max.   :5300108                      42     : 295                     
##                                       (Other):2464                     
##     CAPITAL          IBGE_RES_POP      IBGE_RES_POP_BRAS  IBGE_RES_POP_ESTR  
##  Min.   :0.000000   Min.   :       0   Min.   :       0   Min.   :     0.00  
##  1st Qu.:0.000000   1st Qu.:    5224   1st Qu.:    5217   1st Qu.:     0.00  
##  Median :0.000000   Median :   10932   Median :   10920   Median :     0.00  
##  Mean   :0.004847   Mean   :   34247   Mean   :   34170   Mean   :    77.44  
##  3rd Qu.:0.000000   3rd Qu.:   23409   3rd Qu.:   23380   3rd Qu.:    10.00  
##  Max.   :1.000000   Max.   :11253503   Max.   :11133776   Max.   :119727.00  
##                                                                              
##     IBGE_DU        IBGE_DU_URBAN     IBGE_DU_RURAL      IBGE_POP       
##  Min.   :      0   Min.   :      0   Min.   :    0   Min.   :       0  
##  1st Qu.:   1567   1st Qu.:    871   1st Qu.:  471   1st Qu.:    2790  
##  Median :   3170   Median :   1840   Median :  917   Median :    6158  
##  Mean   :  10290   Mean   :   8848   Mean   : 1442   Mean   :   27570  
##  3rd Qu.:   6722   3rd Qu.:   4619   3rd Qu.: 1813   3rd Qu.:   15299  
##  Max.   :3576148   Max.   :3548433   Max.   :33809   Max.   :10463636  
##                                                                        
##      IBGE_1            IBGE_1.4           IBGE_5.9          IBGE_10.14      
##  Min.   :     0.0   Min.   :     0.0   Min.   :     0.0   Min.   :     0.0  
##  1st Qu.:    38.0   1st Qu.:   158.0   1st Qu.:   219.2   1st Qu.:   258.2  
##  Median :    92.0   Median :   376.0   Median :   514.5   Median :   587.0  
##  Mean   :   382.9   Mean   :  1543.1   Mean   :  2067.5   Mean   :  2379.3  
##  3rd Qu.:   232.0   3rd Qu.:   949.8   3rd Qu.:  1299.0   3rd Qu.:  1477.5  
##  Max.   :129464.0   Max.   :514794.0   Max.   :684443.0   Max.   :783702.0  
##                                                                             
##    IBGE_15.59         IBGE_60.       IBGE_PLANTED_AREA   IBGE_CROP_PRODUCTION_.
##  Min.   :      0   Min.   :      0   Min.   :      0.0   Min.   :      0       
##  1st Qu.:   1730   1st Qu.:    340   1st Qu.:    910.2   1st Qu.:   2326       
##  Median :   3837   Median :    721   Median :   3471.5   Median :  13846       
##  Mean   :  18196   Mean   :   3002   Mean   :  14179.9   Mean   :  57384       
##  3rd Qu.:   9591   3rd Qu.:   1723   3rd Qu.:  11194.2   3rd Qu.:  55619       
##  Max.   :7058221   Max.   :1293012   Max.   :1205669.0   Max.   :3274885       
##                                                                                
##  IDHM.Ranking.2010      IDHM          IDHM_Renda     IDHM_Longevidade
##  Min.   :   0      Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:1387      1st Qu.:0.5990   1st Qu.:0.5720   1st Qu.:0.7690  
##  Median :2780      Median :0.6650   Median :0.6540   Median :0.8080  
##  Mean   :2780      Mean   :0.6585   Mean   :0.6422   Mean   :0.8007  
##  3rd Qu.:4172      3rd Qu.:0.7180   3rd Qu.:0.7070   3rd Qu.:0.8360  
##  Max.   :5565      Max.   :0.8620   Max.   :0.8910   Max.   :0.8940  
##                                                                      
##  IDHM_Educacao         ALT               PAY_TV         FIXED_PHONES    
##  Min.   :0.0000   Min.   :     0.0   Min.   :      0   Min.   :      0  
##  1st Qu.:0.4900   1st Qu.:   168.9   1st Qu.:     88   1st Qu.:    118  
##  Median :0.5600   Median :   406.3   Median :    247   Median :    327  
##  Mean   :0.5585   Mean   :   892.8   Mean   :   3094   Mean   :   6567  
##  3rd Qu.:0.6310   3rd Qu.:   628.7   3rd Qu.:    815   3rd Qu.:   1151  
##  Max.   :0.8250   Max.   :874579.0   Max.   :2047668   Max.   :5543127  
##                                                                         
##       AREA                         REGIAO_TUR   CATEGORIA_TUR
##  Min.   :     0.0                       :2286    :2286       
##  1st Qu.:   204.3   Corredores Das Águas:  59   A:  51       
##  Median :   415.9   Vale Do Contestado  :  45   B: 168       
##  Mean   :  1515.6   Amazônia Atlântica  :  40   C: 521       
##  3rd Qu.:  1026.2   Araguaia-Tocantins  :  39   D:1891       
##  Max.   :159533.3   Cariri              :  37   E: 653       
##                     (Other)             :3064                
##  ESTIMATED_POP                       RURAL_URBAN    GVA_AGROPEC     
##  Min.   :       0                          :   0   Min.   :      0  
##  1st Qu.:    5451   Intermediário Adjacente: 686   1st Qu.:   4189  
##  Median :   11590   Intermediário Remoto   :  60   Median :  20426  
##  Mean   :   37430   Rural Adjacente        :3040   Mean   :  47271  
##  3rd Qu.:   25296   Rural Remoto           : 323   3rd Qu.:  51227  
##  Max.   :12176866   Sem classificação      :   5   Max.   :1402282  
##                     Urbano                 :1456                    
##   GVA_INDUSTRY       GVA_SERVICES         GVA_PUBLIC         GVA_TOTAL        
##  Min.   :       1   Min.   :        2   Min.   :       7   Min.   :       17  
##  1st Qu.:    1726   1st Qu.:    10112   1st Qu.:   17267   1st Qu.:    42253  
##  Median :    7424   Median :    31211   Median :   35866   Median :   119492  
##  Mean   :  175928   Mean   :   489451   Mean   :  123768   Mean   :   832987  
##  3rd Qu.:   41022   3rd Qu.:   115406   3rd Qu.:   89245   3rd Qu.:   313963  
##  Max.   :63306755   Max.   :464656988   Max.   :41902893   Max.   :569910503  
##                                                                               
##      TAXES                GDP               POP_GDP           GDP_CAPITA    
##  Min.   :   -14159   Min.   :       15   Min.   :     815   Min.   :  3191  
##  1st Qu.:     1305   1st Qu.:    43709   1st Qu.:    5483   1st Qu.:  9058  
##  Median :     5100   Median :   125153   Median :   11578   Median : 15870  
##  Mean   :   118864   Mean   :   954584   Mean   :   36998   Mean   : 21126  
##  3rd Qu.:    22197   3rd Qu.:   329539   3rd Qu.:   25085   3rd Qu.: 26155  
##  Max.   :117125387   Max.   :687035890   Max.   :12038175   Max.   :314638  
##                                                                             
##                                                                                  GVA_MAIN   
##  Administração, defesa, educação e saúde públicas e seguridade social                :2725  
##  Demais serviços                                                                     :1477  
##  Agricultura, inclusive apoio à agricultura e a pós colheita                         : 735  
##  Indústrias de transformação                                                         : 261  
##  Pecuária, inclusive apoio à pecuária                                                : 161  
##  Eletricidade e gás, água, esgoto, atividades de gestão de resíduos e descontaminação:  98  
##  (Other)                                                                             : 113  
##   MUN_EXPENDIT          COMP_TOT            COMP_A            COMP_B       
##  Min.   :0.000e+00   Min.   :     6.0   Min.   :   0.00   Min.   :  0.000  
##  1st Qu.:0.000e+00   1st Qu.:    68.0   1st Qu.:   1.00   1st Qu.:  0.000  
##  Median :1.774e+07   Median :   162.0   Median :   2.00   Median :  0.000  
##  Mean   :7.641e+07   Mean   :   906.8   Mean   :  18.25   Mean   :  1.852  
##  3rd Qu.:4.150e+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  
##                                                                            
##      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  
##                                                                            
##      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  
##                                                                          
##      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  
##                                                                            
##      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  
##                                                                           
##      COMP_S             COMP_T      COMP_U              HOTELS       
##  Min.   :    0.00   Min.   :0   Min.   :  0.00000   Min.   : 0.0000  
##  1st Qu.:    5.00   1st Qu.:0   1st Qu.:  0.00000   1st Qu.: 0.0000  
##  Median :   12.00   Median :0   Median :  0.00000   Median : 0.0000  
##  Mean   :   51.61   Mean   :0   Mean   :  0.05027   Mean   : 0.4986  
##  3rd Qu.:   31.00   3rd Qu.:0   3rd Qu.:  0.00000   3rd Qu.: 0.0000  
##  Max.   :24832.00   Max.   :0   Max.   :123.00000   Max.   :97.0000  
##                                                                      
##       BEDS        Pr_Agencies       Pu_Agencies         Pr_Bank       
##  Min.   :    0   Min.   :   0.00   Min.   :  0.000   Min.   : 0.0000  
##  1st Qu.:    0   1st Qu.:   0.00   1st Qu.:  0.000   1st Qu.: 0.0000  
##  Median :    0   Median :   0.00   Median :  1.000   Median : 0.0000  
##  Mean   :   41   Mean   :   2.03   Mean   :  1.698   Mean   : 0.7873  
##  3rd Qu.:    0   3rd Qu.:   1.00   3rd Qu.:  2.000   3rd Qu.: 1.0000  
##  Max.   :13247   Max.   :1693.00   Max.   :626.000   Max.   :83.0000  
##                                                                       
##     Pu_Bank         Pr_Assets           Pu_Assets              Cars        
##  Min.   :0.0000   Min.   :0.000e+00   Min.   :0.000e+00   Min.   :      0  
##  1st Qu.:0.0000   1st Qu.:0.000e+00   1st Qu.:0.000e+00   1st Qu.:    599  
##  Median :1.0000   Median :0.000e+00   Median :2.323e+07   Median :   1433  
##  Mean   :0.9479   Mean   :5.512e+09   Mean   :3.603e+09   Mean   :   9845  
##  3rd Qu.:2.0000   3rd Qu.:4.775e+07   3rd Qu.:1.994e+08   3rd Qu.:   4084  
##  Max.   :8.0000   Max.   :1.950e+13   Max.   :8.020e+12   Max.   :5740995  
##                                                                            
##   Motorcycles        Wheeled_tractor         UBER              MAC          
##  Min.   :      0.0   Min.   :   0.000   Min.   :0.00000   Min.   :  0.0000  
##  1st Qu.:    589.2   1st Qu.:   0.000   1st Qu.:0.00000   1st Qu.:  0.0000  
##  Median :   1282.5   Median :   0.000   Median :0.00000   Median :  0.0000  
##  Mean   :   4871.5   Mean   :   5.745   Mean   :0.02244   Mean   :  0.1275  
##  3rd Qu.:   3292.8   3rd Qu.:   1.000   3rd Qu.:0.00000   3rd Qu.:  0.0000  
##  Max.   :1134570.0   Max.   :3236.000   Max.   :1.00000   Max.   :130.0000  
##                                                                             
##     WAL.MART        POST_OFFICES              geometry   
##  Min.   : 0.0000   Min.   :  0.000   POINT        :5570  
##  1st Qu.: 0.0000   1st Qu.:  1.000   epsg:29101   :   0  
##  Median : 0.0000   Median :  1.000   +proj=poly...:   0  
##  Mean   : 0.0377   Mean   :  2.037                       
##  3rd Qu.: 0.0000   3rd Qu.:  2.000                       
##  Max.   :26.0000   Max.   :225.000                       
## 

From the summary report above, we can see that the are a few columns which is not in the form of numerical data type and it is in the categorical data type. In order to make the information useful need to change it. Therefore, now we need to extract the particular column which we going to tranform. In this case, will be the RURAL_URBAN.

RURAL_URBAN <- dplyr::select(final_br.point,"RURAL_URBAN")

Now we going to transfrom it into dummy avariable by using a need function call dummy_cols from the package called fastDummies. After, apply the function we change to binary type of data and there are total 6 neew columns been created.

