Untitled
Adenilson Borba Lopes da Silva
5 de março de 2019
R Markdown
dados<- read.table("C:\\Users\\USER\\Desktop\\Nova pasta\\Dados_Aula1.txt", header = T)
dadosPrimeiramente iremos ler os dados.
attach(dados)
library(fBasics)## Loading required package: timeDate## Loading required package: timeSerieslibrary(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:fBasics':
##
## tr## The following object is masked from 'package:timeSeries':
##
## outlierApós leitura dos dados iremos analisar!
describe(dados)analisando as variaveis em estudo vemos que PEMED E PIMED tem media igual à 100.67 e 78.31 respectivamente, como tánbem desvio padrões iguais à 28.07 e 23.84. Uma observação importante seria que todas as variaveis tem a média bem proxima da mediana, com excessão da variavel TOTAFIS que tánem tem o maior dos desvios padrão.
a<-round(basicStats(dados),3)
histPlot(as.timeSeries(PEMED))
histPlot(as.timeSeries(PIMED))
histPlot(as.timeSeries(IDADE))
histPlot(as.timeSeries(IMC))
histPlot(as.timeSeries(HRSEDCAL))
histPlot(as.timeSeries(NMEDPAS))
histPlot(as.timeSeries(NMEDPAD))
histPlot(as.timeSeries(MEDCABDO))
histPlot(as.timeSeries(TOTAFIS))
histPlot(as.timeSeries(HDL))
histPlot(as.timeSeries(TG))
histPlot(as.timeSeries(GLICEMIA))
histPlot(as.timeSeries(ESCMATER))
# Comparando os histogramas percebemos que apenas as variáveis GLICEMIA, NMEDPAS E NMEDPAD. Com isso iremos usar o gráfico QQplot para sabermos se as variaveis seguem ou não uma distribuição normal.
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logit## The following object is masked from 'package:fBasics':
##
## densityPlotpar(mfrow= c(2,2))
qqPlot(PEMED)## [1] 337 377qqPlot(PIMED)## [1] 305 369qqPlot(IDADE)## [1] 282 369qqPlot(IMC)
## [1] 385 252qqPlot(HRSEDCAL)## [1] 364 306qqPlot(NMEDPAS)## [1] 64 256qqPlot(NMEDPAD)## [1] 379 210qqPlot(MEDCABDO)
## [1] 75 42qqPlot(TOTAFIS)## [1] 486 441qqPlot(HDL)## [1] 56 164qqPlot(TG)## [1] 213 485qqPlot(GLICEMIA)
## [1] 74 274qqPlot(ESCMATER)## [1] 12 17
#Como era esperado apenas as variáveis GLICEMIA, NMEDPAS E NMEDPAD seguem aproximadamente uma distribuição normal. ## O gráfico de Correlação é dado por:
library(corrplot)## corrplot 0.84 loadedcorrplot(cor(dados), order = "hclust",tl.col = 'black', tl.cex = 0.75)
Após verificarmos a normalidade das variáveis junto a corelção entre elas, iremos em busca de um modelo linear da relação das variáveis de interesse com as demais variáveis.
modelo1<-lm(PEMED~IDADE+IMC+HRSEDCAL+NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+TG+GLICEMIA+ESCMATER)
summary(modelo1)##
## Call:
## lm(formula = PEMED ~ IDADE + IMC + HRSEDCAL + NMEDPAS + NMEDPAD +
## MEDCABDO + TOTAFIS + HDL + TG + GLICEMIA + ESCMATER)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.319 -15.392 -3.154 11.919 132.494
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.915719 26.835516 0.407 0.684351
## IDADE -0.425695 1.106764 -0.385 0.700671
## IMC -1.265368 0.699488 -1.809 0.071038 .
## HRSEDCAL 0.372214 0.627307 0.593 0.553207
## NMEDPAS 0.957581 0.157876 6.065 2.56e-09 ***
## NMEDPAD -0.913729 0.210209 -4.347 1.67e-05 ***
## MEDCABDO 0.915734 0.328320 2.789 0.005481 **
## TOTAFIS 0.013892 0.003573 3.888 0.000115 ***
## HDL -0.302855 0.123333 -2.456 0.014396 *
## TG -0.051642 0.030733 -1.680 0.093496 .
## GLICEMIA 0.288259 0.165993 1.737 0.083062 .
## ESCMATER 0.446438 0.318520 1.402 0.161639
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.42 on 513 degrees of freedom
## Multiple R-squared: 0.1969, Adjusted R-squared: 0.1797
## F-statistic: 11.44 on 11 and 513 DF, p-value: < 2.2e-16Retirando a variável IDADE já que foi ela quem teve maior p-valor.
