A 23 factorial experiment with only one replicate (8 runs) has been run in a chemical process. The response variable is molecular weight. The engineer has used the following factors:   Factor Natural levels Coded levels (x’s) A – time 80, 100 (minutes) -1, 1 B – temperature 150, 200 (deg C) -1, 1 C – concentration 30, 60 (percent) -1, 1 After conducting the experiment, the engineer computes the quantities in the following table (using coded units):   Term Effect Estimate Sum of Squares % Contribution A X 32.00 X B 6.50 X 65.44 C 1.50 4.50 3.48 AB 0.75 1.125 3.86 AC -0.50 0.50 0.39 BC 1.50 4.50 3.48 ABC -1.00 2.00 1.55   Answer the following questions (15 – 19) about this experiment.  Each question is worth 5 points.

9. Screening experiments should use conservative spacing of the factor levels.

Consider a time series with 200 observations.  Suppose that

2. When using a 2-level factorial design and the block size is not a power of 2, an optimal design can be used to construct an appropriate design.

The variance of the observations from the Hanning filter, if it is applied to a time series consisting of independent observations with constant variance σ2, is

Folding over a resolution III design is a technique to separate main effects from their two-factor interaction aliases. 

You are performing an experiment with a deterministic computer model. A reasonable choice of experimental design is 

Construct a 95% confidence interval for the regression coefficient for X1. The UCL is _______________.  

The advantage of the REML method is that it provides the standard errors of the variance components so that confidence intervals can be easily obtained. 

For a half fraction of a two-level factorial design the maximum resolution possible is equal to the number of factors.