This report captures work done for the individual homework for Week 14. R code along with the results are provided. The required homework problems were taken from “Design and Analysis of Experiments 8th Edition”:
   1) 14.3

Setting Things Up

# setup Libraries
library(knitr)
library(dplyr)
library(tidyr)
library(GAD)
library(tinytex)
library(ggplot2)
library(ggfortify)
library(car)
library(DoE.base)
library(FrF2)

Problem 1 (14.3)

A manufacturing engineer is studying the dimensional variability of a particular component that is produced on three machines. Each machine has two spindles, and four components are randomly selected from each spindle. The results follow [as shown in book]. Analyze the data, assuming that machines and spindles are fixed factors.

NOTE: CODE USED FROM CLASS YOUTUBE ASSIGNMENT

Machine <- c(rep(1,8),rep(2,8),rep(3,8))
Spindle <- rep(c(rep(1,4),rep(2,4)),3)
Obs <- c(12,9,11,12,8,9,10,8,14,15,13,14,12,10,11,13,14,10,12,11,16,15,15,14)
Table <- data.frame(Machine,Spindle,Obs)
library(GAD)
Machine <- as.fixed(Machine)
Spindle <- as.random(Spindle)
model <- lm(Obs~Machine+Spindle%in%Machine)
kable(gad(model))
Df Sum Sq Mean Sq F value Pr(>F)
Machine 2 55.75 27.875000 1.911429 0.2915630
Machine:Spindle 3 43.75 14.583333 9.905660 0.0004428
Residual 18 26.50 1.472222 NA NA

With a p-value of less than 0.001, the nested factor of Spindle in Machine is statistically significant to an alpha of 0.05.