modelo1 <- lm(PEMED~+IMC+HRSEDCAL+NMEDPAS+NMEDPAD+MEDCABDO+TOTAFIS+HDL+TG+GLICEMIA+ESCMATER)
summary(modelo1)##
## Call:
## lm(formula = PEMED ~ +IMC + HRSEDCAL + NMEDPAS + NMEDPAD + MEDCABDO +
## TOTAFIS + HDL + TG + GLICEMIA + ESCMATER)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.007 -15.617 -3.132 12.247 133.238
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.616437 18.958009 0.191 0.848789
## IMC -1.264080 0.698900 -1.809 0.071086 .
## HRSEDCAL 0.381736 0.626298 0.610 0.542454
## NMEDPAS 0.951391 0.156924 6.063 2.59e-09 ***
## NMEDPAD -0.905115 0.208839 -4.334 1.76e-05 ***
## MEDCABDO 0.908534 0.327514 2.774 0.005738 **
## TOTAFIS 0.013972 0.003564 3.920 0.000101 ***
## HDL -0.303869 0.123202 -2.466 0.013972 *
## TG -0.051071 0.030671 -1.665 0.096502 .
## GLICEMIA 0.294755 0.164994 1.786 0.074615 .
## ESCMATER 0.466305 0.314044 1.485 0.138199
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.4 on 514 degrees of freedom
## Multiple R-squared: 0.1967, Adjusted R-squared: 0.1811
## F-statistic: 12.59 on 10 and 514 DF, p-value: < 2.2e-16retirando a variável HRSEDCAL
modelo1<-lm(PEMED~IMC+NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+TG+GLICEMIA+ESCMATER)
summary(modelo1)##
## Call:
## lm(formula = PEMED ~ IMC + NMEDPAS + NMEDPAD + MEDCABDO + TOTAFIS +
## HDL + TG + GLICEMIA + ESCMATER)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.182 -15.768 -3.251 12.198 132.480
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.819005 18.943526 0.202 0.840309
