Chemometrics regression model problem set

Section 2.2.3 of the course text includes a data set outlining 20 experiments conducted at various pH's, temperature, and concentrations to optimize reaction rate response that was measured for each of these experiments.

Develop a ten factor linear model to predict reaction response as a function of each variable, of the square of each variable, as a function of cross terms (pH-temperature, pH-concentration, and concentration-temperature) and as a function of an intercept.

Write out the matrices used for your model, use Matlab to develop the model parameters and include your specific Matlab commands and output as part of your submission.

Do the following:
 

• Outline the equation that represents a least squares, ten parameter, fit of the data.
• Calculate and tabulate each of the actual responses, the predicted responses, and the root-mean-square error of calibration.
• Then separate the data set into two groups of 15 and 5 experiments respectively
• Calculate a ten parameter model using the 15 experiment data set
• Use this ten parameter model to predict responses for the other five experiments
• Calculate the root-mean-square error of prediction (RMSEP) and the root-mean-square error of calibration (RMSEC), both in absolute and relative terms.