Flipped Assignment 18
IE 5342 - Dr. Timothy I. Matis
Jesus Rosila Mares, Hunter Swerdloff, Fred Gersdorff
Nov 30 2021
Problems
- Nested Designs using R
Setup
Setup Libraries
# Setup Libraries
library(dplyr)
library(tidyr)
library(readr)
library(knitr)
library(agricolae)
library(lawstat)
library(car)
library(GAD)
library(BSDA)
library(pwr)
library(WebPower)
library(ggplot2)
library(ggfortify)
library(ggpubr)Nested Designs using R
A rocket propellant manufacturer is studying the burning rate of propellant from three production processes. Four batches of propellant are randomly selected from the output of each process, and three determinations of burning rate are made on each batch. The results follow. State the model equation and hypotheses to be tested. Perform the analysis and draw conclusions, using alpha=0.05 where applicable.
process <- c(rep(1:3,each = 4,3))
batch <- c(rep(1:4,9))
obs <- c(rep(1:3,each = 4*3))
response <- c(25, 19, 15, 15, 19, 23, 18, 35, 14, 35, 38, 25,
30, 28, 17, 16, 17, 24, 21, 27, 15, 21, 54, 29,
26, 20, 14, 13, 14, 21, 17, 25, 20, 24, 50, 33)
dat <- data.frame(process,batch,obs,response)
dat## process batch obs response
## 1 1 1 1 25
## 2 1 2 1 19
## 3 1 3 1 15
## 4 1 4 1 15
## 5 2 1 1 19
## 6 2 2 1 23
## 7 2 3 1 18
## 8 2 4 1 35
## 9 3 1 1 14
## 10 3 2 1 35
## 11 3 3 1 38
## 12 3 4 1 25
## 13 1 1 2 30
## 14 1 2 2 28
## 15 1 3 2 17
## 16 1 4 2 16
## 17 2 1 2 17
## 18 2 2 2 24
## 19 2 3 2 21
## 20 2 4 2 27
## 21 3 1 2 15
## 22 3 2 2 21
## 23 3 3 2 54
## 24 3 4 2 29
## 25 1 1 3 26
## 26 1 2 3 20
## 27 1 3 3 14
## 28 1 4 3 13
## 29 2 1 3 14
## 30 2 2 3 21
## 31 2 3 3 17
## 32 2 4 3 25
## 33 3 1 3 20
## 34 3 2 3 24
## 35 3 3 3 50
## 36 3 4 3 33process <- as.fixed(process)
batch <- as.random(batch)
obs <- as.random(obs)
model <- lm(response~
process +
batch%in%process)
model##
## Call:
## lm(formula = response ~ process + batch %in% process)
##
## Coefficients:
## (Intercept) process2 process3 process1:batch2
## 27.000 -10.333 -10.667 -4.667
## process2:batch2 process3:batch2 process1:batch3 process2:batch3
## 6.000 10.333 -11.667 2.000
## process3:batch3 process1:batch4 process2:batch4 process3:batch4
## 31.000 -12.333 12.333 12.667summary(model)##
## Call:
## lm(formula = response ~ process + batch %in% process)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.333 -2.083 -0.500 2.333 8.333
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 27.000 2.511 10.752 1.17e-10 ***
## process2 -10.333 3.551 -2.910 0.00768 **
## process3 -10.667 3.551 -3.004 0.00615 **
## process1:batch2 -4.667 3.551 -1.314 0.20123
## process2:batch2 6.000 3.551 1.690 0.10406
## process3:batch2 10.333 3.551 2.910 0.00768 **
## process1:batch3 -11.667 3.551 -3.285 0.00312 **
## process2:batch3 2.000 3.551 0.563 0.57853
## process3:batch3 31.000 3.551 8.729 6.51e-09 ***
## process1:batch4 -12.333 3.551 -3.473 0.00197 **
## process2:batch4 12.333 3.551 3.473 0.00197 **
## process3:batch4 12.667 3.551 3.567 0.00156 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.349 on 24 degrees of freedom
## Multiple R-squared: 0.8585, Adjusted R-squared: 0.7936
## F-statistic: 13.23 on 11 and 24 DF, p-value: 1.177e-07autoplot(model)
gad(model)## Analysis of Variance Table
##
## Response: response
## Df Sum Sq Mean Sq F value Pr(>F)
## process 2 676.06 338.03 1.4643 0.2815
## process:batch 9 2077.58 230.84 12.2031 5.477e-07 ***
## Residual 24 454.00 18.92
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Source Code
# clear memory and environment
rm(list = ls())
gc()
# Flip 18
# IE 5342 - Dr. Timothy I. Matis
# Jesus R. Rosila Mares
# Nov 29 2021
# Problems:
# Nested Designs using R
#-------------------------------------------------------------------------------
# Setup Libraries
library(dplyr)
library(tidyr)
library(readr)
library(knitr)
library(agricolae)
library(lawstat)
library(car)
library(GAD)
library(BSDA)
library(pwr)
library(WebPower)
library(ggplot2)
library(ggfortify)
library(ggpubr)
library(SixSigma)
library(DoE.base)
#-------------------------------------------------------------------------------
#
# Nested Designs using R
#
# A rocket propellant manufacturer is studying the burning rate
# of propellant from three production processes. Four batches of
# propellant are randomly selected from the output of each process,
# and three determinations of burning rate are made on each batch.
# The results follow. State the model equation and hypotheses to be tested.
# Perform the analysis and draw conclusions, using alpha=0.05 where applicable.
process <- c(rep(1:3,each = 4,3))
batch <- c(rep(1:4,9))
obs <- c(rep(1:3,each = 4*3))
response <- c(25, 19, 15, 15, 19, 23, 18, 35, 14, 35, 38, 25,
30, 28, 17, 16, 17, 24, 21, 27, 15, 21, 54, 29,
26, 20, 14, 13, 14, 21, 17, 25, 20, 24, 50, 33)
dat <- data.frame(process,batch,obs,response)
dat
process <- as.fixed(process)
batch <- as.random(batch)
obs <- as.random(obs)
model <- lm(response~
process +
batch%in%process)
model
summary(model)
autoplot(model)
gad(model)
#-------------------------------------------------------------------------------