RURAL_URBAN <- fastDummies::dummy_cols(RURAL_URBAN)
RURAL_URBAN
##                  RURAL_URBAN RURAL_URBAN_ RURAL_URBAN_Intermediário Adjacente
## 1    Intermediário Adjacente            0                                   1
## 2                     Urbano            0                                   0
## 3            Rural Adjacente            0                                   0
## 4                     Urbano            0                                   0
## 5                     Urbano            0                                   0
## 6    Intermediário Adjacente            0                                   1
## 7               Rural Remoto            0                                   0
## 8               Rural Remoto            0                                   0
## 9    Intermediário Adjacente            0                                   1
## 10                    Urbano            0                                   0
## 11                    Urbano            0                                   0
## 12                    Urbano            0                                   0
## 13              Rural Remoto            0                                   0
## 14           Rural Adjacente            0                                   0
## 15                    Urbano            0                                   0
## 16                    Urbano            0                                   0
## 17                    Urbano            0                                   0
## 18   Intermediário Adjacente            0                                   1
## 19           Rural Adjacente            0                                   0
## 20                    Urbano            0                                   0
## 21           Rural Adjacente            0                                   0
## 22                    Urbano            0                                   0
## 23              Rural Remoto            0                                   0
## 24              Rural Remoto            0                                   0
## 25           Rural Adjacente            0                                   0
## 26           Rural Adjacente            0                                   0
## 27           Rural Adjacente            0                                   0
## 28      Intermediário Remoto            0                                   0
## 29           Rural Adjacente            0                                   0
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## 5570                        0                             0                  1

By using the select function, we can only extract those columns we going to use.

RURAL_URBAN <- dplyr ::  select(RURAL_URBAN,3:8)

Now we going to join the newly created columns with our original data set by using cbind() function.

final_br.point <- cbind(final_br.point,RURAL_URBAN)

Using the names function to change the name of each column variables.

names(final_br.point)[names(final_br.point) == 'RURAL_URBAN_Intermediário Adjacente'] <- 'Intermediario_Adjacente' 
names(final_br.point)[names(final_br.point) == 'RURAL_URBAN_Intermediário Remoto'] <- 'Intermediario_Remoto' 
names(final_br.point)[names(final_br.point) == 'RURAL_URBAN_Rural Adjacente'] <- 'Rural_Adjacente' 
names(final_br.point)[names(final_br.point) == 'RURAL_URBAN_Rural Remoto'] <- 'Rural_Remoto'
names(final_br.point)[names(final_br.point) == 'RURAL_URBAN_Sem classificação'] <- 'Sem_classificacao' 
names(final_br.point)[names(final_br.point) == 'RURAL_URBAN_Urbano'] <- 'Urbano'

Since, we already converted the RURAL_URBAN values into dummy variable. Therefore, we can remove the RURAL_URBAN from our data set by using subset(dataset.name, select = -c(x)). In order to remove the variable we need to add a minus sign in front of the “c”.

final_br.point <- subset(final_br.point, select = -c(RURAL_URBAN))

After done with the transforming, we can use the summary function to have a look of our data set final_br.point.

summary(final_br.point)
##    code_muni        name_muni           code_state   abbrev_state      
##  Min.   :1100015   Length:5570        31     : 853   Length:5570       
##  1st Qu.:2512126   Class :character   35     : 645   Class :character  
##  Median :3146280   Mode  :character   43     : 497   Mode  :character  
##  Mean   :3253591                      29     : 417                     
##  3rd Qu.:4119190                      41     : 399                     
##  Max.   :5300108                      42     : 295                     
##                                       (Other):2464                     
##     CAPITAL          IBGE_RES_POP      IBGE_RES_POP_BRAS  IBGE_RES_POP_ESTR  
##  Min.   :0.000000   Min.   :       0   Min.   :       0   Min.   :     0.00  
##  1st Qu.:0.000000   1st Qu.:    5224   1st Qu.:    5217   1st Qu.:     0.00  
##  Median :0.000000   Median :   10932   Median :   10920   Median :     0.00  
##  Mean   :0.004847   Mean   :   34247   Mean   :   34170   Mean   :    77.44  
##  3rd Qu.:0.000000   3rd Qu.:   23409   3rd Qu.:   23380   3rd Qu.:    10.00  
##  Max.   :1.000000   Max.   :11253503   Max.   :11133776   Max.   :119727.00  
##                                                                              
##     IBGE_DU        IBGE_DU_URBAN     IBGE_DU_RURAL      IBGE_POP       
##  Min.   :      0   Min.   :      0   Min.   :    0   Min.   :       0  
##  1st Qu.:   1567   1st Qu.:    871   1st Qu.:  471   1st Qu.:    2790  
##  Median :   3170   Median :   1840   Median :  917   Median :    6158  
##  Mean   :  10290   Mean   :   8848   Mean   : 1442   Mean   :   27570  
##  3rd Qu.:   6722   3rd Qu.:   4619   3rd Qu.: 1813   3rd Qu.:   15299  
##  Max.   :3576148   Max.   :3548433   Max.   :33809   Max.   :10463636  
##                                                                        
##      IBGE_1            IBGE_1.4           IBGE_5.9          IBGE_10.14      
##  Min.   :     0.0   Min.   :     0.0   Min.   :     0.0   Min.   :     0.0  
##  1st Qu.:    38.0   1st Qu.:   158.0   1st Qu.:   219.2   1st Qu.:   258.2  
##  Median :    92.0   Median :   376.0   Median :   514.5   Median :   587.0  
##  Mean   :   382.9   Mean   :  1543.1   Mean   :  2067.5   Mean   :  2379.3  
##  3rd Qu.:   232.0   3rd Qu.:   949.8   3rd Qu.:  1299.0   3rd Qu.:  1477.5  
##  Max.   :129464.0   Max.   :514794.0   Max.   :684443.0   Max.   :783702.0  
##                                                                             
##    IBGE_15.59         IBGE_60.       IBGE_PLANTED_AREA   IBGE_CROP_PRODUCTION_.
##  Min.   :      0   Min.   :      0   Min.   :      0.0   Min.   :      0       
##  1st Qu.:   1730   1st Qu.:    340   1st Qu.:    910.2   1st Qu.:   2326       
##  Median :   3837   Median :    721   Median :   3471.5   Median :  13846       
##  Mean   :  18196   Mean   :   3002   Mean   :  14179.9   Mean   :  57384       
##  3rd Qu.:   9591   3rd Qu.:   1723   3rd Qu.:  11194.2   3rd Qu.:  55619       
##  Max.   :7058221   Max.   :1293012   Max.   :1205669.0   Max.   :3274885       
##                                                                                
##  IDHM.Ranking.2010      IDHM          IDHM_Renda     IDHM_Longevidade
##  Min.   :   0      Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:1387      1st Qu.:0.5990   1st Qu.:0.5720   1st Qu.:0.7690  
##  Median :2780      Median :0.6650   Median :0.6540   Median :0.8080  
##  Mean   :2780      Mean   :0.6585   Mean   :0.6422   Mean   :0.8007  
##  3rd Qu.:4172      3rd Qu.:0.7180   3rd Qu.:0.7070   3rd Qu.:0.8360  
##  Max.   :5565      Max.   :0.8620   Max.   :0.8910   Max.   :0.8940  
##                                                                      
##  IDHM_Educacao         ALT               PAY_TV         FIXED_PHONES    
##  Min.   :0.0000   Min.   :     0.0   Min.   :      0   Min.   :      0  
##  1st Qu.:0.4900   1st Qu.:   168.9   1st Qu.:     88   1st Qu.:    118  
##  Median :0.5600   Median :   406.3   Median :    247   Median :    327  
##  Mean   :0.5585   Mean   :   892.8   Mean   :   3094   Mean   :   6567  
##  3rd Qu.:0.6310   3rd Qu.:   628.7   3rd Qu.:    815   3rd Qu.:   1151  
##  Max.   :0.8250   Max.   :874579.0   Max.   :2047668   Max.   :5543127  
##                                                                         
##       AREA                         REGIAO_TUR   CATEGORIA_TUR
##  Min.   :     0.0                       :2286    :2286       
##  1st Qu.:   204.3   Corredores Das Águas:  59   A:  51       
##  Median :   415.9   Vale Do Contestado  :  45   B: 168       
##  Mean   :  1515.6   Amazônia Atlântica  :  40   C: 521       
##  3rd Qu.:  1026.2   Araguaia-Tocantins  :  39   D:1891       
##  Max.   :159533.3   Cariri              :  37   E: 653       
##                     (Other)             :3064                
##  ESTIMATED_POP       GVA_AGROPEC       GVA_INDUSTRY       GVA_SERVICES      
##  Min.   :       0   Min.   :      0   Min.   :       1   Min.   :        2  
##  1st Qu.:    5451   1st Qu.:   4189   1st Qu.:    1726   1st Qu.:    10112  
##  Median :   11590   Median :  20426   Median :    7424   Median :    31211  
##  Mean   :   37430   Mean   :  47271   Mean   :  175928   Mean   :   489451  
##  3rd Qu.:   25296   3rd Qu.:  51227   3rd Qu.:   41022   3rd Qu.:   115406  
##  Max.   :12176866   Max.   :1402282   Max.   :63306755   Max.   :464656988  
##                                                                             
##    GVA_PUBLIC         GVA_TOTAL             TAXES                GDP           
##  Min.   :       7   Min.   :       17   Min.   :   -14159   Min.   :       15  
##  1st Qu.:   17267   1st Qu.:    42253   1st Qu.:     1305   1st Qu.:    43709  
##  Median :   35866   Median :   119492   Median :     5100   Median :   125153  
##  Mean   :  123768   Mean   :   832987   Mean   :   118864   Mean   :   954584  
##  3rd Qu.:   89245   3rd Qu.:   313963   3rd Qu.:    22197   3rd Qu.:   329539  
##  Max.   :41902893   Max.   :569910503   Max.   :117125387   Max.   :687035890  
##                                                                                
##     POP_GDP           GDP_CAPITA    
##  Min.   :     815   Min.   :  3191  
##  1st Qu.:    5483   1st Qu.:  9058  
##  Median :   11578   Median : 15870  
##  Mean   :   36998   Mean   : 21126  
##  3rd Qu.:   25085   3rd Qu.: 26155  
##  Max.   :12038175   Max.   :314638  
##                                     
##                                                                                  GVA_MAIN   
##  Administração, defesa, educação e saúde públicas e seguridade social                :2725  
##  Demais serviços                                                                     :1477  
##  Agricultura, inclusive apoio à agricultura e a pós colheita                         : 735  
##  Indústrias de transformação                                                         : 261  
##  Pecuária, inclusive apoio à pecuária                                                : 161  
##  Eletricidade e gás, água, esgoto, atividades de gestão de resíduos e descontaminação:  98  
##  (Other)                                                                             : 113  
##   MUN_EXPENDIT          COMP_TOT            COMP_A            COMP_B       
##  Min.   :0.000e+00   Min.   :     6.0   Min.   :   0.00   Min.   :  0.000  
##  1st Qu.:0.000e+00   1st Qu.:    68.0   1st Qu.:   1.00   1st Qu.:  0.000  
##  Median :1.774e+07   Median :   162.0   Median :   2.00   Median :  0.000  
##  Mean   :7.641e+07   Mean   :   906.8   Mean   :  18.25   Mean   :  1.852  
##  3rd Qu.:4.150e+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  
##                                                                            
##      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  
##                                                                            
##      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  
##                                                                          
##      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  
##                                                                            
##      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  
##                                                                           
##      COMP_S             COMP_T      COMP_U              HOTELS       
##  Min.   :    0.00   Min.   :0   Min.   :  0.00000   Min.   : 0.0000  
##  1st Qu.:    5.00   1st Qu.:0   1st Qu.:  0.00000   1st Qu.: 0.0000  
##  Median :   12.00   Median :0   Median :  0.00000   Median : 0.0000  
##  Mean   :   51.61   Mean   :0   Mean   :  0.05027   Mean   : 0.4986  
##  3rd Qu.:   31.00   3rd Qu.:0   3rd Qu.:  0.00000   3rd Qu.: 0.0000  
##  Max.   :24832.00   Max.   :0   Max.   :123.00000   Max.   :97.0000  
##                                                                      
##       BEDS        Pr_Agencies       Pu_Agencies         Pr_Bank       
##  Min.   :    0   Min.   :   0.00   Min.   :  0.000   Min.   : 0.0000  
##  1st Qu.:    0   1st Qu.:   0.00   1st Qu.:  0.000   1st Qu.: 0.0000  
##  Median :    0   Median :   0.00   Median :  1.000   Median : 0.0000  
##  Mean   :   41   Mean   :   2.03   Mean   :  1.698   Mean   : 0.7873  
##  3rd Qu.:    0   3rd Qu.:   1.00   3rd Qu.:  2.000   3rd Qu.: 1.0000  
##  Max.   :13247   Max.   :1693.00   Max.   :626.000   Max.   :83.0000  
##                                                                       
##     Pu_Bank         Pr_Assets           Pu_Assets              Cars        
##  Min.   :0.0000   Min.   :0.000e+00   Min.   :0.000e+00   Min.   :      0  
##  1st Qu.:0.0000   1st Qu.:0.000e+00   1st Qu.:0.000e+00   1st Qu.:    599  
##  Median :1.0000   Median :0.000e+00   Median :2.323e+07   Median :   1433  
##  Mean   :0.9479   Mean   :5.512e+09   Mean   :3.603e+09   Mean   :   9845  
##  3rd Qu.:2.0000   3rd Qu.:4.775e+07   3rd Qu.:1.994e+08   3rd Qu.:   4084  
##  Max.   :8.0000   Max.   :1.950e+13   Max.   :8.020e+12   Max.   :5740995  
##                                                                            
##   Motorcycles        Wheeled_tractor         UBER              MAC          
##  Min.   :      0.0   Min.   :   0.000   Min.   :0.00000   Min.   :  0.0000  
##  1st Qu.:    589.2   1st Qu.:   0.000   1st Qu.:0.00000   1st Qu.:  0.0000  
##  Median :   1282.5   Median :   0.000   Median :0.00000   Median :  0.0000  
##  Mean   :   4871.5   Mean   :   5.745   Mean   :0.02244   Mean   :  0.1275  
##  3rd Qu.:   3292.8   3rd Qu.:   1.000   3rd Qu.:0.00000   3rd Qu.:  0.0000  
##  Max.   :1134570.0   Max.   :3236.000   Max.   :1.00000   Max.   :130.0000  
##                                                                             
##     WAL.MART        POST_OFFICES              geometry   
##  Min.   : 0.0000   Min.   :  0.000   POINT        :5570  
##  1st Qu.: 0.0000   1st Qu.:  1.000   epsg:29101   :   0  
##  Median : 0.0000   Median :  1.000   +proj=poly...:   0  
##  Mean   : 0.0377   Mean   :  2.037                       
##  3rd Qu.: 0.0000   3rd Qu.:  2.000                       
##  Max.   :26.0000   Max.   :225.000                       
##                                                          
##  Intermediario_Adjacente Intermediario_Remoto Rural_Adjacente 
##  Min.   :0.0000          Min.   :0.00000      Min.   :0.0000  
##  1st Qu.:0.0000          1st Qu.:0.00000      1st Qu.:0.0000  
##  Median :0.0000          Median :0.00000      Median :1.0000  
##  Mean   :0.1232          Mean   :0.01077      Mean   :0.5458  
##  3rd Qu.:0.0000          3rd Qu.:0.00000      3rd Qu.:1.0000  
##  Max.   :1.0000          Max.   :1.00000      Max.   :1.0000  
##                                                               
##   Rural_Remoto     Sem_classificacao       Urbano      
##  Min.   :0.00000   Min.   :0.0000000   Min.   :0.0000  
##  1st Qu.:0.00000   1st Qu.:0.0000000   1st Qu.:0.0000  
##  Median :0.00000   Median :0.0000000   Median :0.0000  
##  Mean   :0.05799   Mean   :0.0008977   Mean   :0.2614  
##  3rd Qu.:0.00000   3rd Qu.:0.0000000   3rd Qu.:1.0000  
##  Max.   :1.00000   Max.   :1.0000000   Max.   :1.0000  
## 

