MANE 6313
Week 7, Module E
Student Learning Outcome
- Select an appropriate experimental design with one or more factors,
- Select an appropriate model with one or more factors,
- Evaluate statistical analyses of experimental designs,
- Assess the model adequacy of any experimental design, and
- Interpret model results.
Module Learning Outcome
Describe the use of linear regression models in design of experiments
Regression Model
- Alternative to fixed effects model
\[
y=\beta_0+\beta_1x+\varepsilon
\]
- Introduced in section 3.5 on page 76
Types of Factors
Montgomery classifies factors as either quantitative or qualitative
- Quantitative factors
A factor whose levels can be associated with points on a numerical scaoe, such as temperature, pressure, or time
- Qualitative
A factor for which levels cannot be arrangede in order of magnitude. Operators, batches of raw materia, and shifts are typical qualitatve factors becuase there is no reason to rank them in any particular numerical order
Problem 6.9 using Quantitative Variables
- Factor A - Bit size
- Lo setting: 1/16 = 0.0625
- Hi setting: 1/8 = 0.125
- Factor B - Speed
- Lo setting: 40 rpm
- Hi setting: 90 rpm
Data Frame
- Must be created so that vectors are numeric not factor!
- Cannot use fac.design
Linear (Regression) Model
Estimated Model
\[
\begin{aligned}
\hat{y}&=\hat{\beta}_0+\hat{\beta}_1A+\hat{\beta}_2B+\hat{\beta_{12}}AB\\
\hat{y}&=26.775-152.0A+-0.465B+6.97AB
\end{aligned}
\]
Residual Analysis
- Identical procedure to the fixed effects model
Contour Plots
- Explanation
3-D Plot