## IMC -1.240335 0.697387 -1.779 0.075904 .
## NMEDPAS 0.942461 0.156143 6.036 3.03e-09 ***
## NMEDPAD -0.889417 0.207119 -4.294 2.10e-05 ***
## MEDCABDO 0.907415 0.327309 2.772 0.005767 **
## TOTAFIS 0.013925 0.003561 3.910 0.000105 ***
## HDL -0.302036 0.123091 -2.454 0.014467 *
## TG -0.050901 0.030651 -1.661 0.097393 .
## GLICEMIA 0.299799 0.164686 1.820 0.069274 .
## ESCMATER 0.471972 0.313714 1.504 0.133075
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.38 on 515 degrees of freedom
## Multiple R-squared: 0.1961, Adjusted R-squared: 0.1821
## F-statistic: 13.96 on 9 and 515 DF, p-value: < 2.2e-16retirando a variável ESCMATER
modelo1<-lm(PEMED~IMC+NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+TG+GLICEMIA)
summary(modelo1)##
## Call:
## lm(formula = PEMED ~ IMC + NMEDPAS + NMEDPAD + MEDCABDO + TOTAFIS +
## HDL + TG + GLICEMIA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -57.931 -15.891 -3.683 12.657 132.266
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.862387 18.953989 0.257 0.79764
## IMC -1.362617 0.693482 -1.965 0.04996 *
## NMEDPAS 0.920554 0.155653 5.914 6.08e-09 ***
## NMEDPAD -0.878236 0.207239 -4.238 2.67e-05 ***
## MEDCABDO 0.973064 0.324784 2.996 0.00287 **
## TOTAFIS 0.014203 0.003561 3.989 7.61e-05 ***
## HDL -0.288495 0.122911 -2.347 0.01929 *
## TG -0.050492 0.030688 -1.645 0.10051
## GLICEMIA 0.326482 0.163929 1.992 0.04694 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.41 on 516 degrees of freedom
## Multiple R-squared: 0.1926, Adjusted R-squared: 0.1801
## F-statistic: 15.38 on 8 and 516 DF, p-value: < 2.2e-16retirando a variável TG
modelo1<-lm(PEMED~IMC+NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+GLICEMIA)
summary(modelo1)##
## Call:
## lm(formula = PEMED ~ IMC + NMEDPAS + NMEDPAD + MEDCABDO + TOTAFIS +
## HDL + GLICEMIA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -57.830 -15.865 -3.662 12.924 132.629
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.678006 18.953055 0.352 0.72472
## IMC -1.391634 0.694401 -2.004 0.04558 *
## NMEDPAS 0.935003 0.155661 6.007 3.57e-09 ***
## NMEDPAD -0.932204 0.204964 -4.548 6.75e-06 ***
## MEDCABDO 0.929307 0.324228 2.866 0.00432 **
## TOTAFIS 0.014332 0.003566 4.019 6.71e-05 ***
## HDL -0.251250 0.121008 -2.076 0.03836 *
## GLICEMIA 0.302468 0.163547 1.849 0.06497 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.46 on 517 degrees of freedom
## Multiple R-squared: 0.1884, Adjusted R-squared: 0.1774
## F-statistic: 17.14 on 7 and 517 DF, p-value: < 2.2e-16retirando a variável glicemia
modelo1<-lm(PEMED~IMC+NMEDPAS+NMEDPAD+MEDCABDO+TOTAFIS+HDL)
summary(modelo1)##
## Call:
## lm(formula = PEMED ~ IMC + NMEDPAS + NMEDPAD + MEDCABDO + TOTAFIS +
## HDL)
##
## Residuals:
## Min 1Q Median 3Q Max
## -61.04 -15.70 -3.41 11.69 134.07
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 24.584180 16.331486 1.505 0.132850
## IMC -1.458466 0.695079 -2.098 0.036365 *
## NMEDPAS 0.965939 0.155121 6.227 9.84e-10 ***
## NMEDPAD -0.956936 0.205005 -4.668 3.88e-06 ***
## MEDCABDO 0.986000 0.323528 3.048 0.002424 **
## TOTAFIS 0.013974 0.003569 3.915 0.000102 ***
## HDL -0.231477 0.120816 -1.916 0.055922 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.52 on 518 degrees of freedom
## Multiple R-squared: 0.183, Adjusted R-squared: 0.1735
## F-statistic: 19.34 on 6 and 518 DF, p-value: < 2.2e-16retirando a variavel HDL
modelo1<-lm(PEMED~IMC+NMEDPAS+NMEDPAD+MEDCABDO+TOTAFIS)
summary(modelo1)##
## Call:
## lm(formula = PEMED ~ IMC + NMEDPAS + NMEDPAD + MEDCABDO + TOTAFIS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -62.592 -15.986 -3.646 11.463 134.977
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.74726 14.41573 0.676 0.49924
## IMC -1.64006 0.69036 -2.376 0.01788 *
## NMEDPAS 0.96243 0.15551 6.189 1.23e-09 ***
## NMEDPAD -0.95586 0.20553 -4.651 4.20e-06 ***
## MEDCABDO 1.11495 0.31726 3.514 0.00048 ***
## TOTAFIS 0.01442 0.00357 4.040 6.15e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.58 on 519 degrees of freedom
## Multiple R-squared: 0.1772, Adjusted R-squared: 0.1693
## F-statistic: 22.35 on 5 and 519 DF, p-value: < 2.2e-16Por fim chegamos ao modelo final que descreve a variavel PEMED = 9.7472 - 1.64IMC +0.9624NMEDPAS -0.95586NMEDPAD + 1.1149MEDCABDO +0.01442TOTAFIS
Fazendo o mesmo para a variável PIMED.