5.2 Derive new variables using dplyr

In this case, we know we going to use GDP_CAPITA as our dependent variable. During the information selection stage, we filter out that we going to use IBGE_15.59 as one of our independent varibles. Therefore, we would like to get the percentage of the IBGE_15.59 out of IBGE_RES_POP in order to get an more accurate data, with the calculation we name it as Economy_gp.

final_br.point <- final_br.point %>%
  mutate(Economy_gp = `IBGE_15.59`/`IBGE_RES_POP`)

As we can see there are NA values in Economy_gp’s colums, however this NA is slighly different as when we open up the data set it shows NAn. The Nan is due the calculation. Therefore, we need to use is.nan() function to change to 0.

final_br.point$Economy_gp[is.nan(final_br.point$Economy_gp)] <- 0

5.3 Correlation Analysis

Multiple Linear Regression Method when come to corrplot() function, we would like to group those columns we going use together. Therefore, we can use colnames() function to view the position of each variable name.

final_br.point.1 <- final_br.point
colnames(final_br.point.1)
##  [1] "code_muni"               "name_muni"              
##  [3] "code_state"              "abbrev_state"           
##  [5] "CAPITAL"                 "IBGE_RES_POP"           
##  [7] "IBGE_RES_POP_BRAS"       "IBGE_RES_POP_ESTR"      
##  [9] "IBGE_DU"                 "IBGE_DU_URBAN"          
## [11] "IBGE_DU_RURAL"           "IBGE_POP"               
## [13] "IBGE_1"                  "IBGE_1.4"               
## [15] "IBGE_5.9"                "IBGE_10.14"             
## [17] "IBGE_15.59"              "IBGE_60."               
## [19] "IBGE_PLANTED_AREA"       "IBGE_CROP_PRODUCTION_." 
## [21] "IDHM.Ranking.2010"       "IDHM"                   
## [23] "IDHM_Renda"              "IDHM_Longevidade"       
## [25] "IDHM_Educacao"           "ALT"                    
## [27] "PAY_TV"                  "FIXED_PHONES"           
## [29] "AREA"                    "REGIAO_TUR"             
## [31] "CATEGORIA_TUR"           "ESTIMATED_POP"          
## [33] "GVA_AGROPEC"             "GVA_INDUSTRY"           
## [35] "GVA_SERVICES"            "GVA_PUBLIC"             
## [37] "GVA_TOTAL"               "TAXES"                  
## [39] "GDP"                     "POP_GDP"                
## [41] "GDP_CAPITA"              "GVA_MAIN"               
## [43] "MUN_EXPENDIT"            "COMP_TOT"               
## [45] "COMP_A"                  "COMP_B"                 
## [47] "COMP_C"                  "COMP_D"                 
## [49] "COMP_E"                  "COMP_F"                 
## [51] "COMP_G"                  "COMP_H"                 
## [53] "COMP_I"                  "COMP_J"                 
## [55] "COMP_K"                  "COMP_L"                 
## [57] "COMP_M"                  "COMP_N"                 
## [59] "COMP_O"                  "COMP_P"                 
## [61] "COMP_Q"                  "COMP_R"                 
## [63] "COMP_S"                  "COMP_T"                 
## [65] "COMP_U"                  "HOTELS"                 
## [67] "BEDS"                    "Pr_Agencies"            
## [69] "Pu_Agencies"             "Pr_Bank"                
## [71] "Pu_Bank"                 "Pr_Assets"              
## [73] "Pu_Assets"               "Cars"                   
## [75] "Motorcycles"             "Wheeled_tractor"        
## [77] "UBER"                    "MAC"                    
## [79] "WAL.MART"                "POST_OFFICES"           
## [81] "geometry"                "Intermediario_Adjacente"
## [83] "Intermediario_Remoto"    "Rural_Adjacente"        
## [85] "Rural_Remoto"            "Sem_classificacao"      
## [87] "Urbano"                  "Economy_gp"

Now we can give the position number of each variable in the sequence that we would like to appear as.

final_br.point.1 <- final_br.point.1[, c(1:9,12:18,26,29:32,37,39,40,42,44,64,66:71,76:80,81,83,88,87,10,11,20:25,27,28,33:36,38,43,45:63,65,72:75,82,84:86,19,41)]
colnames(final_br.point.1)
##  [1] "code_muni"               "name_muni"              
##  [3] "code_state"              "abbrev_state"           
##  [5] "CAPITAL"                 "IBGE_RES_POP"           
##  [7] "IBGE_RES_POP_BRAS"       "IBGE_RES_POP_ESTR"      
##  [9] "IBGE_DU"                 "IBGE_POP"               
## [11] "IBGE_1"                  "IBGE_1.4"               
## [13] "IBGE_5.9"                "IBGE_10.14"             
## [15] "IBGE_15.59"              "IBGE_60."               
## [17] "ALT"                     "AREA"                   
## [19] "REGIAO_TUR"              "CATEGORIA_TUR"          
## [21] "ESTIMATED_POP"           "GVA_TOTAL"              
## [23] "GDP"                     "POP_GDP"                
## [25] "GVA_MAIN"                "COMP_TOT"               
## [27] "COMP_T"                  "HOTELS"                 
## [29] "BEDS"                    "Pr_Agencies"            
## [31] "Pu_Agencies"             "Pr_Bank"                
## [33] "Pu_Bank"                 "Wheeled_tractor"        
## [35] "UBER"                    "MAC"                    
## [37] "WAL.MART"                "POST_OFFICES"           
## [39] "geometry"                "Intermediario_Remoto"   
## [41] "Economy_gp"              "Urbano"                 
## [43] "IBGE_DU_URBAN"           "IBGE_DU_RURAL"          
## [45] "IBGE_CROP_PRODUCTION_."  "IDHM.Ranking.2010"      
## [47] "IDHM"                    "IDHM_Renda"             
## [49] "IDHM_Longevidade"        "IDHM_Educacao"          
## [51] "PAY_TV"                  "FIXED_PHONES"           
## [53] "GVA_AGROPEC"             "GVA_INDUSTRY"           
## [55] "GVA_SERVICES"            "GVA_PUBLIC"             
## [57] "TAXES"                   "MUN_EXPENDIT"           
## [59] "COMP_A"                  "COMP_B"                 
## [61] "COMP_C"                  "COMP_D"                 
## [63] "COMP_E"                  "COMP_F"                 
## [65] "COMP_G"                  "COMP_H"                 
## [67] "COMP_I"                  "COMP_J"                 
## [69] "COMP_K"                  "COMP_L"                 
## [71] "COMP_M"                  "COMP_N"                 
## [73] "COMP_O"                  "COMP_P"                 
## [75] "COMP_Q"                  "COMP_R"                 
## [77] "COMP_S"                  "COMP_U"                 
## [79] "Pr_Assets"               "Pu_Assets"              
## [81] "Cars"                    "Motorcycles"            
## [83] "Intermediario_Adjacente" "Rural_Adjacente"        
## [85] "Rural_Remoto"            "Sem_classificacao"      
## [87] "IBGE_PLANTED_AREA"       "GDP_CAPITA"

Before we perform MLR, it is important for us to ensure that the input variables use are not highly correlated. To visualise and analyse the correlation of the input variables. Before, we need to check the class of the final_br.point1 to make sure it is in data.frame format.

class(final_br.point.1)
## [1] "data.frame"

As we know there are around 50 independent variable in our list and when we try plotting the corrplot it definately will overlap with over another and the same of the output is very small. Therefore, if we do not adjust the size of the corrplot there is not way for us to identify the highly correlated variable. In order to solve this problem, we can adjust the size of the output by adding code to {r}.

