MANE 6313

Week 15, Module A

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

Apply the method of steepest descent.

Resources for the Week 14, Module A micro-lecture are:

Step 0

Read Example 11.1 on pages 493 - 497.

Step 1 - Find Coded Regression Model

Note that Example 11.1 uses both coded and natural (uncoded) models.

You must be very careful and ensure that for each step you are using the correct model. The coded model is

\[ \hat{y}=40.44+0.775x_1+0.325x_2 \]

Step 2 - Take derivates

Calculate the derivate for each term in the model.

\[ \frac{d\hat{y}}{dx_1}=0.775 \]

\[ \frac{d\hat{y}}{dx_2}=0.325 \]

Step 3 - Determine slope

Consider the pair of variables \(x_1\) and \(x_2\) determine the slope.

\[ \mathrm{slope}=\frac{\Delta x_2}{\Delta x_1}=\frac{d\hat{y}/{dx_2}}{d\hat{y}/{dx_1}}=\frac{0.325}{0.775}=0.42 \]

Step 4 - Determine step size

This step involves guess work. In Example 11. 1, a step of size of 1 coded unit in \(x_1\) is selected. Notice that corresponds to a change of 5 in the \(x_1\) direction of the uncoded model. Once the step size (in coded units) is select for \(x_1\), use the slope to find the step size (in coded units) for \(x_2\).