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[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Example and Worksheet Checklist"]
[null,null,null,null,null,null,"\t\nStatistical Measurement Methods in Excel: Intermediate"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Controlled Experiments"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Estimating Distributions"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Univariate Regression"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Multivariate Regression"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Log Odds Ratio"]
[]
[]
[null,null,null,null,null,"Hubbard Decision Research"]
[null,null,null,null,null,"2S410 Canterbury Ct"]
[null,null,null,null,null,"Glen Ellyn, IL 60137"]
[null,null,null,null,null,"www.hubbardresearch.com"]

{"sheet":"Reference Slides","index":1,"n_rows":2,"n_cols":20,"rows_kept":2,"cut":false,"hidden":false,"merged":[[3,2,3,16],[1,2,1,16],[1,19,1,33],[0,0,0,35]]}
["Reference Slides"]
[null,null,"Regression Shortcuts",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Types of Functions to Try"]

{"sheet":"Data","index":2,"n_rows":206,"n_cols":18,"rows_kept":206,"cut":false,"hidden":false,"merged":[[203,1,203,8],[29,10,29,11],[28,10,28,14],[0,0,0,18],[1,0,2,18],[8,11,8,17],[4,10,4,17],[5,13,5,14],[5,10,5,11],[4,1,4,8],[29,13,29,14]]}
["Data for the Worksheets and Quiz"]
["Instructions: This page contains data that is on the designated worksheets so the user can use them to see the original results or reset the worksheets after using them."]
[]
[]
[null,"Multivariate Regression Data",null,null,null,null,null,null,null,null,"Log Odds Ratio Data"]
[null,"Months / Years","BLS Unemployment Report in percent","Google Trends: Unemployment","Google Trends: Work","Google Trends: Jobs","Google Trends: Labor","Google Trends: Employment","Google Trends: Job Openings",null,"Time Period for Estimates (years):",null,5,"Initial Probability of Event per Time Period: P(E)",null,0.1]
[null,"2004-01-03",5.7,5,47,56,45,100,80]
[null,"2004-02-02T12:00:00",5.6,5,48,52,49,87,66]
[null,"2004-03-04",5.8,5,48,52,48,91,65,null,null,"Conditions"]
[null,"2004-04-03T12:00:00",5.6,4,49,53,50,93,71,null,null,"Web","Platform","Pen Results","Server/ Vendor","Age","Users","Data"]
[null,"2004-05-04",5.6,4,48,55,47,94,83,null,"X1","Web","MS","Pos Pen","Internal","<1 Year","Less than 5","PHI, PII, PCI, $"]
[null,"2004-06-03T12:00:00",5.6,4,45,57,47,99,79,null,"X2","No Web","Not MS","Neg Pen","External US","1 to 5 Years","5 to 200","Critical IP"]
[null,"2004-07-04",5.5,4,43,56,51,100,75,null,"X3",null,null,null,"Foreign","5+ Years","200 to 2000","No Critical Data"]
[null,"2004-08-03T12:00:00",5.4,4,43,54,66,96,74,null,"X4",null,null,null,null,null,"Over 2000"]
[null,"2004-09-03",5.4,4,46,50,60,85,66]
[null,"2004-10-03T12:00:00",5.5,4,48,48,45,82,69,null,"P(E|X1)",0.15,0.2,0.3,7.0000000000000007E-2,0.15,0.05,0.32]
[null,"2004-11-03",5.4,4,49,46,45,77,68,null,"P(E|X2)",0.05,0.09,0.05,0.09,0.1,0.08,0.12]
[null,"2004-12-03T12:00:00",5.4,4,44,42,40,68,59,null,"P(E|X3)",null,null,null,0.13,0.05,0.15,0.02]
[null,"2005-01-03",5.3,5,49,53,43,88,75,null,"P(E|X4)",null,null,null,null,null,0.36]
[null,"2005-02-02T12:00:00",5.4,4,50,50,46,77,65]
[null,"2005-03-05",5.2,4,49,49,45,83,76,null,"P(X1)",0.5,0.09,0.2,0.4,0.33300000000000002,0.15,0.15]
