Worksheets/Week3

Part 1

A factorial experiment was run to investigate the settings that minimize the production of an unwanted side product. The two factors being investigated are called A and B for simplicity.

# A = additive at 20mL and 30mL for low and high levels A <- c(-1, +1, -1, +1) # B = without (-) or with (+) boiling B <- c(-1, -1, +1, +1) # Response y is the amount of side product formed, y [grams] y <- c(89, 268, 179, 448) # Fit a linear model mod.siderxn <- lm(y ~ A + B + A*B) summary(mod.siderxn) # Uncomment this line if you run the code in RStudio #library(pid) # Comment this line if you run this code in RStudio source('https://yint.org/contourPlot.R') # See how the two factors affect the response: contourPlot(mod.siderxn) interaction.plot(A, B, y) interaction.plot(B, A, y)

Part 2

Continuing from above, with 2 extra experimental points:

# A = additive at 20mL and 30mL for low and high levels A <- c(-1, +1, -1, +1, 0, 0) # B = without (-) or with (+) boiling B <- c(-1, -1, +1, +1, -1, +1) # Response y is the amount of side product formed, y [grams] y <- c(89, 268, 179, 448, 186, 290) mod.siderxn.cp <- lm(y ~ A + B + A*B) summary(mod.siderxn.cp) # Uncomment this line if you run the code in RStudio #library(pid) # Comment this line if you run this code in RStudio source('https://yint.org/contourPlot.R') contourPlot(mod.siderxn.cp)

Part 3

Your family runs a small business selling products online. The first factor of interest is whether to provide free shipping over €30 or over €50. The second factor is whether or not the purchaser must first create a profile before completing the transaction. The purchaser can still complete their transaction without creating a profile. Below are the data collected, showing the 8 experiments.

# S = Free shipping if order amount is €30 or more [-1], # of if order amount is over €50 [+1] S <- c(-1, +1, -1, +1, -1, +1, -1, +1) # Does the purchaser need to create a profile first [+1] or not [-1]? P <- c(-1, -1, +1, +1, -1, -1, +1, +1) # Response: daily sales amount y <- c(348, 359, 327, 243, 356, 363, 296, 257) # Linear model using S, P and S*P to predict the response mod.sales <- lm(y ~ S*P) summary(mod.sales) # Uncomment this line if you run the code in RStudio #library(pid) # Comment this line if you run this code in RStudio source('https://yint.org/contourPlot.R') contourPlot(mod.sales) interaction.plot(S, P, y) interaction.plot(P, S, y)

Part 4

Continuing with the case above:

# S = Free shipping if order amount is €30 or more [-1], # of if order amount is over €50 [+1] S <- c(-1, +1, -1, +1, -1, +1, -1, +2) # Does the purchaser need to create a profile first [+1] or not [-1]? P <- c(-1, -1, +1, +1, -1, -1, +1, +1) # Response: daily sales amount y <- c(348, 359, 327, 243, 356, 363, 296, 220) # Linear model using S, P and S*P to predict the response mod.sales.mistake <- lm(y ~ S*P) summary(mod.sales.mistake) # Uncomment this line if you run the code in RStudio #library(pid) # Comment this line if you run this code in RStudio source('https://yint.org/contourPlot.R') contourPlot(mod.sales.mistake)