{r fig1, fig.height=9, fig.width=10}

corrplot(cor(final_br.point.1[, 40:87]), diag = FALSE, order = "FPC",
         tl.pos = "td", tl.cex = 0.5, method = "number", type = "upper",number.cex = .45)

After first round of elimination, we would to use corrplot again to show the second of correlation testing.

final_br.point.2 <- final_br.point
colnames(final_br.point.2)
##  [1] "code_muni"               "name_muni"              
##  [3] "code_state"              "abbrev_state"           
##  [5] "CAPITAL"                 "IBGE_RES_POP"           
##  [7] "IBGE_RES_POP_BRAS"       "IBGE_RES_POP_ESTR"      
##  [9] "IBGE_DU"                 "IBGE_DU_URBAN"          
## [11] "IBGE_DU_RURAL"           "IBGE_POP"               
## [13] "IBGE_1"                  "IBGE_1.4"               
## [15] "IBGE_5.9"                "IBGE_10.14"             
## [17] "IBGE_15.59"              "IBGE_60."               
## [19] "IBGE_PLANTED_AREA"       "IBGE_CROP_PRODUCTION_." 
## [21] "IDHM.Ranking.2010"       "IDHM"                   
## [23] "IDHM_Renda"              "IDHM_Longevidade"       
## [25] "IDHM_Educacao"           "ALT"                    
## [27] "PAY_TV"                  "FIXED_PHONES"           
## [29] "AREA"                    "REGIAO_TUR"             
## [31] "CATEGORIA_TUR"           "ESTIMATED_POP"          
## [33] "GVA_AGROPEC"             "GVA_INDUSTRY"           
## [35] "GVA_SERVICES"            "GVA_PUBLIC"             
## [37] "GVA_TOTAL"               "TAXES"                  
## [39] "GDP"                     "POP_GDP"                
## [41] "GDP_CAPITA"              "GVA_MAIN"               
## [43] "MUN_EXPENDIT"            "COMP_TOT"               
## [45] "COMP_A"                  "COMP_B"                 
## [47] "COMP_C"                  "COMP_D"                 
## [49] "COMP_E"                  "COMP_F"                 
## [51] "COMP_G"                  "COMP_H"                 
## [53] "COMP_I"                  "COMP_J"                 
## [55] "COMP_K"                  "COMP_L"                 
## [57] "COMP_M"                  "COMP_N"                 
## [59] "COMP_O"                  "COMP_P"                 
## [61] "COMP_Q"                  "COMP_R"                 
## [63] "COMP_S"                  "COMP_T"                 
## [65] "COMP_U"                  "HOTELS"                 
## [67] "BEDS"                    "Pr_Agencies"            
## [69] "Pu_Agencies"             "Pr_Bank"                
## [71] "Pu_Bank"                 "Pr_Assets"              
## [73] "Pu_Assets"               "Cars"                   
## [75] "Motorcycles"             "Wheeled_tractor"        
## [77] "UBER"                    "MAC"                    
## [79] "WAL.MART"                "POST_OFFICES"           
## [81] "geometry"                "Intermediario_Adjacente"
## [83] "Intermediario_Remoto"    "Rural_Adjacente"        
## [85] "Rural_Remoto"            "Sem_classificacao"      
## [87] "Urbano"                  "Economy_gp"

We re-adjusting the position to the second testing output.

final_br.point.2 <- final_br.point.2[, c(1:10,12:18,21,22,23,26,27,28,30,31,19,87,80,68:71,43,72,32,73,34,35,36,37,39,38,40,42,86,44,46,47,48,49,50,51,52,53,54,55,56,57,58,61,62,63,66,67,81,74:79,60,64,88,11,20,24,25,45,59,65,82:85,33,29,41)]
colnames(final_br.point.2)
##  [1] "code_muni"               "name_muni"              
##  [3] "code_state"              "abbrev_state"           
##  [5] "CAPITAL"                 "IBGE_RES_POP"           
##  [7] "IBGE_RES_POP_BRAS"       "IBGE_RES_POP_ESTR"      
##  [9] "IBGE_DU"                 "IBGE_DU_URBAN"          
## [11] "IBGE_POP"                "IBGE_1"                 
## [13] "IBGE_1.4"                "IBGE_5.9"               
## [15] "IBGE_10.14"              "IBGE_15.59"             
## [17] "IBGE_60."                "IDHM.Ranking.2010"      
## [19] "IDHM"                    "IDHM_Renda"             
## [21] "ALT"                     "PAY_TV"                 
## [23] "FIXED_PHONES"            "REGIAO_TUR"             
## [25] "CATEGORIA_TUR"           "IBGE_PLANTED_AREA"      
## [27] "Urbano"                  "POST_OFFICES"           
## [29] "Pr_Agencies"             "Pu_Agencies"            
## [31] "Pr_Bank"                 "Pu_Bank"                
## [33] "MUN_EXPENDIT"            "Pr_Assets"              
## [35] "ESTIMATED_POP"           "Pu_Assets"              
## [37] "GVA_INDUSTRY"            "GVA_SERVICES"           
## [39] "GVA_PUBLIC"              "GVA_TOTAL"              
## [41] "GDP"                     "TAXES"                  
## [43] "POP_GDP"                 "GVA_MAIN"               
## [45] "Sem_classificacao"       "COMP_TOT"               
## [47] "COMP_B"                  "COMP_C"                 
## [49] "COMP_D"                  "COMP_E"                 
## [51] "COMP_F"                  "COMP_G"                 
## [53] "COMP_H"                  "COMP_I"                 
## [55] "COMP_J"                  "COMP_K"                 
## [57] "COMP_L"                  "COMP_M"                 
## [59] "COMP_N"                  "COMP_Q"                 
## [61] "COMP_R"                  "COMP_S"                 
## [63] "HOTELS"                  "BEDS"                   
## [65] "geometry"                "Cars"                   
## [67] "Motorcycles"             "Wheeled_tractor"        
## [69] "UBER"                    "MAC"                    
## [71] "WAL.MART"                "COMP_P"                 
## [73] "COMP_T"                  "Economy_gp"             
## [75] "IBGE_DU_RURAL"           "IBGE_CROP_PRODUCTION_." 
## [77] "IDHM_Longevidade"        "IDHM_Educacao"          
## [79] "COMP_A"                  "COMP_O"                 
## [81] "COMP_U"                  "Intermediario_Adjacente"
## [83] "Intermediario_Remoto"    "Rural_Adjacente"        
## [85] "Rural_Remoto"            "GVA_AGROPEC"            
## [87] "AREA"                    "GDP_CAPITA"

With the latest set of independent variables, we managed to figure out those without high correlation.

corrplot(cor(final_br.point.2[, 74:87]), diag = FALSE, order = "FPC",
         tl.pos = "td", tl.cex = 0.5, method = "number", type = "upper",number.cex = .6)

Now we going to convert the final_br.sf to Simple feature format by using st_as_sf.

final_br.sf <-  st_as_sf(final_br.point.2)

6 Multiple Linear Regression

6.1 Building a hedonic pricing model using multiple linear regression method

Building a hedonic pricing model using multiple linear regression method

gdp.mlr <- lm(formula = GDP_CAPITA ~Economy_gp + IBGE_DU_RURAL + `IBGE_CROP_PRODUCTION_.` + IDHM_Longevidade + IDHM_Educacao + COMP_A + COMP_O + COMP_U + Intermediario_Adjacente + Intermediario_Remoto + Rural_Adjacente + Rural_Remoto + Sem_classificacao + GVA_AGROPEC + AREA, data=final_br.sf)
summary(gdp.mlr)
## 
## Call:
## lm(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL + IBGE_CROP_PRODUCTION_. + 
##     IDHM_Longevidade + IDHM_Educacao + COMP_A + COMP_O + COMP_U + 
##     Intermediario_Adjacente + Intermediario_Remoto + Rural_Adjacente + 
##     Rural_Remoto + Sem_classificacao + GVA_AGROPEC + AREA, data = final_br.sf)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -63197  -7165  -2821   2316 278811 
## 
## Coefficients:
##                           Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             -7.443e+04  4.933e+03 -15.089  < 2e-16 ***
## Economy_gp              -6.215e+03  2.571e+03  -2.417  0.01569 *  
## IBGE_DU_RURAL           -1.208e+00  1.613e-01  -7.490 7.96e-14 ***
## IBGE_CROP_PRODUCTION_.   1.529e-02  2.354e-03   6.496 8.97e-11 ***
## IDHM_Longevidade         8.227e+04  7.213e+03  11.406  < 2e-16 ***
## IDHM_Educacao            5.783e+04  4.134e+03  13.989  < 2e-16 ***
## COMP_A                  -2.420e+00  2.977e+00  -0.813  0.41635    
## COMP_O                   4.052e+01  5.149e+01   0.787  0.43132    
## COMP_U                   3.044e+02  1.598e+02   1.905  0.05684 .  
## Intermediario_Adjacente -2.394e+03  8.347e+02  -2.868  0.00415 ** 
## Intermediario_Remoto     2.272e+03  2.419e+03   0.939  0.34761    
## Rural_Adjacente         -1.610e+03  7.764e+02  -2.073  0.03820 *  
## Rural_Remoto             9.232e+01  1.248e+03   0.074  0.94103    
## Sem_classificacao        1.000e+05  9.175e+03  10.904  < 2e-16 ***
## GVA_AGROPEC              3.661e-02  4.076e-03   8.982  < 2e-16 ***
## AREA                    -3.854e-02  4.646e-02  -0.830  0.40682    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17260 on 5554 degrees of freedom
## Multiple R-squared:  0.2817, Adjusted R-squared:  0.2798 
## F-statistic: 145.2 on 15 and 5554 DF,  p-value: < 2.2e-16

With reference to the report above, it is clear that not all the indepent variables are statistically significant. We will revised the model by removing those variables which are not statistically significant.

Now we going to construct another lm model based on the singnificant independent avariable provided in the above code chunk.

gdp.mlr1 <- lm(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL + `IBGE_CROP_PRODUCTION_.` + IDHM_Longevidade + IDHM_Educacao +Intermediario_Adjacente  + Rural_Adjacente  + Sem_classificacao + GVA_AGROPEC, data=final_br.sf)
ols_regress(gdp.mlr1)
##                             Model Summary                             
## ---------------------------------------------------------------------
## R                       0.529       RMSE                   17264.012 
## R-Squared               0.280       Coef. Var                 81.719 
## Adj. R-Squared          0.279       MSE                298046100.669 
## Pred R-Squared          0.275       MAE                     8430.665 
## ---------------------------------------------------------------------
##  RMSE: Root Mean Square Error 
##  MSE: Mean Square Error 
##  MAE: Mean Absolute Error 
## 
##                                        ANOVA                                        
## -----------------------------------------------------------------------------------
##                         Sum of                                                     
##                        Squares          DF        Mean Square       F         Sig. 
## -----------------------------------------------------------------------------------
## Regression    645181165672.854           9    71686796185.873    240.523    0.0000 
## Residual          1.657136e+12        5560      298046100.669                      
## Total             2.302317e+12        5569                                         
## -----------------------------------------------------------------------------------
## 
##                                                Parameter Estimates                                                
## -----------------------------------------------------------------------------------------------------------------
##                   model          Beta    Std. Error    Std. Beta       t        Sig          lower         upper 
## -----------------------------------------------------------------------------------------------------------------
##             (Intercept)    -74951.259      4791.660                 -15.642    0.000    -84344.785    -65557.733 
##              Economy_gp     -5747.810      2396.876       -0.041     -2.398    0.017    -10446.623     -1048.997 
##           IBGE_DU_RURAL        -1.102         0.151       -0.092     -7.317    0.000        -1.398        -0.807 
##  IBGE_CROP_PRODUCTION_.         0.015         0.002        0.109      6.410    0.000         0.010         0.020 
##        IDHM_Longevidade     82233.019      7202.425        0.210     11.417    0.000     68113.451     96352.586 
##           IDHM_Educacao     58301.049      4005.114        0.273     14.557    0.000     50449.461     66152.637 
## Intermediario_Adjacente     -2456.778       779.241       -0.040     -3.153    0.002     -3984.396      -929.161 
##         Rural_Adjacente     -1542.778       631.002       -0.038     -2.445    0.015     -2779.790      -305.767 
##       Sem_classificacao    100554.804      9102.512        0.148     11.047    0.000     82710.324    118399.284 
##             GVA_AGROPEC         0.037         0.004        0.160      9.124    0.000         0.029         0.045 
## -----------------------------------------------------------------------------------------------------------------

In this case it provides a R-Squared of 0.28, however, we should not look at the R-Squared as we know that by adding more independent variables to the MLR, the R-Squared will automatically increase. Therefore, in this case we should look at the Adj R-Squared, as it will not increase when there is a not significant independent variable added to the MLR. By having 0.283 of adj R-Square, it means that this MLR only can explain 27.9% of GDP per CAPITA.

  1. When there is a 1% percent increase in Enconomy group, there will be 6635.918 reais decrease in GDP per CAPTIA.

  2. When there is a 1 unit of increase in Domestic Units Urban, there will be 1.292 reais decrease in GDP per CAPITA.

  3. When there is a $1,000 reais increase in Crop Production, there will be 0.015 reais decrease in GDP per CAPITA.

  4. When there is a 1 unit of increase in HDI Life Expectancy index, there will be 82233.019 reais increase in GDP per CAPITA.

  5. When there is a 1 unit of increase in HDI Education index, there will be 57072.281 reais increase in GDP per CAPITA.

  6. When the municipality is class under Intermediario Adjacente, there will be 2456.778 reais decrease in GDP per CAPITA.

  7. When the municipality is class under Rural Adjacente, there will be 1542.778 reais decrease in GDP per CAPITA.

  8. When the municipality is class under Sem classificacao, there will be 100554.804 reais increase in GDP per CAPITA.

  9. When there is a $1,000 reais increase in Agropecuary, there will be 0.037 reais increase in GDP per CAPITA.

6.2 Checking for multicolinearity

Now we will be using ols_vif_tol to test if there are sign of multicollinearity.

ols_vif_tol(gdp.mlr1)
##                 Variables Tolerance      VIF
## 1              Economy_gp 0.4357954 2.294655
## 2           IBGE_DU_RURAL 0.8245643 1.212762
## 3  IBGE_CROP_PRODUCTION_. 0.4444613 2.249915
## 4        IDHM_Longevidade 0.3840886 2.603566
## 5           IDHM_Educacao 0.3691966 2.708584
## 6 Intermediario_Adjacente 0.8160087 1.225477
## 7         Rural_Adjacente 0.5421040 1.844665
## 8       Sem_classificacao 0.7200803 1.388734
## 9             GVA_AGROPEC 0.4197194 2.382544

Since all the VIF are below 8, therefore we cna safely conclude that there is not mulitcollinearity between the independent varibles.

