análises de dados
DESCRIPTION
Análise de dados usando R para construir AnovaTRANSCRIPT
-
Planejamento de Experimento
Aplicacao em dados de usinagem
Modelo Linear e ANOVA
SAO CARLOS - SP21 de julho de 2014
-
1 Dados
Fatores RespostasS f e Temp Dureza T Residual modulo T escoamento
1350 50 0.10 25 329.40 263.80 175235 900.001350 60 0.01 200 360.40 264.70 164729 785.381350 70 0.00 340 330.80 282.00 151254 663.701500 50 0.01 340 333.20 217.50 159514 728.971500 60 0.00 25 346.40 243.20 180175 932.261500 70 0.10 200 319.20 228.10 154635 805.371650 50 0.00 200 317.80 226.50 150000 800.001650 60 0.10 340 331.80 231.80 156571 734.521650 70 0.01 25 323.80 241.20 164109 853.11
2 Analise para Dureza
1
-
2.1 Modelo Linear
lm(formula = Dureza ~ S + f + S * f - 1, data = dados)
Residuals:
Min 1Q Median 3Q Max
-15.0228 -12.7023 0.1528 6.3127 20.9378
Coefficients:
Estimate Std. Error t value Pr(>|t|)
S 0.2239397 0.0244252 9.168 9.48e-05 ***
f 6.7058182 1.0058742 6.667 0.000551 ***
S:f -0.0045087 0.0007787 -5.790 0.001162 **
Residual standard error: 14.87 on 6 degrees of freedom
Multiple R-squared: 0.9987,Adjusted R-squared: 0.998
F-statistic: 1500 on 3 and 6 DF, p-value: 5.157e-09
Analysis of Variance Table
Response: Dureza
Df Sum Sq Mean Sq F value Pr(>F)
S 1 985499 985499 4456.890 7.598e-10 ***
f 1 2422 2422 10.952 0.016217 *
S:f 1 7412 7412 33.520 0.001162 **
Residuals 6 1327 221
2.2 Modelo Ajustado
2
-
2.3 Graficos de Diagnostico e Resduos
2.4 Teste de Normalidade dos Resduos
Test Statistic Valor-pK Smirnov 0.1702 0.7875
Shapiro.Wilk 0.966 0.8429Ad.Darling 0.2458 0.7004
3
-
3 Analise para Tensao Residual
3.1 Modelo
lm(formula = T_Residual ~ -1 + S + f + e + S * f + f * e, data = dados)
Residuals:
1 2 3 4 5 6 7
-0.4067 6.4931 0.5928 -11.9560 -2.2009 -1.3092 8.3407
8 9
2.4105 -2.1560
4
-
Coefficients:
Estimate Std. Error t value Pr(>|t|)
S 8.814e-02 1.738e-02 5.073 0.007116 **
f 6.269e+00 5.899e-01 10.628 0.000444 ***
e 1.886e+03 4.663e+02 4.044 0.015548 *
S:f -2.922e-03 5.313e-04 -5.499 0.005332 **
f:e -3.192e+01 7.755e+00 -4.117 0.014651 *
Residual standard error: 8.249 on 4 degrees of freedom
Multiple R-squared: 0.9995,Adjusted R-squared: 0.9989
F-statistic: 1589 on 5 and 4 DF, p-value: 1.108e-06
anova(modelo)
Analysis of Variance Table
Response: T_Residual
Df Sum Sq Mean Sq F value Pr(>F)
S 1 528260 528260 7762.5630 9.949e-08 ***
f 1 4766 4766 70.0306 0.001115 **
e 1 8 8 0.1134 0.753199
S:f 1 6415 6415 94.2667 0.000630 ***
f:e 1 1153 1153 16.9475 0.014651 *
Residuals 4 272 68
Obs: N~ao se retira a covaravel "e" do modelo porque a
interac~ao f:e e significativa
3.2 Modelo Ajustado
5
-
3.3 Graficos de Diagnostico e Resduos
3.4 Teste de Normalidade dos Resduos
Test Statistic Valor-pK Smirnov 0.177 0.895
Shapiro.Wilk 0.971 0.900Ad.Darling 0.223 0.752
6
-
4 Analise para Modulo
4.1 Modelo
lm(formula = modulo ~ -1 + S + f + Temp + S:f, data = dados)
Residuals:
1 2 3 4 5 6 7
885.2 864.9 -4514.8 5963.9 7253.0 -4194.4 -13824.5
8 9
8055.6 -171.4
7
-
Coefficients:
Estimate Std. Error t value Pr(>|t|)
S 124.9834 14.8370 8.424 0.000387 ***
f 3392.7811 605.0462 5.607 0.002494 **
Temp -68.2949 23.0054 -2.969 0.031206 *
S:f -2.4046 0.4682 -5.136 0.003658 **
Residual standard error: 8760 on 5 degrees of freedom
Multiple R-squared: 0.9984,Adjusted R-squared: 0.9971
F-statistic: 769.1 on 4 and 5 DF, p-value: 3.708e-07
anova(modelo)
Analysis of Variance Table
Response: modulo
Df Sum Sq Mean Sq F value Pr(>F)
S 1 2.3340e+11 2.3340e+11 3041.2701 3.708e-08 ***
f 1 3.7615e+08 3.7615e+08 4.9013 0.077723 .