[null,"2005-04-04T12:00:00",5.2,4,49,49,48,81,71,null,"P(X2)",0.5,0.91,0.8,0.3,0.33300000000000002,0.18,0.35]
[null,"2005-05-05",5.0999999999999996,4,47,51,44,81,78,null,"P(X3)",null,null,null,0.3,0.33300000000000002,0.42,0.5]
[null,"2005-06-04T12:00:00",5,4,44,55,44,85,74,null,"P(X4)",null,null,null,null,null,0.25]
[null,"2005-07-05",5,4,42,51,47,83,77]
[null,"2005-08-04T12:00:00",4.9000000000000004,4,43,51,61,83,71]
[null,"2005-09-04",5,4,46,50,57,77,67]
[null,"2005-10-04T12:00:00",5,4,47,45,42,71,61]
[null,"2005-11-04",5,4,47,43,41,66,58,null,"Data for the Review Quiz"]
[null,"2005-12-04T12:00:00",4.9000000000000004,4,44,39,38,59,54,null,"Data for Q1",null,null,"Data for Q2"]
[null,"2006-01-04",4.7,5,47,51,43,75,73,null,4.9200000000000001E-2,4.4299999999999999E-2,null,4.9200000000000001E-2,4.4299999999999999E-2]
[null,"2006-02-03T12:00:00",4.8,4,47,45,41,69,67,null,-1.6E-2,4.4999999999999997E-3,null,-1.6E-2,4.4999999999999997E-3]
[null,"2006-03-06",4.7,4,46,46,42,72,68,null,3.8100000000000002E-2,8.6599999999999996E-2,null,3.8100000000000002E-2,8.6599999999999996E-2]
[null,"2006-04-05T12:00:00",4.7,4,48,47,43,69,69,null,4.5900000000000003E-2,9.0700000000000003E-2,null,4.5900000000000003E-2,9.0700000000000003E-2]
[null,"2006-05-06",4.5999999999999996,4,47,51,42,73,81,null,5.4899999999999997E-2,3.1600000000000003E-2,null,5.4899999999999997E-2,3.1600000000000003E-2]
[null,"2006-06-05T12:00:00",4.5999999999999996,4,44,51,41,75,74,null,7.3099999999999998E-2,2.3199999999999998E-2,null,7.3099999999999998E-2,2.3199999999999998E-2]
[null,"2006-07-06",4.7,4,42,50,44,74,70,null,5.9499999999999997E-2,4.5100000000000001E-2,null,5.9499999999999997E-2,4.5100000000000001E-2]
[null,"2006-08-05T12:00:00",4.7,4,43,51,61,75,71,null,8.2699999999999996E-2,6.1199999999999997E-2,null,8.2699999999999996E-2,6.1199999999999997E-2]
[null,"2006-09-05",4.5,4,45,47,53,69,69,null,7.7499999999999999E-2,9.7500000000000003E-2,null,7.7499999999999999E-2,9.7500000000000003E-2]
[null,"2006-10-05T12:00:00",4.4000000000000004,4,46,45,39,66,63,null,4.7500000000000001E-2,0.1714,null,4.7500000000000001E-2,0.1714]
[null,"2006-11-05",4.5,4,44,43,36,59,57,null,5.9799999999999999E-2,9.74E-2,null,5.9799999999999999E-2,9.74E-2]
[null,"2006-12-05T12:00:00",4.4000000000000004,4,43,39,34,53,55,null,4.3299999999999998E-2,1.1000000000000001E-3,null,4.3299999999999998E-2,1.1000000000000001E-3]
[null,"2007-01-05",4.5999999999999996,5,48,53,40,72,73,null,6.5699999999999995E-2,0.1205,null,6.5699999999999995E-2,0.1205]
[null,"2007-02-04T12:00:00",4.5,4,48,47,39,63,64,null,4.7699999999999999E-2,2.1100000000000001E-2,null,4.7699999999999999E-2,2.1100000000000001E-2]
[null,"2007-03-07",4.4000000000000004,4,47,48,39,65,69,null,1.55E-2,2.3599999999999999E-2,null,1.55E-2,2.3599999999999999E-2]
[null,"2007-04-06T12:00:00",4.5,4,50,49,39,68,73,null,5.28E-2,9.8000000000000004E-2,null,5.28E-2,9.8000000000000004E-2]
[null,"2007-05-07",4.4000000000000004,4,50,52,41,69,77,null,4.4299999999999999E-2,2.1100000000000001E-2,null,4.4299999999999999E-2,2.1100000000000001E-2]
[null,"2007-06-06T12:00:00",4.5999999999999996,4,47,54,41,72,75,null,2.9600000000000001E-2,6.8099999999999994E-2,null,2.9600000000000001E-2,6.8099999999999994E-2]
[null,"2007-07-07",4.7,4,47,56,47,72,77,null,6.8900000000000003E-2,2.3599999999999999E-2,null,6.8900000000000003E-2,2.3599999999999999E-2]
[null,"2007-08-06T12:00:00",4.5999999999999996,4,48,53,66,72,72,null,7.5800000000000006E-2,8.4500000000000006E-2,null,7.5800000000000006E-2,8.4500000000000006E-2]
