# set up coded factor levelsand pure factor errors
codes = c(1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1)
responses = codes[-c(1, 9, 17, 25, 33, 41, 49)]
errors = c(0.1135, 0.0095, -0.0075, 0.0330, -0.0060, 0.0055, 0.1000)

# solve for responses
R = matrix(data=responses, nrow=7, ncol=7, byrow=TRUE)
E = matrix(data=errors*4 - 0.9899, nrow=7, ncol=1)
S = solve(R, E)
R1 = 0.9899
R2 = S[1, 1]
R3 = S[2, 1]
R4 = S[3, 1]
R5 = S[4, 1]
R6 = S[5, 1]
R7 = S[6, 1]
R8 = S[7, 1]

# build the data with random noise added
gap0 = rnorm(100, 0, 0.005)
std1 = R1 + rnorm(100, 0, 0.005)
gap1 = rnorm(100, 0, 0.005)
std2 = R2 + rnorm(100, 0, 0.005)
gap2 = rnorm(100, 0, 0.005)
std3 = R3 + rnorm(100, 0, 0.005)
gap3 = rnorm(100, 0, 0.005)
std4 = R4 + rnorm(100, 0, 0.005)
gap4 = rnorm(100, 0, 0.005)
std5 = R5 + rnorm(100, 0, 0.005)
gap5 = rnorm(101, 0, 0.005)
std6 = R6 + rnorm(100, 0, 0.005)
gap6 = rnorm(101, 0, 0.005)
std7 = R7 + rnorm(100, 0, 0.005)
gap7 = rnorm(101, 0, 0.005)
std8 = R8 + rnorm(100, 0, 0.005)
gap8 = rnorm(101, 0, 0.005)
signal = c(gap0, std1, gap1, std2, gap2, std3, gap3, std4, gap4, std5, gap5, std6, gap6, std7, gap7, std8, gap8)

# plot the data and annotate with responses
plot(signal, type = "l", ylim = c(0, 1.5), xlab = "time", ylab = "absorbance of standard sample")
r1 = mean(signal[101:200])
r2 = mean(signal[301:400])
r3 = mean(signal[501:600])
r4 = mean(signal[701:800])
r5 = mean(signal[901:1000])
r6 = mean(signal[1101:1200])
r7 = mean(signal[1301:1400])
r8 = mean(signal[1501:1600])
legend(x = "topleft", bty = "n", legend = c(paste0("R1: ", noquote(formatC(r1, format = "f", digits = 4))), paste0("R2: ", noquote(formatC(r2, format = "f", digits = 4))), paste0("R3: ", noquote(formatC(r3, format = "f", digits = 4))), paste0("R4: ", noquote(formatC(r4, format = "f", digits = 4)))))
legend(x = "topright", bty = "n", legend = c(paste0("R5: ", noquote(formatC(r5, format = "f", digits = 4))), paste0("R6: ", noquote(formatC(r6, format = "f", digits = 4))), paste0("R7: ", noquote(formatC(r7, format = "f", digits = 4))), paste0("R8: ", noquote(formatC(r8, format = "f", digits = 4)))))
C = matrix(data=codes, nrow=8, ncol=7, byrow=FALSE)
colnames(C) = c("Factor A", "Factor B", "Factor C", "Factor D", "Factor E", "Factor F", "Factor G")
rownames(C) = c("Expt 1", "Expt 2", "Expt 3", "Expt 4", "Expt 5", "Expt 6", "Expt 7", "Expt 8")
rugtable = as.table(C)
rugtable