Design and analysis of experiments (2013)

Class date(s):	08 March 2013 to 03 April 2013
(PDF)	Course slides
Download video: Link (plays in Google Chrome) [328 M]
Download video: Link (plays in Google Chrome) [385 M]
Download video: Link (plays in Google Chrome) [360 M]

Course notes and slides

• Course textbook (print chapter 5)
• Slides for class

Class materials

• 08 Mar 2013 (Class 08C): Audio and video and guest speaker's slides (Emily Nichols)
• 12 Mar 2013 (Class 09A): Audio and video
• 13 Mar 2013 (Class 09B): Audio and video

Software source code

Use R to estimate the DOE model

T <- c(-1, +1, -1, +1)  # centered and scaled temperature
S <- c(-1, -1, +1, +1)  # centered and scaled substrate concentration
y <- c(69, 60, 64, 53)  # conversion is the response, y
mod <- lm(y ~ T + S + T*S)
summary(mod)

Call:
lm(formula = y ~ T + S + T * S)

Residuals:
ALL 4 residuals are 0: no residual degrees of freedom!

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)     61.5         NA      NA       NA
T               -5.0         NA      NA       NA
S               -3.0         NA      NA       NA
T:S             -0.5         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:     1,	Adjusted R-squared:   NaN 
F-statistic:   NaN on 3 and 0 DF,  p-value: NA

You could also use MATLAB if you prefer:

% Set up the X matrix:

n = 4;
temperature = [-1, +1, -1, +1];
substrate = [-1, -1, +1, +1];

X = [ ones(n, 1), temperature', substrate', (temperature .* substrate)'];

% or you can type it in directly (but this is error prone)
X = [+1 -1 -1 +1; ...
     +1 +1 -1 -1; ...
     +1 -1 +1 -1; ...
     +1 +1 +1 +1];

% Conversion is your y-variable
y = [69, 60, 64, 53]';

% Regression coefficients = b = [Intercept, b_T, b_S, b_{TS}]
b = inv(X'*X)*X'*y