FA 16
Muneeb
11/11/2021
FA 16
In a process development study on yield, four factors were studied, each at two levels: time (A), concentration (B), pressure (C), and temperature (D).
Part A:
a) Display the halfnormal plot for this data and determine which factors appear to be significant.
library(DoE.base)
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)
D <- c(-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1)
Obs <- c(12,18,13,16,17,15,20,15,10,25,13,24,19,21,17,23)
Data <- data.frame(A,B,C,D,Obs)
Model <- lm(Obs~A*B*C*D,data = Data)
coef(Model)## (Intercept) A B C D
## 1.737500e+01 2.250000e+00 2.500000e-01 1.000000e+00 1.625000e+00
## A:B A:C B:C A:D B:D
## -3.750000e-01 -2.125000e+00 1.250000e-01 2.000000e+00 -8.543513e-17
## C:D A:B:C A:B:D A:C:D B:C:D
## 1.110223e-16 5.000000e-01 3.750000e-01 -1.250000e-01 -3.750000e-01
## A:B:C:D
## 5.000000e-01halfnormal(Model)
Answer: So from the half normal plot we can conclude that factors A, D, AC & AD are appear to be significant.
Part B:
b) Pull terms that do not appear to be significant into error and test for the significance of the other effects at the 0.05 level of significance.
Model3 <- aov(Obs~A+C+D+A*C+A*D,data = Data)
summary(Model3)## Df Sum Sq Mean Sq F value Pr(>F)
## A 1 81.00 81.00 49.846 3.46e-05 ***
## C 1 16.00 16.00 9.846 0.010549 *
## D 1 42.25 42.25 26.000 0.000465 ***
## A:C 1 72.25 72.25 44.462 5.58e-05 ***
## A:D 1 64.00 64.00 39.385 9.19e-05 ***
## Residuals 10 16.25 1.62
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1