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# Class Note for STAT 528 at OSU

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Ohio State University taught by a professor in Fall. Since its upload, it has received 24 views.

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Date Created: 02/06/15
The Exponential Explosion Factor Consider the logistical problem of building statistical models involving K predictor variables and R response variables How many different models are possible Consider the case of creating a simple regression model involving the K predictor variables and restrict the variables in the models to rstorder terms and all possible interactions up to and including the one kth order interaction That is consider only terms of the form x xxjz ji 01 as candidates for inclusion in the model In this case there is a total of K K K K Mj J11 2 rstorder terms and cross products that could be chosen for inclusion in the model How many models can be made from these 2K terms Recognizing that the term XIOXEX lt represents the intercept term in the model and if we ignore the model Y E 0 s as a legitimate model then there are 2K 2K K K NZ 112 22 1 10 J possible models for each of the R response variables Given R response variables then there is a total of N NxR total models to consider Example K2 and R 3 Suppose there are two predictor variables X1 and X2 and three response variables The 22 4 possible terms in the model are 0 Xlng o XIIXE o XIOX o 1 COSUStat 6006012C Exponential Explosion Factorthe exponential explosion factordoc The number of possible regression models that can be constructed from these four predictor variables is N 241 15 and these models are the following pW QMrbl N k c k c 5 538 w M w gt3 fog XXX X1 X XXX X11X X11X 15 X1 X XXXX D ID I bu Given R 3 response variables there is a total of N 153 45 models to consider Table 1 presents the total number of models to consider as a function of K and R Table 1 R K1 K2 K3 K4 1 3 15 255 65535 2 6 30 510 131070 3 9 45 765 196605 4 12 60 1020 262140 5 15 75 1275 327675 6 18 90 1530 393210 7 21 105 1785 458745 8 24 120 2040 524280 9 27 135 2295 589815 10 30 150 2550 655350 11 33 165 2805 720885 12 36 180 3060 786420 13 39 195 3315 851955 14 42 210 3570 917490 15 45 225 3825 983025 2 COSUStat 6006012C Exponential Explosion Factorthe exponential explosion factordoc

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