Banco de dados

     Os dados em questão são referentes a quantidade de crianças atendidas em alguma unidade de saúde no munícipio de Campina Grande - PB, com variáveis a respeito da qualidade da água que abastece a cidade.

Crianças com diarréia na cidade de Campina Grande/PB comvariáveis de qualidade da água.
ANO_MES Qtd_c VOLUME Ph COR TURBIDEZ CLORO CLORETO Coli
jan/06 326 87.3 7.7 5.9 0.9 1.4 81.2 N
fev/06 199 85.8 7.7 5.6 0.9 1.6 78.4 N
mar/06 239 85.7 7.6 5.1 1.0 1.6 79.4 N
abr/06 356 94.4 7.6 5.6 0.8 1.4 83.6 N
mai/06 540 100.0 7.4 6.5 1.3 1.4 83.6 N
jun/06 241 100.0 7.1 11.3 2.6 1.6 80.6 N
jul/06 319 100.0 7.2 7.2 1.3 1.6 74.7 N
ago/06 605 99.6 7.2 5.0 0.9 1.6 72.4 N
set/06 385 97.0 7.2 5.2 0.8 1.6 75.3 N
out/06 287 94.3 7.3 7.4 0.6 1.5 77.2 N

Descrição das variáveis

  • AN0_MES: Data de registros dos casos.
  • Qtd_c: Quantidade de registros de crianças por mês com diarréia.
  • VOLUME: Proporção do volume de água no açude Boqueirão (Epitácio Pessoa).
  • Ph: Medida do potencial Hidrogeniônico (pH) encontrado na água.
  • COR: Mede o grau de coloração da água.
  • TURBIDEZ: Mede o nível de transparência da água e tem relação direta com a presença de partículas em suspensão..
  • CLORO: Quantidade de cloro encontrado na água.
  • CLORETO: Quantidade de cloreto encontrado na água.
  • Coli: A presença de coliformes fecais na água.

Análise Descritiva

Primeiras Impressões

Análise descritiva.
Qtd_c VOLUME Ph COR TURBIDEZ CLORO CLORETO
nobs 132.00 132.00 132.00 132.00 132.00 132.00 132.00
NAs 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Minimum 60.00 4.80 6.20 1.40 0.37 0.00 41.70
Maximum 1367.00 100.00 45.50 25.72 6.58 5.00 532.10
1. Quartile 206.50 32.38 7.30 4.55 0.87 1.00 95.75
3. Quartile 439.50 94.30 7.70 8.60 1.58 1.60 316.85
Mean 353.73 66.53 7.77 6.94 1.39 1.52 205.78
Median 300.50 84.75 7.57 6.15 1.12 1.30 155.90
Sum 46693.00 8782.10 1025.97 916.24 182.84 201.28 27162.30
SE Mean 19.05 2.89 0.29 0.33 0.08 0.09 10.79
LCL Mean 316.05 60.81 7.20 6.29 1.24 1.34 184.44
UCL Mean 391.42 72.25 8.34 7.59 1.54 1.71 227.11
Variance 47898.03 1105.00 11.04 14.29 0.76 1.15 15354.62
Stdev 218.86 33.24 3.32 3.78 0.87 1.07 123.91
Skewness 1.54 -0.62 11.09 1.94 2.87 2.00 0.65
Kurtosis 3.37 -1.24 123.02 6.45 11.28 3.74 -0.82

Analisando a variável Coli:

pH

Gráfico

Estimando o valor

     Utilizando o método de métodos das Médias Móveis, com um lag igual a 6:

     A partir da função forecast podemos estimar o valor do pH para Outubro de 2015:

##     Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## 118        7.63122 7.303683 7.958758 7.130295 8.132146

     Substituindo esse valor nos dados:

Cenários

Criança x Volume

Modelo

## 
## Call:
## tsglm(ts = ts_0_9, model = list(past_obs = 1, past_mean = 13), 
##     xreg = ts_var, link = "log", distr = "nbinom")
## 
## Coefficients:
##              Estimate  Std.Error  CI(lower)  CI(upper)
## (Intercept)   2.31291    0.58995    1.15663   3.469183
## beta_1        0.67867    0.07891    0.52402   0.833333
## alpha_13     -0.03739    0.08546   -0.20489   0.130115
## VOLUME       -0.00306    0.00122   -0.00545  -0.000671
## sigmasq       0.14650         NA         NA         NA
## Standard errors and confidence intervals (level =  95 %) obtained
## by normal approximation.
## 
## Link function: log 
## Distribution family: nbinom (with overdispersion coefficient 'sigmasq') 
## Number of coefficients: 5 
## Log-likelihood: -808.0073 
## AIC: 1626.015 
## BIC: 1640.429 
## QIC: 7423.146

Verificando o Ajuste

Gráfico

Criança x pH

Modelo

## 
## Call:
## tsglm(ts = ts_0_9, model = list(past_obs = 1, past_mean = 13), 
##     xreg = ts_var, link = "log", distr = "nbinom")
## 
## Coefficients:
##              Estimate  Std.Error  CI(lower)  CI(upper)
## (Intercept)    5.6315     0.9058      3.856     7.4069
## beta_1         0.4445     0.0672      0.313     0.5762
## alpha_13      -0.0985     0.0744     -0.244     0.0473
## Ph            -0.2333     0.1370     -0.502     0.0353
## sigmasq        0.1954         NA         NA         NA
## Standard errors and confidence intervals (level =  95 %) obtained
## by normal approximation.
## 
## Link function: log 
## Distribution family: nbinom (with overdispersion coefficient 'sigmasq') 
## Number of coefficients: 5 
## Log-likelihood: -837.3023 
## AIC: 1684.605 
## BIC: 1699.019 
## QIC: 10870.98

