0. Datos.

Los datos son tomados del libro Diseño y análisis de experimentos de Douglas Montgomery. Página 232.

A<-c(-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1)
B<-c(-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1)
C<-c(-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1)
altura<-c(-3,-1,0,1,-1,0,2,3,-1,0,2,1,1,1,6,5)
datos<-data.frame(A,B,C,altura)

1. Gráfico de interacciones.

interaction.plot(A,B,altura,legend=TRUE)

interaction.plot(A,C,altura,legend=TRUE)

interaction.plot(B,C,altura,legend=TRUE)

2. Interaccciones triples.

cubePlot(obj = altura, eff1 = A, eff2 = B, eff3 = C, 
         main = " Gráfico de interacción")

3. Efecto de los factores.

redos<-lm(altura~A+B+C+A*B+A*C+B*C+A*B*C)
summary(redos)
## 
## Call:
## lm.default(formula = altura ~ A + B + C + A * B + A * C + B * 
##     C + A * B * C)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##   -1.0   -0.5    0.0    0.5    1.0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.0000     0.1976   5.060 0.000977 ***
## A             1.5000     0.1976   7.589 6.37e-05 ***
## B             1.1250     0.1976   5.692 0.000459 ***
## C             0.8750     0.1976   4.427 0.002205 ** 
## A:B           0.3750     0.1976   1.897 0.094350 .  
## A:C           0.1250     0.1976   0.632 0.544737    
## B:C           0.2500     0.1976   1.265 0.241504    
## A:B:C         0.2500     0.1976   1.265 0.241504    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7906 on 8 degrees of freedom
## Multiple R-squared:  0.9359, Adjusted R-squared:  0.8798 
## F-statistic: 16.69 on 7 and 8 DF,  p-value: 0.0003474
coe<-coefficients(redos)
efectos<-2*coefficients(redos)
EF<-efectos[-1]
EF
##     A     B     C   A:B   A:C   B:C A:B:C 
##  3.00  2.25  1.75  0.75  0.25  0.50  0.50

4. Análisis de varianza.

anova<-aov(altura~A+B+C+A*B+A*C+B*C+A*B*C)
summary(anova)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## A            1  36.00   36.00    57.6 6.37e-05 ***
## B            1  20.25   20.25    32.4 0.000459 ***
## C            1  12.25   12.25    19.6 0.002205 ** 
## A:B          1   2.25    2.25     3.6 0.094350 .  
## A:C          1   0.25    0.25     0.4 0.544737    
## B:C          1   1.00    1.00     1.6 0.241504    
## A:B:C        1   1.00    1.00     1.6 0.241504    
## Residuals    8   5.00    0.63                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

5. Predichos.

pre<-predict(redos);pre
##    1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16 
## -2.0 -2.0  0.5  0.5 -0.5 -0.5  2.5  2.5 -0.5 -0.5  1.5  1.5  1.0  1.0  5.5  5.5

6. Residuos.

resi<-resid(redos);resi
##             1             2             3             4             5 
## -1.000000e+00  1.000000e+00 -5.000000e-01  5.000000e-01 -5.000000e-01 
##             6             7             8             9            10 
##  5.000000e-01 -5.000000e-01  5.000000e-01 -5.000000e-01  5.000000e-01 
##            11            12            13            14            15 
##  5.000000e-01 -5.000000e-01  2.775558e-17  2.775558e-17  5.000000e-01 
##            16 
## -5.000000e-01

7. Gráfico Q-Q.

qqnorm(resi)
qqline(resi)

8. Gráfico Predichos VS Residuos.

plot(pre,resi)
abline(h=0)

9. Gráfico de superficie de respuesta.

x<-seq(-1,1,length=50)
y<-x
f<-function(x,y){
f<-coe[1]+coe[2]*x+coe[3]*y+coe[4]*x*y
}
z<-outer(x,y,f)
persp(x,y,z,theta=45,phi=45)

10. Gráfico de contorno.

contour(x,y,z)

11. Gráfico de Pareto.

efe<-EF
efecto<-abs(efe)
names(efecto)<-c("A","B","C","AB","AC","BC","ABC" )
pareto.chart(efecto, cumperc = seq(0, 100, by = 5), ylab2 = "A finer tickmarks grid")

##      
## Pareto chart analysis for efecto
##        Frequency  Cum.Freq. Percentage Cum.Percent.
##   A     3.000000   3.000000  33.333333    33.333333
##   B     2.250000   5.250000  25.000000    58.333333
##   C     1.750000   7.000000  19.444444    77.777778
##   AB    0.750000   7.750000   8.333333    86.111111
##   ABC   0.500000   8.250000   5.555556    91.666667
##   BC    0.500000   8.750000   5.555556    97.222222
##   AC    0.250000   9.000000   2.777778   100.000000

12. Gráfico de Daniel.

DanielPlot(redos, half = TRUE, main = "Half-Normal Plot")

13. Gráfico de Length.

LenthPlot(redos,main="Length Plot")

##    alpha      PSE       ME      SME 
## 0.050000 0.937500 3.528865 8.445288