Problem Sets

Solutions will to these problem sets will be available electronically.

Problem Set #1 - posted January 14, 2006

Additional practice problems for linear regression analysis -

These are additional problems that you can try to review and/or extend your understanding of linear regression. The problems are from the Fall 2005 offering of CHEE418/801: Strategies for Process Investigations. They contain examples with calculations done by hand, and using JMP. You might find them useful as an introduction for how to interpret JMP output as well.

Additional problem set 1 question sheet (pdf)

Additional problem set 1 solutions (pdf)

Additional problem set 2 question sheet (pdf)

Additional problem set 2 solutions (pdf)

Note - the problem sets below are from the previous offering of the course. The problem sets for Winter 2006 will build from these problems, and will be updated as we progress through the course. I will indicate when the files have been updated.

Old Problem Set #1

Question 5 data

Question 6 data

Question 7 data

Old Problem Set #2

To use the script, load it into the Matlab m-file editor, select the text, and then press F9 (alternatively, you can convert it into a function if you wish. Please feel free to modify). The script file is documented and explains the various commands, so you are welcome to use it as a template as well.

To use the script, you need to provide 3 m-files (function files). The first is a model file that takes in values of the parameters and independent variable(s) and returns predictions of the response variable at each of the run conditions. The second file computes the sensitivity matrix (jacobian of the expectation mapping), given values of the parameters and the independent variable(s). The third file is a setup file that assigns initial parameter values (I always forget these so I wanted to have them in an actual file). You can also load data files here, or directly assign data values rather than loading a file, if you would prefer.

These three files are specified early on in the script (you will see them assigned). If you have different files, simply change the names (for variables "model", "sensmat" and "model_setup". The files below are for the BOD problem (dataset available below), so you can try them out and use them as templates for your own work.

A couple of other points: 1) your functions need to assign values for all runs. If you look in my examples, you will see that I have taken advantage of the Matlab ability to perform operations on vectors and matrices "element-wise". You need to use ./ or .* or .^ to indicate element-wise operation (the "." before the operator tells Matlab that it is element-wise). Functions such "exp" do this automatically; 2) please let me know if you find any errors in the code, and give me suggestions for improvement!

Datasets (all as .mat files):

All datasets were obtained from Bates and Watts (1988).