modelo2<-lm(PIMED~IDADE+IMC+HRSEDCAL+NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+TG+GLICEMIA+ESCMATER)
summary(modelo2)##
## Call:
## lm(formula = PIMED ~ IDADE + IMC + HRSEDCAL + NMEDPAS + NMEDPAD +
## MEDCABDO + TOTAFIS + HDL + TG + GLICEMIA + ESCMATER)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.083 -14.768 -0.931 12.424 86.327
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.466041 22.279458 -0.784 0.433430
## IDADE -0.924230 0.918861 -1.006 0.314965
## IMC -0.706403 0.580731 -1.216 0.224390
## HRSEDCAL -0.531781 0.520804 -1.021 0.307699
## NMEDPAS 0.917379 0.131073 6.999 8.10e-12 ***
## NMEDPAD -0.686498 0.174520 -3.934 9.52e-05 ***
## MEDCABDO 0.697984 0.272579 2.561 0.010732 *
## TOTAFIS 0.010167 0.002967 3.427 0.000659 ***
## HDL -0.204687 0.102394 -1.999 0.046133 *
## TG -0.036578 0.025515 -1.434 0.152296
## GLICEMIA 0.446816 0.137811 3.242 0.001263 **
## ESCMATER -0.254201 0.264443 -0.961 0.336868
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.1 on 513 degrees of freedom
## Multiple R-squared: 0.2325, Adjusted R-squared: 0.216
## F-statistic: 14.13 on 11 and 513 DF, p-value: < 2.2e-16Retirando a variavel IDADE
modelo2<-lm(PIMED~IMC+HRSEDCAL+NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+TG+GLICEMIA+ESCMATER)
summary(modelo2)##
## Call:
## lm(formula = PIMED ~ IMC + HRSEDCAL + NMEDPAS + NMEDPAD + MEDCABDO +
## TOTAFIS + HDL + TG + GLICEMIA + ESCMATER)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.468 -14.576 -0.973 12.562 87.402
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -33.313593 15.752613 -2.115 0.034928 *
## IMC -0.703607 0.580731 -1.212 0.226226
## HRSEDCAL -0.511107 0.520404 -0.982 0.326496
## NMEDPAS 0.903941 0.130391 6.933 1.24e-11 ***
## NMEDPAD -0.667796 0.173529 -3.848 0.000134 ***
## MEDCABDO 0.682353 0.272139 2.507 0.012470 *
## TOTAFIS 0.010340 0.002962 3.491 0.000522 ***
## HDL -0.206891 0.102372 -2.021 0.043800 *
## TG -0.035338 0.025486 -1.387 0.166163
## GLICEMIA 0.460919 0.137097 3.362 0.000831 ***
## ESCMATER -0.211069 0.260945 -0.809 0.418969
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.1 on 514 degrees of freedom
## Multiple R-squared: 0.231, Adjusted R-squared: 0.216
## F-statistic: 15.44 on 10 and 514 DF, p-value: < 2.2e-16Retirando a variável ESCMATER
modelo2<-lm(PIMED~IMC+HRSEDCAL+NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+TG+GLICEMIA)
summary(modelo2)##
## Call:
## lm(formula = PIMED ~ IMC + HRSEDCAL + NMEDPAS + NMEDPAD + MEDCABDO +
## TOTAFIS + HDL + TG + GLICEMIA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -57.187 -15.149 -1.309 12.452 87.543
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -33.773178 15.737078 -2.146 0.032332 *
## IMC -0.648195 0.576482 -1.124 0.261369
## HRSEDCAL -0.523568 0.520002 -1.007 0.314476
## NMEDPAS 0.913437 0.129818 7.036 6.32e-12 ***
## NMEDPAD -0.672279 0.173382 -3.877 0.000119 ***
## MEDCABDO 0.652984 0.269615 2.422 0.015783 *
## TOTAFIS 0.010215 0.002957 3.455 0.000596 ***
## HDL -0.212881 0.102069 -2.086 0.037501 *
## TG -0.035516 0.025476 -1.394 0.163895
## GLICEMIA 0.449161 0.136279 3.296 0.001049 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.1 on 515 degrees of freedom
## Multiple R-squared: 0.23, Adjusted R-squared: 0.2165
## F-statistic: 17.09 on 9 and 515 DF, p-value: < 2.2e-16Retirando a variavel HRSEDCAL
modelo2<-lm(PIMED~IMC+NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+TG+GLICEMIA)
