Residuals are the difference between the model's predicted values for yield and those obtained from 'conducting' the experiment. Return to MULREG.FIT and examine the Residuals by selecting RESIDUALS. go to CUSTOMIZE and change "Add smoothed curve" to Yes. This will plot smoothed best-fit lines onto your graphs. Now /exit and select GRAPH choices to view the graphs.

The graphs allow an assessment of the accuracy of the model and the most relevant graphs are described below. View them by selecting GRAPH and selecting the appropriate name. The other graphs show details beyond the scope of this exercise.

HISTOGRAM : This shows the variation in the size of the residuals (i.e. the error in the model). It should obey a normal distribution as this would mean errors were due to the experiment and not the model. However, due to the limited number of experiments this cannot be seen clearly.  Figure 15

PROBABILITY : This is a method of evaluating whether or not the errors are actually a Guassian Distribution (it is more convenient than the histogram method). As it is cumulative probability on the y-axis, the data corresponding to a Gaussian Distribution will form a straight line.  Figure 16 This will allow the user to see if the model is the correct shape, but does not relate directly to the accuracy of the model.

FITTED : This will again show if the model is inaccurate - if there is a correlation between the models predicted values and the residuals then it suggests an inaccuracy in the model.  Figure 17 (NB: this figure does not include the smoothed line). It is easier to view this correlation (if it exists) if the absolute values of the residuals are used. To achieve this go to SCALE Resids and then ABSSTUD. Your fitted graph should now appear as in  Figure 18.

What does this show?

RELATIONS: This will allow the interactions between various effects to be observed on the output. To use this, select the yield as the output and then the interacting variables, one as the horizontal variable and one as the grouping variable. Only use subsetting if graphing more than one relation graph at a time, and use the [DEFAULT] partition. If an interaction exists between the variables the lines drawn will not be parallel.  For example using yield, energy and pressure repectively, produces the following graph in Figure 19.

We now return to the problem of the low importance of E and T_OX as main effects. It is unusual for an interaction to be important if the main effects themselves are unimportant. To investigate this further, examine the confounding table: Figure 6. It can be seen that E*T_OX is confounded with M*P, both of which are important main effects. To view this we need to use the RELATIONS graph.

Now plot a relations graph using yield as the vertical variable, pressure as the horizontal variable and machine as the grouping variable. The result should be as seen in Figure 22.
 
Archive File

An archive file can be used if a problem occurs, Example.ARX, by clicking on this link while holding shift will open a save as dialogue box. The file can then be saved in your home directory i.e /home/s9904475/.

What has greatest effect on yield?

You should now be in a postion whereby you can generate a model from a set of experiments, refine this model, analyse it and interpret the results. This will allow you to determine using statistical techniques which terms are important and which can be screened out.