Old exams

Question 1 (9p)

You are setting up a new biological assay and you want to improve the signal to noise ratio for your assay. Four factors are believed to influence the ratio Signal/Noise;

X1: amount of protein (pro), 

X2: amount of buffer (buf), 

X3: incubation time (inc), and 

X4: amount of tracer (tra). 

You have made a full factorial design at two levels with three center experiments giving 19 experiments in total. You have made a model based on MLR, and below you see two plots as a result of your model (Figure A and B).

a)      What does ANOVA stands for?

b)      Why is it an appropriate method to use when you have used experimental design?

c)      List the significant effects based on Figure A and describe what settings you should use in order to get a high signal to noise ratio

d)     Experiment no 10 appear to be an outlier based on Figure B. How can one see that? No 10 can be a “true” outlier (e.g. due to experimental error) but the pattern seen can also be due to model error. Give two example of possible model errors. 

Click here for solution

Question 2 (9p)

The significance of an applied regression model can be investigated by applying different diagnostics.

a)      How would you use the results (response values) from centre points in a design in the evaluation of an applied regression model?

b)      How would you use the results (response values) from replicates (i.e. the same experiment repeated more than once) in the evaluation of an applied regression method?

c)      In the field of design of experiments two different F-tests can be conducted to check the significance of a model. Describe in detail how the two tests are done and how you should evaluate them to judge the quality of the model.
Click here for solution

Question 3 (10p)

You have investigated four factors with 11 experiments based on a fractional factorial design (2^4-1) and three center points, and investigated a response y (see table below).

a)      What is the resolution of the fractional factorial design?

b)      Calculate the regression model coefficients for: y= b₀+ b₁X1+ b₂X2+ b₃X3+ b₄X4

-        Interpret the results.

c)      Calculate R² for the model in b).

-        Interpret the results.

d)     What are confounded with your main terms?

-        What does this information mean?

Question 4 (3p)

How do you determine the number of significant components in partial least square regression to latent structures (PLS)?

Question 5 (9p)

Give explanations, equations for a) and c), and its usage in design of experiments and/or multivariate analysis of the below listed items.

a)      RMSEE

b)      Steepest descent

c)      PCA