Temp 1 3.0229e+08 3.0229e+08 3.9389 0.103957
S:f 1 2.0244e+09 2.0244e+09 26.3786 0.003658 **
Residuals 5 3.8372e+08 7.6744e+07
Obs: Modelo selecionado pelo StepAIC
4.2 Modelo Ajustado
8
-
4.3 Graficos de Diagnostico e Resduos
4.4 Teste de Normalidade dos Resduos
Test Statistic Valor-pK Smirnov 0.153 0.964
Shapiro.Wilk 0.957 0.766Ad.Darling 0.188 0.863
9
-
5 Analise para Tensao de Escoamento
5.1 Modelo
lm(formula = T_escoamento ~ -1 + S + f + Temp + S * f, data = dados)
Residuals:
1 2 3 4 5 6
1.25621 0.05991 -30.61351 8.66375 27.35082 29.69778
7 8 9
-33.29145 23.86161 -26.33807
10
-
Coefficients:
Estimate Std. Error t value Pr(>|t|)
S 0.682553 0.053639 12.725 5.33e-05 ***
f 14.098120 2.187392 6.445 0.001337 **
Temp -0.640490 0.083170 -7.701 0.000589 ***
S:f -0.010542 0.001693 -6.228 0.001561 **
Residual standard error: 31.67 on 5 degrees of freedom
Multiple R-squared: 0.9991,Adjusted R-squared: 0.9984
F-statistic: 1450 on 4 and 5 DF, p-value: 7.612e-08
Analysis of Variance Table
Response: T_escoamento
Df Sum Sq Mean Sq F value Pr(>F)
S 1 5733248 5733248 5715.819 7.67e-09 ***
f 1 3005 3005 2.996 0.144025
Temp 1 43583 43583 43.450 0.001207 **
S:f 1 38912 38912 38.793 0.001561 **
Residuals 5 5015 1003
Obs: N~ao se retira a covaravel "f" do modelo porque a
interac~ao S:f e significativa
5.2 Modelo Ajustado
11
-
5.3 Graficos de Diagnostico e Resduos
5.4 Teste de Normalidade dos Resduos
Test Statistic Valor-pK Smirnov 0.252 0.537
Shapiro.Wilk 0.844 0.064Ad.Darling 0.586 0.089
12
-
6 Codigo
# ------------------- Pacotes ----------------------
library(MASS)
require(stats)
require(nortest)
require(xtable)
library(xtable)
# ---------------------------- Dados ------------------
dados
-
"T.Escoamento")
boxplot(T_escoamento~cbind(Temp,e,f,S),col="green",data=data1,add=T)
boxplot(T_escoamento~cbind(f,Temp,e,S),col="cyan",data=data1,add=T)
boxplot(T_escoamento~cbind(S,Temp,e,f),col="red",data=data1,add=T)
title("Tens~ao de Escoamento")
legend("topright", col=c("gold", "green", "cyan", "red") ,
legend = c("e", "T", "f", "S"), bty=n, lty=c(4,3,2,1) ,
cex=0.8, pch=16 )
# ----------------- Modelo - Dureza ----------------
modelo
-
qqnorm(sdres, pch=19, col="red", xlab="Quantis teoricos", ylab="Quantis
amostrais", main="Normal Q-Q plot dos Resduos", cex.main=1)
qqline(sdres, col="blue3")
# grafico resduos x valores ajustados
plot(ajus,sdres,pch=19,col="red", xlab="Valores ajustados", ylab="Resduos
padronizados", main="Resduos x Ajustados", cex.main=1)
lines(c(0,max(ajus)),c(0,0),lty=2)
# resduos x ordem (timeplot)
plot(sdres, main="Resduos x ordem", ylab="Resduos padronizados", pch=19,
col="red3", cex.main=1)
lines(sdres, col="blue3")