summary(modelo2)##
## Call:
## lm(formula = PIMED ~ IMC + NMEDPAS + NMEDPAD + MEDCABDO + TOTAFIS +
## HDL + TG + GLICEMIA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.194 -14.877 -1.359 12.524 86.811
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -34.068190 15.734560 -2.165 0.030831 *
## IMC -0.678748 0.575691 -1.179 0.238936
## NMEDPAS 0.926047 0.129214 7.167 2.67e-12 ***
## NMEDPAD -0.693993 0.172038 -4.034 6.31e-05 ***
## MEDCABDO 0.653438 0.269618 2.424 0.015712 *
## TOTAFIS 0.010275 0.002956 3.476 0.000552 ***
## HDL -0.215619 0.102034 -2.113 0.035063 *
## TG -0.035755 0.025475 -1.404 0.161061
## GLICEMIA 0.441803 0.136084 3.247 0.001244 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.1 on 516 degrees of freedom
## Multiple R-squared: 0.2285, Adjusted R-squared: 0.2165
## F-statistic: 19.1 on 8 and 516 DF, p-value: < 2.2e-16Retirando a variavel IMC
modelo2<-lm(PIMED~NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+TG+GLICEMIA)
summary(modelo2)##
## Call:
## lm(formula = PIMED ~ NMEDPAS + NMEDPAD + MEDCABDO + TOTAFIS +
## HDL + TG + GLICEMIA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -56.286 -14.936 -1.156 12.322 87.195
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -29.255726 15.201637 -1.925 0.054839 .
## NMEDPAS 0.947570 0.127966 7.405 5.37e-13 ***
## NMEDPAD -0.715083 0.171170 -4.178 3.46e-05 ***
## MEDCABDO 0.369939 0.122011 3.032 0.002551 **
## TOTAFIS 0.010184 0.002956 3.445 0.000617 ***
## HDL -0.232759 0.101031 -2.304 0.021628 *
## TG -0.036519 0.025477 -1.433 0.152339
## GLICEMIA 0.450480 0.135937 3.314 0.000985 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.11 on 517 degrees of freedom
## Multiple R-squared: 0.2264, Adjusted R-squared: 0.2159
## F-statistic: 21.61 on 7 and 517 DF, p-value: < 2.2e-16retiramos a variavel TG
modelo2<-lm(PIMED~NMEDPAS+NMEDPAD+MEDCABDO+
TOTAFIS+HDL+GLICEMIA)
summary(modelo2)##
## Call:
## lm(formula = PIMED ~ NMEDPAS + NMEDPAD + MEDCABDO + TOTAFIS +
## HDL + GLICEMIA)
##
## Residuals:
## Min 1Q Median 3Q Max
## -55.516 -14.716 -1.275 12.215 86.441
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -27.792813 15.182774 -1.831 0.067742 .
## NMEDPAS 0.958693 0.127861 7.498 2.83e-13 ***
## NMEDPAD -0.754794 0.169085 -4.464 9.88e-06 ***
## MEDCABDO 0.329498 0.118825 2.773 0.005755 **
## TOTAFIS 0.010275 0.002958 3.473 0.000557 ***
## HDL -0.206334 0.099436 -2.075 0.038476 *
## GLICEMIA 0.433368 0.135549 3.197 0.001473 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21.13 on 518 degrees of freedom
## Multiple R-squared: 0.2233, Adjusted R-squared: 0.2143
## F-statistic: 24.82 on 6 and 518 DF, p-value: < 2.2e-16assim ficou o modelo PIMED= -27.792 +0.9586NMEPAS - 0.7579NMEPAD + 0.3294MEDCABDO + 0.0102TOTAFIS - 0.2063HDL+ 0.4333GLICEMIA
Por fim fizemos a analise dos residuos do cada modelo
par(mfrow= c(1,1))
plot(modelo1)
plot(modelo2)
