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# fac_expmt - Factorial Experiments When something we wish to...

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Factorial Experiments When something we wish to predict depends on two or more factors what we do is fit a multi-linear model i.e. make predictions of the form ˆ y i = b p x p,i + b p - 1 x p - 1 ,i + · · · + b 1 x 1 ,i + b 0 by calculating b p , b p - 1 , . . . , b 0 to minimise n i =1 ( y i - ˆ y i ) 2 by using some software package. We now have to deal with the possibility that different factors interact as their levels are changed. To fit any model we need data and this should come from an experiment which is properly designed i.e. the values of the x j,i must be chosen appropriately. An experiment in which several controllable factors may affect the results should use a factorial design – all possible combinations of factor levels (the different possible values of the x j,i ) should be investigated in the replicates (indexed by i ) of the experiment. The purpose of the experiment is to discover how varying the levels of controllable factors in any combination affects output. Where possible more than one trial should be run at each selected combination of factor levels – this replication makes possible the estimation of the variation caused by uncontrolled factors. Combinations should be tested in randomised order to avoid confounding with uncontrolled factors. Designs that do some fraction e.g. one half or one sixteenth of the total number of combinations exist and are called fractional factorial designs but there won’t be time to discuss them in this set of lectures. Consider the following experiments in which there are two factors each of which are tested at two levels. When factor levels are not numerical we modify our prediction equation to ˆ y i =

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fac_expmt - Factorial Experiments When something we wish to...

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