6.3 Test for Non-Linearity

In multiple linear regression, it is important for us to test the assumption that linearity and additivity of the relationship between dependent and independent variables.
Now we will using ols_plot_resid_fit to test for non-linearity.

ols_plot_resid_fit(gdp.mlr1)

The figure above reveals that most of the data poitns are scattered around the 0 line, hence we can safely conclude that the relationships between the dependent variable and independent variables are linear.

6.4 Test for Normality Assumption

Using ols_plot_resid_hist() function to test for normality assumption test.

ols_plot_resid_hist(gdp.mlr1)

The figure reveals that the residual of the multiple linear regression model (i.e. condo.mlr1) is resemble normal distribution.

6.5 Testing for Spatial Autocorrelation

Now we going to extract out the column of residuals from gdp.mlr1, convert it into data frame format and named it as mlr.outout.

mlr.output <- as.data.frame(gdp.mlr1$residuals)

In the earlier stage, we have pre-created a data set called mun_map. Now we going to drop these 2 rows of municipalitities from this data set as well in order to prepare for furhter mapping purpose.

mun_map <- mun_map[-c(4607,4608),]

Now we going to combine the residuals columns from gdp1.mlr1 data set together mun_map and rename the gdp.mlr1.residuals as MLR_RES.

mun_map.res.sf <- cbind(mun_map, 
                        gdp.mlr1$residuals) %>%
rename(`MLR_RES` = `gdp.mlr1.residuals`)

After the process of combination, we would like to perform a check on the class of mun_map.res.sf. Currently the mun_map.res.sf is in sf format.

class(mun_map.res.sf)
## [1] "sf"         "data.frame"

Now we going to use mun_map.res.sf data set to plot the MLR_RES choropleth map by using tmap function.

tm_shape (mun_map.res.sf) +
  tm_fill (col= "MLR_RES",style = "equal",palette = "Reds",legend.hist = TRUE) +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Distribution of the Residual (GDP per CAPITA)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 1,
          legend.text.size = 0.8,
          legend.position = c("left","bottom"),
          legend.outside = TRUE,
          legend.hist.width = 1,
          legend.bg.alpha = 1,
          outer.bg.color = "lightblue") +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

Based on the choropleth map we can see that there is sign of spatial autocorrelation across the map. The meaning of the residual is the difference between the actual value of a DV and its predicted value. Based one the histogram we can see that most of the municipalitity polygons with residual from -65,808 t0 4446.

Now we also going to combine the residuals data set with final_br.sf. final_br.sf is with municipalitity point geometry.

final_br.res.sf <- cbind(final_br.sf, 
                        gdp.mlr1$residuals) %>%
rename(`MLR_RES` = `gdp.mlr1.residuals`)

Now we going to convert the data set of final_br.res.sf to SpatialPolygonsDataFrame format.

final_br.sp <- as_Spatial(final_br.res.sf)
final_br.sp
## class       : SpatialPointsDataFrame 
## features    : 5570 
## extent      : 2913283, 7394984, 6270906, 10510051  (xmin, xmax, ymin, ymax)
## crs         : +proj=poly +lat_0=0 +lon_0=-54 +x_0=5000000 +y_0=10000000 +ellps=aust_SA +towgs84=-66.87,4.37,-38.52,0,0,0,0 +units=m +no_defs 
## variables   : 88
## names       : code_muni,       name_muni, code_state, abbrev_state, CAPITAL, IBGE_RES_POP, IBGE_RES_POP_BRAS, IBGE_RES_POP_ESTR, IBGE_DU, IBGE_DU_URBAN, IBGE_POP, IBGE_1, IBGE_1.4, IBGE_5.9, IBGE_10.14, ... 
## min values  :   1100015, abadia de goiás,         11,           AC,       0,            0,                 0,                 0,       0,             0,        0,      0,        0,        0,          0, ... 
## max values  :   5300108,          zortéa,         53,           TO,       1,     11253503,          11133776,            119727, 3576148,       3548433, 10463636, 129464,   514794,   684443,     783702, ...

To proof that our observation is indeed true, the Moran’s I test will be performed.
First, we will compute the distance-based weight matrix by using dnearneigh() function.

nb <- dnearneigh(coordinates(final_br.sp), 0, 400000, longlat = FALSE)
summary(nb)
## Neighbour list object:
## Number of regions: 5570 
## Number of nonzero links: 3381502 
## Percentage nonzero weights: 10.89932 
## Average number of links: 607.0919 
## Link number distribution:
## 
##   10   11   12   13   14   15   16   17   18   19   20   21   22   23   24   25 
##    5    3    4    4   12    6    4    6    3    5    5    7    3    2    2    4 
##   26   27   28   29   30   31   32   33   34   35   36   37   38   39   40   41 
##    2    3    1    2    4    3    6    1    5    4    6    3    6    3    5    7 
##   42   43   44   45   46   47   48   49   50   51   52   53   54   55   56   57 
##    3    5    2    4    2    3    3    6    3    4    6    4    5    3    5    6 
##   58   59   60   61   62   63   64   65   66   67   68   69   70   71   72   74 
##    7    7    7    5    2    4    3    5    7    1    4    1    2    1    2    3 
##   75   76   77   78   79   80   81   82   83   84   85   86   87   88   90   91 
##    3    1    1    3    2    6    4    2    1    2    3    2    3    2    2    5 
##   92   93   94   95   96   98   99  100  102  103  104  105  107  108  109  110 
##    2    2    2    4    1    1    4    4    3    2    3    3    2    2    1    3 
##  111  112  113  116  117  118  119  122  123  124  125  126  127  128  129  131 
##    5    1    1    1    4    2    1    2    1    5    3    1    4    4    4    2 
##  132  133  134  135  137  138  139  140  141  142  143  145  146  147  148  149 
##    2    4    1    3    2    2    3    1    2    2    3    1    4    2    2    2 
##  150  151  152  153  154  155  156  157  158  159  160  161  162  163  164  165 
##    7    4    1    3    2    4    4    5    1    2    4    1    6    3    3    7 
##  166  167  168  170  171  172  173  174  175  176  177  178  179  180  181  182 
##    5    3   12    2    3    7    8    6    8    3    4    4    6    7    4    2 
##  183  184  185  186  187  188  189  190  191  192  193  194  195  196  197  198 
##    4    3    3    5    4    4    5    5    1    4    3    2    6    2    1    2 
##  199  200  201  202  204  205  206  207  208  209  210  211  212  213  215  216 
##    2    5    1    3    5    5    3    2    3    3    2    5    4    2    2    2 
##  217  218  219  220  221  222  224  225  227  228  229  230  231  232  233  234 
##    1    2    2    3    2    2    3    6    6    3    2    2    2    2    5    5 
##  235  236  237  238  239  240  241  242  243  244  245  246  247  248  249  250 
##    2    2    8    3    1    4    5    5    4    5    3    3    4    1    1    4 
##  251  252  253  254  255  256  257  259  260  261  262  263  265  266  267  268 
##    4    3    2    5    5    3    9    4    3    2    8    3    5    2    4    1 
##  269  270  271  272  273  274  275  276  277  278  279  280  281  282  283  284 
##    4    8    5    6    6    1    5    6    3    3    3    5    5    4    9    5 
##  285  286  287  288  289  290  291  292  293  294  295  296  297  298  299  300 
##    4    4    2    4    1    3    5    7    8    8    5    3    3    4    8    6 
##  301  302  303  304  305  306  307  308  309  310  311  312  313  314  315  316 
##    7    2    2    2    3    4    9    6    7    5    4    8    5    6    4    4 
##  317  318  319  320  321  322  323  324  325  326  327  328  329  330  331  332 
##    3    8    8    8    6    5    1    5    1    2    3    8    3    5    2    4 
##  333  334  335  336  337  338  339  340  341  342  343  344  345  346  347  348 
##    3    6    4    7    4    3    7    7    4    6    5    5    2    6    8    4 
##  349  350  351  352  353  354  355  356  357  358  359  360  361  362  363  364 
##    4    7    6    9    4    4    5    4    5    4    4    4    3    6    2    7 
##  365  366  367  368  369  370  371  372  373  374  375  376  377  378  379  380 
##    3    8    2   10    5    7    5    3    4    4    5    4    6    7    6    4 
##  381  382  383  384  385  386  387  388  389  390  391  392  393  394  395  396 
##    2    2    8    7    4    3    3    4    5    9    4    6    5    5    4    5 
##  397  398  399  400  401  402  403  404  405  406  407  408  409  410  411  412 
##    9    5    5    7    6    7    2    5    8    9    7    8    9    7    9    9 
##  413  414  415  416  417  418  419  420  421  422  423  424  425  426  427  428 
##    7   10   14    6   13    4    4    5    7    4    8    6    4    6    7    7 
##  429  430  431  432  433  434  435  436  437  438  439  440  441  442  443  444 
##    5    9    3    4    7    4    8    5    6    6    6    5    6    7    4    5 
##  445  446  447  448  449  450  451  452  453  454  455  456  457  458  459  460 
##    3    4    3    6    3    2    6    2    3    5   10   10    6    5    3    3 
##  461  462  463  464  465  466  467  468  469  470  471  472  473  475  476  477 
##    7    3    5    7    3    4    6    4    5    3    4    4    3    5    2    1 
##  478  479  480  481  482  483  484  485  486  487  488  489  490  491  492  493 
##    3    1    8    3    3    4    2    2    5    4    3    2    2    2    4    3 
##  494  495  496  497  498  499  500  501  502  503  504  505  506  507  508  509 
##    5    7    3    4    2    5    1    1    1    7    9    4    2    6    2    4 
##  512  514  515  516  517  518  519  520  521  522  523  524  525  526  527  528 
##    3    1    3    1    3    3    3    3    3    4    1    2    2    6    5    2 
##  530  531  533  534  535  536  537  538  539  540  541  542  543  544  545  546 
##    1    3    1    4    8    4    2    2    5    1    7    3    1    4    3    1 
##  547  548  549  550  551  552  553  554  555  556  557  558  559  560  561  562 
##    2    4    3    2    4    7    3    5    6    7    6    5    5    6    8    5 
##  563  564  565  566  567  568  569  570  571  572  573  574  575  576  578  579 
##    4    6    1    9    3    2    8    7    2    4    4    4    1    5    8    1 
##  580  581  582  583  584  585  586  587  588  589  590  591  592  593  594  595 
##    5    3    6    3    2    8    2    1    3    3    7    4    5    6    7    3 
##  596  597  598  599  600  601  602  603  604  605  606  607  608  609  610  611 
##    2    3    6    9    6    6    4    8    7    3    7    2    6    5    9    6 
##  612  613  614  615  616  617  618  619  620  621  622  623  624  625  626  627 
##    3    3    6    8   10    5    6   11    2    5    8    6   12    7    9    8 
##  628  629  630  631  632  633  634  635  636  637  638  639  640  641  642  643 
##    9    6    4    9   11    7    5    5   11   13    9    6    7    4    6    3 
##  644  645  646  647  648  649  650  651  652  653  654  655  656  657  658  659 
##   10    5    4    6    6    3   11    7    5   10    4    9    7    2    9    7 
##  660  661  662  663  664  665  666  667  668  669  670  671  672  673  674  675 
##    3    7    6    6    3    5    9    6    5   11   11    5    5   10    5   11 
##  676  677  678  679  680  681  682  683  684  685  686  687  688  689  690  691 
##    6    5    7   11    6   10   11    5    7    9    4   10    5    7   11    7 
##  692  693  694  695  696  697  698  699  700  701  702  703  704  705  706  707 
##   10    9    7    6    7    4   11    9    6    6    5    8   10    7    5    9 
##  708  709  710  711  712  713  714  715  716  717  718  719  720  721  722  723 
##   13    6    9    6    2    9    8    7    9    8    6    8    8    7    9    6 
##  724  725  726  727  728  729  730  731  732  733  734  735  736  737  738  739 
##    8   14    3   14    7    9    8    5    4    9   11   10   14    7    5    4 
##  740  741  742  743  744  745  746  747  748  749  750  751  752  753  754  755 
##    7   11   11    5   10   11    9    9   10   12    6   11    8    8    6    3 
##  756  757  758  759  760  761  762  763  764  765  766  767  768  769  770  771 
##    7    8    5   12   11   11   10   10    9    9    8    8   11    5   14   11 
##  772  773  774  775  776  777  778  779  780  781  782  783  784  785  786  787 
##    8    7    9   11    8    5    9   11   10    9   11   11   11    9   10   12 
##  788  789  790  791  792  793  794  795  796  797  798  799  800  801  802  803 
##   12    6   10    8   12    6   11    6   10    8    7    8   10   12   10   16 
##  804  805  806  807  808  809  810  811  812  813  814  815  816  817  818  819 
##   11   13   10    7    8    9    6    8    7    6    8   11   13   10    3   13 
##  820  821  822  823  824  825  826  827  828  829  830  831  832  833  834  835 
##   16    6   14    7    5   10    7    4    9   10    8    8    9   10    2   10 
##  836  837  838  839  840  841  842  843  844  845  846  847  848  849  850  851 
##    6    5    6    9    9    7   10    9    6    8    8   10    8    2    8    9 
##  852  853  854  855  856  857  858  859  860  861  862  863  864  865  866  867 
##   12    5   11    8    7    8    7    8    4    6    3    3    8    7    6    4 
##  868  869  870  871  872  873  874  875  876  877  878  879  880  881  882  883 
##    2   17    1    7    3    7    7    8    8   11    7    4    5    6   11    9 
##  884  885  886  887  888  889  890  891  892  893  894  895  896  897  898  899 
##    8    7    5    5    3    5    6    8    5    7    5    6    2    8    7    8 
##  900  901  902  903  904  905  906  907  908  909  910  911  912  913  914  915 
##    6    7    5    5    6    7    8    2   12   10    3   10    5    5    9    6 
##  916  917  918  919  920  921  922  923  924  925  926  927  928  929  930  931 
##   10   10    4    9    6    6   12   10    9    4    8    5    6    4    2    5 
##  932  933  934  935  936  937  938  939  940  941  942  943  944  945  946  947 
##    7    9    7    7    9    8    2    4    6    7    8    4    4    7   11    5 
##  948  949  950  951  952  953  954  955  956  957  958  959  960  961  962  963 
##    5    9    7    3    7    5    1    8    6    7    8    3    6   12    7    7 
##  964  965  966  967  968  969  970  971  972  973  974  975  976  977  978  979 
##    9    3    7    3    7    3    3    9    4    6    8    5    8    5    8    5 
##  980  981  982  983  984  985  986  987  988  989  990  991  992  993  994  995 
##    7   10    5    6    7    8    4    3    4    8    4    5    9    4    5    7 
##  996  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 
##    1    7   11    5    4    2    9    8    2    6    8   11    9    9    6    9 
## 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 
##   12   11   14    7   15   15    3   11   12   10   10    9    6    8    3    2 
## 1028 1029 1030 1031 1033 1034 1035 1036 1038 1039 1041 1043 1044 1045 1051 1052 
##    3    8    8    2    3    3    3    1    2    2    1    2    1    1    2    1 
## 1053 1062 1069 1075 1077 1080 1082 1092 
##    2    1    4    1    1    1    1    1 
## 5 least connected regions:
## 124 126 147 306 1526 with 10 links
## 1 most connected region:
## 3947 with 1092 links