Verificando o Ajuste

Gráfico

Criança x COR

Modelo

## 
## Call:
## tsglm(ts = ts_0_9, model = list(past_obs = 1, past_mean = 13), 
##     xreg = ts_var, link = "log", distr = "nbinom")
## 
## Coefficients:
##              Estimate  Std.Error  CI(lower)  CI(upper)
## (Intercept)    1.2868     0.5415     0.2255     2.3480
## beta_1         0.7826     0.0747     0.6361     0.9290
## alpha_13       0.0104     0.0905    -0.1671     0.1878
## COR           -0.0069     0.0104    -0.0273     0.0135
## sigmasq        0.1638         NA         NA         NA
## Standard errors and confidence intervals (level =  95 %) obtained
## by normal approximation.
## 
## Link function: log 
## Distribution family: nbinom (with overdispersion coefficient 'sigmasq') 
## Number of coefficients: 5 
## Log-likelihood: -811.7259 
## AIC: 1633.452 
## BIC: 1647.866 
## QIC: 7922.617

Verificando o Ajuste

Gráfico

Criança x Turbidez

Modelo

## 
## Call:
## tsglm(ts = ts_0_9, model = list(past_obs = 1, past_mean = 13), 
##     xreg = ts_var, link = "log", distr = "nbinom")
## 
## Coefficients:
##               Estimate  Std.Error  CI(lower)  CI(upper)
## (Intercept)   1.400384     0.5609      0.301     2.4997
## beta_1        0.769270     0.0730      0.626     0.9124
## alpha_13      0.000703     0.0923     -0.180     0.1815
## TURBIDEZ     -0.017777     0.0439     -0.104     0.0682
## sigmasq       0.160085         NA         NA         NA
## Standard errors and confidence intervals (level =  95 %) obtained
## by normal approximation.
## 
## Link function: log 
## Distribution family: nbinom (with overdispersion coefficient 'sigmasq') 
## Number of coefficients: 5 
## Log-likelihood: -811.5445 
## AIC: 1633.089 
## BIC: 1647.503 
## QIC: 7903.594

Verificando o Ajuste

Gráfico

Criança x Cloro

Modelo

## 
## Call:
## tsglm(ts = ts_0_9, model = list(past_obs = 1, past_mean = 13), 
##     xreg = ts_var, link = "log", distr = "nbinom")
## 
## Coefficients:
##               Estimate  Std.Error  CI(lower)  CI(upper)
## (Intercept)   1.468787     0.5673     0.3568     2.5807
## beta_1        0.759892     0.0732     0.6165     0.9033
## alpha_13     -0.000333     0.0918    -0.1802     0.1795
## CLORO        -0.020234     0.0364    -0.0916     0.0511
## sigmasq       0.158208         NA         NA         NA
## Standard errors and confidence intervals (level =  95 %) obtained
## by normal approximation.
## 
## Link function: log 
## Distribution family: nbinom (with overdispersion coefficient 'sigmasq') 
## Number of coefficients: 5 
## Log-likelihood: -811.3673 
## AIC: 1632.735 
## BIC: 1647.149 
## QIC: 7868.411

Verificando o Ajuste

Gráfico

Criança x Cloreto

Modelo

## 
## Call:
## tsglm(ts = ts_0_9, model = list(past_obs = 1, past_mean = 13), 
##     xreg = ts_var, link = "log", distr = "nbinom")
## 
## Coefficients:
##               Estimate  Std.Error  CI(lower)  CI(upper)
## (Intercept)   1.616711   0.584892   4.70e-01    2.76308
## beta_1        0.709379   0.076182   5.60e-01    0.85869
## alpha_13     -0.001884   0.098959  -1.96e-01    0.19207
## CLORETO       0.000586   0.000326  -5.33e-05    0.00123
## sigmasq       0.149758         NA         NA         NA
## Standard errors and confidence intervals (level =  95 %) obtained
## by normal approximation.
## 
## Link function: log 
## Distribution family: nbinom (with overdispersion coefficient 'sigmasq') 
## Number of coefficients: 5 
## Log-likelihood: -809.1632 
## AIC: 1628.326 
## BIC: 1642.74 
## QIC: 7494.836

Verificando o Ajuste

Gráfico

Criança x Coliformes

Modelo

## 
## Call:
## tsglm(ts = ts_0_9, model = list(past_obs = 1, past_mean = 13), 
##     xreg = ts_var, link = "log", distr = "nbinom")
## 
## Coefficients:
##              Estimate  Std.Error  CI(lower)  CI(upper)
## (Intercept)   1.37288     0.5955      0.206      2.540
## beta_1        0.75856     0.0792      0.603      0.914
## alpha_13      0.00305     0.0973     -0.188      0.194
## Coli          0.04572     0.1080     -0.166      0.257
## sigmasq       0.15769         NA         NA         NA
## Standard errors and confidence intervals (level =  95 %) obtained
## by normal approximation.
## 
## Link function: log 
## Distribution family: nbinom (with overdispersion coefficient 'sigmasq') 
## Number of coefficients: 5 
## Log-likelihood: -810.956 
## AIC: 1631.912 
## BIC: 1646.326 
## QIC: 7851.867

Verificando o Ajuste

EDA

Matriz de correlação

Volume x Cloreto

Previsões