Free Course on Response Surface Methodology with R
R Code for Lesson 7: Analyzing a Central Composite Design – R tutorial
Copy and paste the code below in your R Studio to follow the example in Lesson 7: Analyzing a Central Composite Design – R tutorial
(Video-Lesson Available on April 17, 2023)
# Analysis of a Central Composite Design for 2 Factors
# Author: Rosane Rech, January 2021.
# This code is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
# https://creativecommons.org/licenses/by-nc-sa/4.0/
# Data source:
# Design and analysis of experiments / Douglas C. Montgomery. — Eighth edition.
# ISBN 978-1-118-14692-7
# Data file: DoEOpt06
# Time (x1): Time (min)
# Temp (x2): Temperature (ºC)
# Y: Yield (%)
# building the data set
# (run this code to build the DoEOpt05 data set before following the analysis)
<- data.frame(x1 = c(-1, -1, 1, 1, 0, 0, 0, 0, 0, 1.414, -1.414, 0, 0),
DoEOpt06 x2 = c(-1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1.414, -1.414),
Time = c(80, 80, 90, 90, 85, 85, 85, 85, 85, 92.07, 77.93, 85, 85),
Temp = c(170, 180, 170, 180, 175, 175, 175, 175, 175, 175, 175, 182.07, 167.93),
Y = c(76.5, 77, 78, 79.5, 79.9, 80.3, 80, 79.7, 79.8, 78.4, 75.6, 78.5, 77)
)
# loading Response Surface Methodology package
library(rsm)
# checking file structure
str(DoEOpt06)
# setting the realtionship between the coded and the natural variables
<- as.coded.data(DoEOpt06,
DoEOpt06 ~ (Time-85)/5,
x1 ~ (Temp-175)/5)
x2
###
##
# regression model for the Yield
<- rsm(Y ~ SO(x1,x2), data = DoEOpt06)
model_Y
<- rsm(Y ~ FO(x1,x2) + TWI(x1,x2) + PQ(x1,x2), data = DoEOpt06)
model_Y summary(model_Y)
# contour and perspective plots
contour(model_Y, x1~x2, image = TRUE,
xlabs=c("Time (min)", "Temperature (ºC)"))
persp(model_Y, x1~x2, col = terrain.colors(50), contours = "colors",
zlab = "Yield (%)",
xlabs=c("Time (min)", "Temperature (ºC)"))
# predictig the Yield at the stationary point
<- data.frame(x1 = 0.361, x2 = 0.257)
max predict(model_Y, max)