lines(c(0,max(ajus)),c(0,0),lty=2)
par(mfrow = c(1,1))
# ----------------- Modelo - Tens~ao Residual ----------------
dados
modelo
-
## Analise grafica para verificac~ao das suposic~oes
## do modelo (normalidade e igualdade de varia^ncias)
par(mfrow = c(1,2))
# histograma dos resduos
hist(sdres, col = "bisque", xlab="Resduos padronizados",
main="Histograma dos Resduos", cex.main=1)
# grafico normal qq-plot dos resduos
qqnorm(sdres, pch=19, col="red", xlab="Quantis teoricos", ylab="Quantis
amostrais", main="Normal Q-Q plot dos Resduos", cex.main=1)
qqline(sdres, col="blue3")
# grafico resduos x valores ajustados
plot(ajus,sdres,pch=19,col="red", xlab="Valores ajustados", ylab="Resduos
padronizados", main="Resduos x Ajustados", cex.main=1)
lines(c(0,max(ajus)),c(0,0),lty=2)
# resduos x ordem (timeplot)
plot(sdres, main="Resduos x ordem", ylab="Resduos padronizados", pch=19,
col="red3", cex.main=1)
lines(sdres, col="blue3")
lines(c(0,max(ajus)),c(0,0),lty=2)
par(mfrow = c(1,1))
# ----------------- Modelo - Modulo ----------------
dados
modelo
-
hist(sdres, col = "bisque", xlab="Resduos padronizados", main="Histograma
dos Resduos", cex.main=1)
# grafico normal qq-plot dos resduos
qqnorm(sdres, pch=19, col="red", xlab="Quantis teoricos", ylab="Quantis
amostrais", main="Normal Q-Q plot dos Resduos", cex.main=1)
qqline(sdres, col="blue3")
# grafico resduos x valores ajustados
plot(ajus,sdres,pch=19,col="red", xlab="Valores ajustados", ylab="Resduos
padronizados", main="Resduos x Ajustados", cex.main=1)
lines(c(0,max(ajus)),c(0,0),lty=2)
# resduos x ordem (timeplot)
plot(sdres, main="Resduos x ordem", ylab="Resduos padronizados", pch=19,
col="red3", cex.main=1)
lines(sdres, col="blue3")
lines(c(0,max(ajus)),c(0,0),lty=2)
par(mfrow = c(1,1))
KS
-
" = 0.682*S + 14.098*f -0.641*T -0.011*S:f "))), bty="n", cex=0.8)
## Analise grafica para verificac~ao das suposic~oes
## do modelo (normalidade e igualdade de varia^ncias)
par(mfrow = c(1,2))
# histograma dos resduos
hist(sdres, col = "bisque", xlab="Resduos padronizados", main="Histograma
dos Resduos", cex.main=1)
# grafico normal qq-plot dos resduos
qqnorm(sdres, pch=19, col="red", xlab="Quantis teoricos", ylab="Quantis
amostrais", main="Normal Q-Q plot dos Resduos", cex.main=1)
qqline(sdres, col="blue3")
# grafico resduos x valores ajustados
plot(ajus,sdres,pch=19,col="red", xlab="Valores ajustados", ylab="Resduos
padronizados", main="Resduos x Ajustados", cex.main=1)
lines(c(0,max(ajus)),c(0,0),lty=2)
# resduos x ordem (timeplot)
plot(sdres, main="Resduos x ordem", ylab="Resduos padronizados",
pch=19, col="red3", cex.main=1)
lines(sdres, col="blue3")
lines(c(0,max(ajus)),c(0,0),lty=2)
par(mfrow = c(1,1))
KS