To convert the output neighbours lists (i.e. nb) into a spatial weights.

nb_lw <- nb2listw(nb, style = 'W')
summary(nb_lw)
## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 5570 
## Number of nonzero links: 3381502 
## Percentage nonzero weights: 10.89932 
## Average number of links: 607.0919 
## Link number distribution:
## 
##   10   11   12   13   14   15   16   17   18   19   20   21   22   23   24   25 
##    5    3    4    4   12    6    4    6    3    5    5    7    3    2    2    4 
##   26   27   28   29   30   31   32   33   34   35   36   37   38   39   40   41 
##    2    3    1    2    4    3    6    1    5    4    6    3    6    3    5    7 
##   42   43   44   45   46   47   48   49   50   51   52   53   54   55   56   57 
##    3    5    2    4    2    3    3    6    3    4    6    4    5    3    5    6 
##   58   59   60   61   62   63   64   65   66   67   68   69   70   71   72   74 
##    7    7    7    5    2    4    3    5    7    1    4    1    2    1    2    3 
##   75   76   77   78   79   80   81   82   83   84   85   86   87   88   90   91 
##    3    1    1    3    2    6    4    2    1    2    3    2    3    2    2    5 
##   92   93   94   95   96   98   99  100  102  103  104  105  107  108  109  110 
##    2    2    2    4    1    1    4    4    3    2    3    3    2    2    1    3 
##  111  112  113  116  117  118  119  122  123  124  125  126  127  128  129  131 
##    5    1    1    1    4    2    1    2    1    5    3    1    4    4    4    2 
##  132  133  134  135  137  138  139  140  141  142  143  145  146  147  148  149 
##    2    4    1    3    2    2    3    1    2    2    3    1    4    2    2    2 
##  150  151  152  153  154  155  156  157  158  159  160  161  162  163  164  165 
##    7    4    1    3    2    4    4    5    1    2    4    1    6    3    3    7 
##  166  167  168  170  171  172  173  174  175  176  177  178  179  180  181  182 
##    5    3   12    2    3    7    8    6    8    3    4    4    6    7    4    2 
##  183  184  185  186  187  188  189  190  191  192  193  194  195  196  197  198 
##    4    3    3    5    4    4    5    5    1    4    3    2    6    2    1    2 
##  199  200  201  202  204  205  206  207  208  209  210  211  212  213  215  216 
##    2    5    1    3    5    5    3    2    3    3    2    5    4    2    2    2 
##  217  218  219  220  221  222  224  225  227  228  229  230  231  232  233  234 
##    1    2    2    3    2    2    3    6    6    3    2    2    2    2    5    5 
##  235  236  237  238  239  240  241  242  243  244  245  246  247  248  249  250 
##    2    2    8    3    1    4    5    5    4    5    3    3    4    1    1    4 
##  251  252  253  254  255  256  257  259  260  261  262  263  265  266  267  268 
##    4    3    2    5    5    3    9    4    3    2    8    3    5    2    4    1 
##  269  270  271  272  273  274  275  276  277  278  279  280  281  282  283  284 
##    4    8    5    6    6    1    5    6    3    3    3    5    5    4    9    5 
##  285  286  287  288  289  290  291  292  293  294  295  296  297  298  299  300 
##    4    4    2    4    1    3    5    7    8    8    5    3    3    4    8    6 
##  301  302  303  304  305  306  307  308  309  310  311  312  313  314  315  316 
##    7    2    2    2    3    4    9    6    7    5    4    8    5    6    4    4 
##  317  318  319  320  321  322  323  324  325  326  327  328  329  330  331  332 
##    3    8    8    8    6    5    1    5    1    2    3    8    3    5    2    4 
##  333  334  335  336  337  338  339  340  341  342  343  344  345  346  347  348 
##    3    6    4    7    4    3    7    7    4    6    5    5    2    6    8    4 
##  349  350  351  352  353  354  355  356  357  358  359  360  361  362  363  364 
##    4    7    6    9    4    4    5    4    5    4    4    4    3    6    2    7 
##  365  366  367  368  369  370  371  372  373  374  375  376  377  378  379  380 
##    3    8    2   10    5    7    5    3    4    4    5    4    6    7    6    4 
##  381  382  383  384  385  386  387  388  389  390  391  392  393  394  395  396 
##    2    2    8    7    4    3    3    4    5    9    4    6    5    5    4    5 
##  397  398  399  400  401  402  403  404  405  406  407  408  409  410  411  412 
##    9    5    5    7    6    7    2    5    8    9    7    8    9    7    9    9 
##  413  414  415  416  417  418  419  420  421  422  423  424  425  426  427  428 
##    7   10   14    6   13    4    4    5    7    4    8    6    4    6    7    7 
##  429  430  431  432  433  434  435  436  437  438  439  440  441  442  443  444 
##    5    9    3    4    7    4    8    5    6    6    6    5    6    7    4    5 
##  445  446  447  448  449  450  451  452  453  454  455  456  457  458  459  460 
##    3    4    3    6    3    2    6    2    3    5   10   10    6    5    3    3 
##  461  462  463  464  465  466  467  468  469  470  471  472  473  475  476  477 
##    7    3    5    7    3    4    6    4    5    3    4    4    3    5    2    1 
##  478  479  480  481  482  483  484  485  486  487  488  489  490  491  492  493 
##    3    1    8    3    3    4    2    2    5    4    3    2    2    2    4    3 
##  494  495  496  497  498  499  500  501  502  503  504  505  506  507  508  509 
##    5    7    3    4    2    5    1    1    1    7    9    4    2    6    2    4 
##  512  514  515  516  517  518  519  520  521  522  523  524  525  526  527  528 
##    3    1    3    1    3    3    3    3    3    4    1    2    2    6    5    2 
##  530  531  533  534  535  536  537  538  539  540  541  542  543  544  545  546 
##    1    3    1    4    8    4    2    2    5    1    7    3    1    4    3    1 
##  547  548  549  550  551  552  553  554  555  556  557  558  559  560  561  562 
##    2    4    3    2    4    7    3    5    6    7    6    5    5    6    8    5 
##  563  564  565  566  567  568  569  570  571  572  573  574  575  576  578  579 
##    4    6    1    9    3    2    8    7    2    4    4    4    1    5    8    1 
##  580  581  582  583  584  585  586  587  588  589  590  591  592  593  594  595 
##    5    3    6    3    2    8    2    1    3    3    7    4    5    6    7    3 
##  596  597  598  599  600  601  602  603  604  605  606  607  608  609  610  611 
##    2    3    6    9    6    6    4    8    7    3    7    2    6    5    9    6 
##  612  613  614  615  616  617  618  619  620  621  622  623  624  625  626  627 
##    3    3    6    8   10    5    6   11    2    5    8    6   12    7    9    8 
##  628  629  630  631  632  633  634  635  636  637  638  639  640  641  642  643 
##    9    6    4    9   11    7    5    5   11   13    9    6    7    4    6    3 
##  644  645  646  647  648  649  650  651  652  653  654  655  656  657  658  659 
##   10    5    4    6    6    3   11    7    5   10    4    9    7    2    9    7 
##  660  661  662  663  664  665  666  667  668  669  670  671  672  673  674  675 
##    3    7    6    6    3    5    9    6    5   11   11    5    5   10    5   11 
##  676  677  678  679  680  681  682  683  684  685  686  687  688  689  690  691 
##    6    5    7   11    6   10   11    5    7    9    4   10    5    7   11    7 
##  692  693  694  695  696  697  698  699  700  701  702  703  704  705  706  707 
##   10    9    7    6    7    4   11    9    6    6    5    8   10    7    5    9 
##  708  709  710  711  712  713  714  715  716  717  718  719  720  721  722  723 
##   13    6    9    6    2    9    8    7    9    8    6    8    8    7    9    6 
##  724  725  726  727  728  729  730  731  732  733  734  735  736  737  738  739 
##    8   14    3   14    7    9    8    5    4    9   11   10   14    7    5    4 
##  740  741  742  743  744  745  746  747  748  749  750  751  752  753  754  755 
##    7   11   11    5   10   11    9    9   10   12    6   11    8    8    6    3 
##  756  757  758  759  760  761  762  763  764  765  766  767  768  769  770  771 
##    7    8    5   12   11   11   10   10    9    9    8    8   11    5   14   11 
##  772  773  774  775  776  777  778  779  780  781  782  783  784  785  786  787 
##    8    7    9   11    8    5    9   11   10    9   11   11   11    9   10   12 
##  788  789  790  791  792  793  794  795  796  797  798  799  800  801  802  803 
##   12    6   10    8   12    6   11    6   10    8    7    8   10   12   10   16 
##  804  805  806  807  808  809  810  811  812  813  814  815  816  817  818  819 
##   11   13   10    7    8    9    6    8    7    6    8   11   13   10    3   13 
##  820  821  822  823  824  825  826  827  828  829  830  831  832  833  834  835 
##   16    6   14    7    5   10    7    4    9   10    8    8    9   10    2   10 
##  836  837  838  839  840  841  842  843  844  845  846  847  848  849  850  851 
##    6    5    6    9    9    7   10    9    6    8    8   10    8    2    8    9 
##  852  853  854  855  856  857  858  859  860  861  862  863  864  865  866  867 
##   12    5   11    8    7    8    7    8    4    6    3    3    8    7    6    4 
##  868  869  870  871  872  873  874  875  876  877  878  879  880  881  882  883 
##    2   17    1    7    3    7    7    8    8   11    7    4    5    6   11    9 
##  884  885  886  887  888  889  890  891  892  893  894  895  896  897  898  899 
##    8    7    5    5    3    5    6    8    5    7    5    6    2    8    7    8 
##  900  901  902  903  904  905  906  907  908  909  910  911  912  913  914  915 
##    6    7    5    5    6    7    8    2   12   10    3   10    5    5    9    6 
##  916  917  918  919  920  921  922  923  924  925  926  927  928  929  930  931 
##   10   10    4    9    6    6   12   10    9    4    8    5    6    4    2    5 
##  932  933  934  935  936  937  938  939  940  941  942  943  944  945  946  947 
##    7    9    7    7    9    8    2    4    6    7    8    4    4    7   11    5 
##  948  949  950  951  952  953  954  955  956  957  958  959  960  961  962  963 
##    5    9    7    3    7    5    1    8    6    7    8    3    6   12    7    7 
##  964  965  966  967  968  969  970  971  972  973  974  975  976  977  978  979 
##    9    3    7    3    7    3    3    9    4    6    8    5    8    5    8    5 
##  980  981  982  983  984  985  986  987  988  989  990  991  992  993  994  995 
##    7   10    5    6    7    8    4    3    4    8    4    5    9    4    5    7 
##  996  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 
##    1    7   11    5    4    2    9    8    2    6    8   11    9    9    6    9 
## 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 
##   12   11   14    7   15   15    3   11   12   10   10    9    6    8    3    2 
## 1028 1029 1030 1031 1033 1034 1035 1036 1038 1039 1041 1043 1044 1045 1051 1052 
##    3    8    8    2    3    3    3    1    2    2    1    2    1    1    2    1 
## 1053 1062 1069 1075 1077 1080 1082 1092 
##    2    1    4    1    1    1    1    1 
## 5 least connected regions:
## 124 126 147 306 1526 with 10 links
## 1 most connected region:
## 3947 with 1092 links
## 
## Weights style: W 
## Weights constants summary:
##      n       nn   S0       S1       S2
## W 5570 31024900 5570 38.90204 22403.03

To perform Moran’s I test for residual spatial autocorrelation.

Hypothesis Test
Null Hypothesis: The residuals are randomly distributed.
Alternative Hypothesis: The residuals are not randomly distributed.
Confident Interval: 0.05

lm.morantest(gdp.mlr1, nb_lw)
## 
##  Global Moran I for regression residuals
## 
## data:  
## model: lm(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL +
## IBGE_CROP_PRODUCTION_. + IDHM_Longevidade + IDHM_Educacao +
## Intermediario_Adjacente + Rural_Adjacente + Sem_classificacao +
## GVA_AGROPEC, data = final_br.sf)
## weights: nb_lw
## 
## Moran I statistic standard deviate = 20.637, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Observed Moran I      Expectation         Variance 
##     2.093684e-02    -4.155606e-04     1.070537e-06

The Global Moran’s I test for residual spatial autocorrelation shows that it’s p-value is less than 0.00000000000000022 which is less than the alpha value of 0.05. Hence, we will reject the null hypothesis that the residuals are randomly distributed.

Since the Observed Global Moran I = 0.01955789 which is greater than 0, we can infer than the residuals resemble cluster distribution.

7. Building Hedonic Pricing Models using GWmodel

7.1 Building Fixed Bandwidth GWR Model

7.1.1 Computing fixed bandwith

bw.fixed <- bw.gwr(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL + `IBGE_CROP_PRODUCTION_.` + IDHM_Longevidade + IDHM_Educacao + Intermediario_Adjacente  + Rural_Adjacente  + Sem_classificacao + GVA_AGROPEC, data=final_br.sp, approach="CV", kernel="gaussian", adaptive=FALSE, longlat=FALSE)
## Take a cup of tea and have a break, it will take a few minutes.
##           -----A kind suggestion from GWmodel development group
## Fixed bandwidth: 3813094 CV score: 1.664512e+12 
## Fixed bandwidth: 2357093 CV score: 1.658805e+12 
## Fixed bandwidth: 1457235 CV score: 1.647425e+12 
## Fixed bandwidth: 901092 CV score: 1.631103e+12 
## Fixed bandwidth: 557376.8 CV score: 1.614642e+12 
## Fixed bandwidth: 344949 CV score: 1.601464e+12 
## Fixed bandwidth: 213661.5 CV score: 1.585698e+12 
## Fixed bandwidth: 132521.3 CV score: 1.58842e+12 
## Fixed bandwidth: 263808.9 CV score: 1.592431e+12 
## Fixed bandwidth: 182668.7 CV score: 1.582968e+12 
## Fixed bandwidth: 163514.1 CV score: 1.582969e+12 
## Fixed bandwidth: 194506.9 CV score: 1.583721e+12 
## Fixed bandwidth: 175352.3 CV score: 1.582761e+12 
## Fixed bandwidth: 170830.5 CV score: 1.582753e+12 
## Fixed bandwidth: 168035.9 CV score: 1.5828e+12 
## Fixed bandwidth: 172557.7 CV score: 1.582744e+12 
## Fixed bandwidth: 173625.1 CV score: 1.582746e+12 
## Fixed bandwidth: 171898 CV score: 1.582746e+12 
## Fixed bandwidth: 172965.4 CV score: 1.582744e+12 
## Fixed bandwidth: 172305.7 CV score: 1.582745e+12 
## Fixed bandwidth: 172713.4 CV score: 1.582744e+12 
## Fixed bandwidth: 172809.7 CV score: 1.582744e+12 
## Fixed bandwidth: 172653.9 CV score: 1.582744e+12 
## Fixed bandwidth: 172750.2 CV score: 1.582744e+12 
## Fixed bandwidth: 172690.7 CV score: 1.582744e+12 
## Fixed bandwidth: 172727.5 CV score: 1.582744e+12 
## Fixed bandwidth: 172736.2 CV score: 1.582744e+12 
## Fixed bandwidth: 172722.1 CV score: 1.582744e+12 
## Fixed bandwidth: 172718.8 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.2 CV score: 1.582744e+12 
## Fixed bandwidth: 172725.4 CV score: 1.582744e+12 
## Fixed bandwidth: 172723.4 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.6 CV score: 1.582744e+12 
## Fixed bandwidth: 172723.9 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.5 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.4 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12 
## Fixed bandwidth: 172724.3 CV score: 1.582744e+12

As we can see that the recommend fixed bandwidth is 172724.3m. when we sub this value back to our distance-based weight matrix function. The statistical property is important, if the fixed bandwidth are able to provide us at least 15 neighbour data points then will be alright. However, the results provided to us that there are quite a number of municipalitities that with less than 15 neighbours. Therefore, adaptive bandwidth would be recommend and to ensure that each dat point will have enough neighbours.

7.1.2 GWModel method - fixed bandwith

To calibrate the gwr model using fixed bandwidth and gaussian kernel and display the model output.

gwr.fixed <- gwr.basic(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL + `IBGE_CROP_PRODUCTION_.` + IDHM_Longevidade + IDHM_Educacao + Intermediario_Adjacente  + Rural_Adjacente  + Sem_classificacao + GVA_AGROPEC, data=final_br.sp, bw=bw.fixed, kernel = 'gaussian', longlat = FALSE)
gwr.fixed
##    ***********************************************************************
##    *                       Package   GWmodel                             *
##    ***********************************************************************
##    Program starts at: 2020-05-31 23:54:52 
##    Call:
##    gwr.basic(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL + 
##     IBGE_CROP_PRODUCTION_. + IDHM_Longevidade + IDHM_Educacao + 
##     Intermediario_Adjacente + Rural_Adjacente + Sem_classificacao + 
##     GVA_AGROPEC, data = final_br.sp, bw = bw.fixed, kernel = "gaussian", 
##     longlat = FALSE)
## 
##    Dependent (y) variable:  GDP_CAPITA
##    Independent variables:  Economy_gp IBGE_DU_RURAL IBGE_CROP_PRODUCTION_. IDHM_Longevidade IDHM_Educacao Intermediario_Adjacente Rural_Adjacente Sem_classificacao GVA_AGROPEC
##    Number of data points: 5570
##    ***********************************************************************
##    *                    Results of Global Regression                     *
##    ***********************************************************************
## 
##    Call:
##     lm(formula = formula, data = data)
## 
##    Residuals:
##    Min     1Q Median     3Q    Max 
## -63621  -7163  -2815   2273 278767 
## 
##    Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
##    (Intercept)             -7.495e+04  4.792e+03 -15.642  < 2e-16 ***
##    Economy_gp              -5.748e+03  2.397e+03  -2.398  0.01652 *  
##    IBGE_DU_RURAL           -1.102e+00  1.507e-01  -7.317 2.89e-13 ***
##    IBGE_CROP_PRODUCTION_.   1.501e-02  2.342e-03   6.410 1.57e-10 ***
##    IDHM_Longevidade         8.223e+04  7.202e+03  11.417  < 2e-16 ***
##    IDHM_Educacao            5.830e+04  4.005e+03  14.557  < 2e-16 ***
##    Intermediario_Adjacente -2.457e+03  7.792e+02  -3.153  0.00163 ** 
##    Rural_Adjacente         -1.543e+03  6.310e+02  -2.445  0.01452 *  
##    Sem_classificacao        1.006e+05  9.103e+03  11.047  < 2e-16 ***
##    GVA_AGROPEC              3.675e-02  4.028e-03   9.124  < 2e-16 ***
## 
##    ---Significance stars
##    Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
##    Residual standard error: 17260 on 5560 degrees of freedom
##    Multiple R-squared: 0.2802
##    Adjusted R-squared: 0.2791 
##    F-statistic: 240.5 on 9 and 5560 DF,  p-value: < 2.2e-16 
##    ***Extra Diagnostic information
##    Residual sum of squares: 1.657136e+12
##    Sigma(hat): 17251.6
##    AIC:  124505
##    AICc:  124505.1
##    ***********************************************************************
##    *          Results of Geographically Weighted Regression              *
##    ***********************************************************************
## 
##    *********************Model calibration information*********************
##    Kernel function: gaussian 
##    Fixed bandwidth: 172724.3 
##    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.
##    Intercept               -3.2974e+05 -6.3917e+04 -3.5937e+04 -7.9466e+03
##    Economy_gp              -1.0159e+05 -3.0241e+03  2.0655e+03  9.1162e+03
##    IBGE_DU_RURAL           -1.1914e+01 -1.7218e+00 -5.0167e-01 -1.2401e-01
##    IBGE_CROP_PRODUCTION_.  -3.5553e-02 -1.9852e-03  8.1693e-03  1.7023e-02
##    IDHM_Longevidade        -5.8173e+04  1.4138e+04  4.2633e+04  6.9730e+04
##    IDHM_Educacao           -6.9830e+04  1.3288e+04  3.5099e+04  5.8784e+04
##    Intermediario_Adjacente -1.4310e+04 -4.2302e+03 -2.4478e+03 -7.3936e+02
##    Rural_Adjacente         -1.8041e+04 -3.0839e+03 -1.1341e+03  1.2406e+03
##    Sem_classificacao       -3.3311e+04  2.9937e+04  7.8972e+04  1.1229e+05
##    GVA_AGROPEC             -1.7860e-01  2.2599e-02  3.8407e-02  5.0350e-02
##                                  Max.
##    Intercept               8.7056e+04
##    Economy_gp              6.8319e+04
##    IBGE_DU_RURAL           1.2904e+00
##    IBGE_CROP_PRODUCTION_.  1.6140e-01
##    IDHM_Longevidade        3.8785e+05
##    IDHM_Educacao           1.6850e+05
##    Intermediario_Adjacente 1.9274e+04
##    Rural_Adjacente         1.4167e+04
##    Sem_classificacao       4.1208e+05
##    GVA_AGROPEC             1.2110e-01
##    ************************Diagnostic information*************************
##    Number of data points: 5570 
##    Effective number of parameters (2trace(S) - trace(S'S)): 432.6981 
##    Effective degrees of freedom (n-2trace(S) + trace(S'S)): 5137.302 
##    AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 124265.7 
##    AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 123904.3 
##    Residual sum of squares: 1.410218e+12 
##    R-square value:  0.3874791 
##    Adjusted R-square value:  0.3358784 
## 
##    ***********************************************************************
##    Program stops at: 2020-05-31 23:55:08

To perform a check on final_br.sp to ensure that it is in SpatialPointsDataFrame format.

class(final_br.sp)
## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"

7.2 Building Adaptive Bandwidth GWR Model

7.2.1 Computing the adaptive bandwidth

DM <- gw.dist(dp.locat = coordinates(final_br.sp))
bw.adaptive <- bw.gwr(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL + IBGE_CROP_PRODUCTION_. + IDHM_Longevidade + IDHM_Educacao + Intermediario_Adjacente  + Rural_Adjacente  + Sem_classificacao + GVA_AGROPEC, data=final_br.sp, approach="CV", kernel="gaussian",
adaptive=TRUE, longlat=FALSE, dMat = DM)
## Take a cup of tea and have a break, it will take a few minutes.
##           -----A kind suggestion from GWmodel development group
## Adaptive bandwidth: 3450 CV score: 1.652144e+12 
## Adaptive bandwidth: 2140 CV score: 1.637647e+12 
## Adaptive bandwidth: 1330 CV score: 1.618697e+12 
## Adaptive bandwidth: 829 CV score: 1.606789e+12 
## Adaptive bandwidth: 520 CV score: 1.594909e+12 
## Adaptive bandwidth: 328 CV score: 1.584767e+12 
## Adaptive bandwidth: 210 CV score: 1.580083e+12 
## Adaptive bandwidth: 136 CV score: 1.579053e+12 
## Adaptive bandwidth: 91 CV score: 1.582314e+12 
## Adaptive bandwidth: 164 CV score: 1.57883e+12 
## Adaptive bandwidth: 181 CV score: 1.579366e+12 
## Adaptive bandwidth: 153 CV score: 1.578835e+12 
## Adaptive bandwidth: 170 CV score: 1.578838e+12 
## Adaptive bandwidth: 159 CV score: 1.578568e+12 
## Adaptive bandwidth: 157 CV score: 1.578733e+12 
## Adaptive bandwidth: 161 CV score: 1.578906e+12 
## Adaptive bandwidth: 158 CV score: 1.578715e+12 
## Adaptive bandwidth: 160 CV score: 1.57877e+12 
## Adaptive bandwidth: 159 CV score: 1.578568e+12

The result shows that 159 is the recommended data points to be used.

7.2.2 Constructing the adaptive bandwidth gwr model

gwr.adaptive <- gwr.basic(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL + IBGE_CROP_PRODUCTION_. + IDHM_Longevidade + IDHM_Educacao + Intermediario_Adjacente  + Rural_Adjacente  + Sem_classificacao + GVA_AGROPEC, data=final_br.sp, bw=bw.adaptive, kernel = 'gaussian', adaptive = TRUE, longlat=FALSE)
gwr.adaptive
##    ***********************************************************************
##    *                       Package   GWmodel                             *
##    ***********************************************************************
##    Program starts at: 2020-05-31 23:57:55 
##    Call:
##    gwr.basic(formula = GDP_CAPITA ~ Economy_gp + IBGE_DU_RURAL + 
##     IBGE_CROP_PRODUCTION_. + IDHM_Longevidade + IDHM_Educacao + 
##     Intermediario_Adjacente + Rural_Adjacente + Sem_classificacao + 
##     GVA_AGROPEC, data = final_br.sp, bw = bw.adaptive, kernel = "gaussian", 
##     adaptive = TRUE, longlat = FALSE)
## 
##    Dependent (y) variable:  GDP_CAPITA
##    Independent variables:  Economy_gp IBGE_DU_RURAL IBGE_CROP_PRODUCTION_. IDHM_Longevidade IDHM_Educacao Intermediario_Adjacente Rural_Adjacente Sem_classificacao GVA_AGROPEC
##    Number of data points: 5570
##    ***********************************************************************
##    *                    Results of Global Regression                     *
##    ***********************************************************************
## 
##    Call:
##     lm(formula = formula, data = data)
## 
##    Residuals:
##    Min     1Q Median     3Q    Max 
## -63621  -7163  -2815   2273 278767 
## 
##    Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
##    (Intercept)             -7.495e+04  4.792e+03 -15.642  < 2e-16 ***
##    Economy_gp              -5.748e+03  2.397e+03  -2.398  0.01652 *  
##    IBGE_DU_RURAL           -1.102e+00  1.507e-01  -7.317 2.89e-13 ***
##    IBGE_CROP_PRODUCTION_.   1.501e-02  2.342e-03   6.410 1.57e-10 ***
##    IDHM_Longevidade         8.223e+04  7.202e+03  11.417  < 2e-16 ***
##    IDHM_Educacao            5.830e+04  4.005e+03  14.557  < 2e-16 ***
##    Intermediario_Adjacente -2.457e+03  7.792e+02  -3.153  0.00163 ** 
##    Rural_Adjacente         -1.543e+03  6.310e+02  -2.445  0.01452 *  
##    Sem_classificacao        1.006e+05  9.103e+03  11.047  < 2e-16 ***
##    GVA_AGROPEC              3.675e-02  4.028e-03   9.124  < 2e-16 ***
## 
##    ---Significance stars
##    Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
##    Residual standard error: 17260 on 5560 degrees of freedom
##    Multiple R-squared: 0.2802
##    Adjusted R-squared: 0.2791 
##    F-statistic: 240.5 on 9 and 5560 DF,  p-value: < 2.2e-16 
##    ***Extra Diagnostic information
##    Residual sum of squares: 1.657136e+12
##    Sigma(hat): 17251.6
##    AIC:  124505
##    AICc:  124505.1
##    ***********************************************************************
##    *          Results of Geographically Weighted Regression              *
##    ***********************************************************************
## 
##    *********************Model calibration information*********************
##    Kernel function: gaussian 
##    Adaptive bandwidth: 159 (number of nearest neighbours)
##    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.
##    Intercept               -1.2073e+05 -7.0463e+04 -4.2700e+04 -1.0028e+04
##    Economy_gp              -1.8170e+04 -2.8547e+03  3.3032e+03  9.1181e+03
##    IBGE_DU_RURAL           -5.0801e+00 -1.6808e+00 -5.9163e-01 -2.4026e-01
##    IBGE_CROP_PRODUCTION_.  -4.6265e-02 -1.5558e-03  8.8873e-03  1.7413e-02
##    IDHM_Longevidade        -5.2514e+04  1.5048e+04  4.5740e+04  7.5061e+04
##    IDHM_Educacao           -5.6198e+04  1.7337e+04  3.8331e+04  5.9385e+04
##    Intermediario_Adjacente -1.2010e+04 -3.9773e+03 -2.3019e+03 -1.1038e+03
##    Rural_Adjacente         -1.3601e+04 -2.8961e+03 -9.7557e+02  1.0019e+03
##    Sem_classificacao       -2.8667e+04  4.5223e+04  8.6610e+04  1.1767e+05
##    GVA_AGROPEC             -9.5862e-04  2.4915e-02  3.7626e-02  4.9127e-02
##                                  Max.
##    Intercept               3.9952e+04
##    Economy_gp              4.9518e+04
##    IBGE_DU_RURAL           1.4315e+00
##    IBGE_CROP_PRODUCTION_.  7.0300e-02
##    IDHM_Longevidade        1.2971e+05
##    IDHM_Educacao           1.0377e+05
##    Intermediario_Adjacente 1.9509e+03
##    Rural_Adjacente         6.2975e+03
##    Sem_classificacao       1.9488e+05
##    GVA_AGROPEC             1.1370e-01
##    ************************Diagnostic information*************************
##    Number of data points: 5570 
##    Effective number of parameters (2trace(S) - trace(S'S)): 226.0997 
##    Effective degrees of freedom (n-2trace(S) + trace(S'S)): 5343.9 
##    AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 124091.9 
##    AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 123920 
##    Residual sum of squares: 1.455328e+12 
##    R-square value:  0.3678856 
##    Adjusted R-square value:  0.3411359 
## 
##    ***********************************************************************
##    Program stops at: 2020-05-31 23:58:15

Based on the results we can see that the Adjusted R-square value is 0.3411359, which means that with location of each municipalitity and the independent variables it can explain 34.11359 percent the GDP per CAPITA in Brazil.

GDP Per Capita = -7.495e+04 + -5.748e+03(Economy_gp) + -1.102e+00(IBGE_DU_RURAL) + 1.501e-02(IBGE_CROP_PRODUCTION) + -5.2514e+04(IDHM_Longevidade) + -5.6198e+04(IDHM_Educacao) + 1.2010e+04(Intermediario_Adjacente) + -1.3601e+04(Rural_Adjacente) + -2.8667e+04(Sem_classificacao) + -9.5862e-04(GVA_AGROPEC)

8. Visualising GWR Output

8.1 Converting SDF into sf data.frame

Now we going to extract the all the information fall under SDF from gwr.adaptive data set and convert it into sf format with epsg 29101.

gdp_br.sf.adaptive <- st_as_sf(gwr.adaptive$SDF) %>%
  st_transform(crs=29101)

Now we going to drop the geometry columns of the municipalitity point and named it as gdp_br.adaptive.output.

gdp_br.adaptive.output <- gdp_br.sf.adaptive %>%
  st_set_geometry(NULL)

Next we going to combine mun_map.res.sf with as.matrix(gdp_br.adaptive.output). In this data set the geometry is referring to the polygons.

gdp_br.sf.adaptive <- cbind(mun_map.res.sf, as.matrix(gdp_br.adaptive.output))

8.2 Visualising distribution of the Local R2

tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Local_R2",style = "quantile",palette = "Reds",legend.hist = TRUE) +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Distribution of the Local R2 (GDP per CAPITA)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 1,
          legend.text.size = 0.8,
          legend.position = c("left","bottom"),
          legend.outside = TRUE,
          legend.hist.width = 1,
          legend.bg.alpha = 1,
          outer.bg.color = "lightblue") +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

Based on the Local_R2, we can see that the explanation of the GDP per CAPITA can be explained well up to 79% where the location of the municipalitity is at the top-right of the Brazil. The percentage of the explanation start reducing when location of the municipalitity moving down. When the location reaches around center-right, it only can explain around 20% of the GDP per CAPITA. However, when the location continue moving down, it start increases again.

8.3 Visualising Y and Yhat

 map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "y",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = " Y (GDP per CAPITA)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 1,
          legend.text.size = 0.7,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "yhat",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Yhat (GDP per CAPITA)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 1,
          legend.text.size = 0.7,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

The estimated of the GDP per Capita for most of the municipalitities tend to fall within the same category as the actual GDP per Captia. However, there are some municipalitities located around top-left of the Brazil map, which have a slight difference between the acutal and estimated of the GDP per Captia.

8.4 Visualising Economy Group

 map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Economy_gp_SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(Economy Group)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Economy_gp_TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(Econmy Group)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

8.5 Visualising IBGE DU RURAL

map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "IBGE_DU_RURAL_SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(IBGE DU RURAL)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "IBGE_DU_RURAL_TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(IBGE DU RURAL)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

8.6 Visualising IBGE CROP PRODUCTION

map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "IBGE_CROP_PRODUCTION_._SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(IBGE CROP PRODUCTION)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "IBGE_CROP_PRODUCTION_._TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(IBGE CROP PRODUCTION)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

8.7 Visualising IDHM Longevidade

map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "IDHM_Longevidade_SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(IDHM Longevidade)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "IDHM_Longevidade_TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(IDHM Longevidade)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

8.8 Visualising IDHM Educacao

map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "IDHM_Educacao_SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(IDHM Educacao)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "IDHM_Educacao_TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(IDHM Educacao)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

8.9 Visualising Intermediário Adjacente

map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Intermediario_Adjacente_SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(Intermediário Adjacente)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Intermediario_Adjacente_TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(Intermediário Adjacente)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

8.10 Visualising Rural Adjacente

map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Rural_Adjacente_SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(Rural Adjacente)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Rural_Adjacente_TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(Rural Adjacente)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

8.11 Visualising Sem classificação

map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Sem_classificacao_SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(Sem classificação)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "Sem_classificacao_TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(Sem classificação)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)

8.12 Visualising GVA AGROPEC

map1 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "GVA_AGROPEC_SE",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Standard error of the coefficient \n(GVA AGROPEC)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))


map2 <- tm_shape (gdp_br.sf.adaptive) +
  tm_fill (col= "GVA_AGROPEC_TV",style = "quantile",palette = "Reds") +
  tm_borders(alpha = 0.1)+
  tm_layout(main.title = "Variation rate of the coefficient \n(GVA AGROPEC)",
            main.title.position = "center",
          main.title.size = 1.2,
          frame = TRUE,
          legend.title.size = 0.7,
          legend.text.size = 0.6,
          legend.position = c("left","bottom")) +
  tm_compass(cardinal.directions = c("N","E","S","W"),
          type = "4star",
          show.labels = 2, 
          position = c("right","bottom"))

tmap_arrange(map1, map2)