[null,"2007-09-06",4.7,4,50,52,54,66,71,null,4.8399999999999999E-2,9.1999999999999998E-2,null,4.8399999999999999E-2,9.1999999999999998E-2]
[null,"2007-10-06T12:00:00",4.7,4,51,51,39,66,69,null,7.7999999999999996E-3,0.15509999999999999,null,7.7999999999999996E-3,0.15509999999999999]
[null,"2007-11-06",4.7,4,50,47,37,61,63,null,5.2499999999999998E-2,8.9499999999999996E-2,null,5.2499999999999998E-2,8.9499999999999996E-2]
[null,"2007-12-06T12:00:00",5,5,48,43,33,52,55,null,4.7599999999999996E-2,7.6899999999999996E-2,null,4.7599999999999996E-2,7.6899999999999996E-2]
[null,"2008-01-06",5,6,55,59,38,71,83,null,4.2500000000000003E-2,7.0699999999999999E-2,null,4.2500000000000003E-2,7.0699999999999999E-2]
[null,"2008-02-06",4.9000000000000004,5,54,52,37,63,67,null,1.9400000000000001E-2,0.1202,null,1.9400000000000001E-2,0.1202]
[null,"2008-03-06",5.0999999999999996,5,54,55,39,65,72,null,6.9400000000000003E-2,8.2400000000000001E-2,null,6.9400000000000003E-2,8.2400000000000001E-2]
[null,"2008-04-06",5,5,57,57,41,67,81,null,5.1400000000000001E-2,0.1414,null,5.1400000000000001E-2,0.1414]
[null,"2008-05-06",5.4,5,54,58,40,65,78,null,6.54E-2,4.9599999999999998E-2,null,6.54E-2,4.9599999999999998E-2]
[null,"2008-06-06",5.6,6,54,61,41,68,83,null,3.5200000000000002E-2,8.0100000000000005E-2,null,3.5200000000000002E-2,8.0100000000000005E-2]
[null,"2008-07-06",5.8,6,54,61,48,69,82,null,null,null,null,4.7899999999999998E-2,0.14219999999999999]
[null,"2008-08-06",6.1,6,52,59,74,66,80,null,null,null,null,5.1999999999999998E-3,5.2499999999999998E-2]
[null,"2008-09-06",6.1,7,56,64,48,66,78,null,null,null,null,5.5399999999999998E-2,5.11E-2]
[null,"2008-10-06",6.5,8,56,62,39,62,73,null,null,null,null,4.0500000000000001E-2,0.1013]
[null,"2008-11-06",6.8,10,54,60,37,60,63,null,null,null,null,3.0099999999999998E-2,9.3200000000000005E-2]
[null,"2008-12-06",7.3,12,54,56,38,56,60,null,null,null,null,7.6200000000000004E-2,5.4100000000000002E-2]
[null,"2009-01-06",7.8,14,59,76,40,73,86,null,null,null,null,7.4999999999999997E-3,2.53E-2]
[null,"2009-02-06",8.3000000000000007,14,59,67,44,64,77,null,null,null,null,0.1033,0.1208]
[null,"2009-03-06",8.6999999999999993,14,58,65,44,65,81,null,null,null,null,2.7799999999999998E-2,0.1167]
[null,"2009-04-06",9,13,59,61,43,64,78,null,null,null,null,7.3899999999999993E-2,7.8399999999999997E-2]
[null,"2009-05-06",9.4,12,57,65,43,63,86]
[null,"2009-06-06",9.5,13,58,71,46,68,97]
[null,"2009-07-06",9.5,14,56,69,51,68,93]
[null,"2009-08-06",9.6,14,56,68,69,67,90]
[null,"2009-09-06",9.8000000000000007,13,60,66,69,64,86]
[null,"2009-10-06",10,14,61,65,40,61,82]
[null,"2009-11-06",9.9,15,60,60,39,57,75]
[null,"2009-12-06",9.9,14,58,53,37,52,65]
[null,"2010-01-06",9.8000000000000007,15,64,70,38,65,93]
[null,"2010-02-06",9.8000000000000007,14,64,63,39,60,81]
[null,"2010-03-06",9.9,15,63,64,40,63,83]
[null,"2010-04-06",9.9,14,63,65,41,63,85]
[null,"2010-05-06",9.6,13,62,66,39,63,88]
[null,"2010-06-06",9.4,16,60,70,40,70,96]
[null,"2010-07-06",9.4,19,57,66,46,60,85]
[null,"2010-08-06",9.5,13,57,65,65,57,82]
[null,"2010-09-06",9.5,11,58,61,67,51,73]
[null,"2010-10-06",9.4,11,58,58,36,49,62]
[null,"2010-11-06",9.8000000000000007,12,58,55,35,46,61]
[null,"2010-12-06",9.3000000000000007,14,57,47,33,42,57]
[null,"2011-01-06",9.1,16,71,71,40,60,90]
[null,"2011-02-06",9,13,70,66,42,54,80]
[null,"2011-03-06",9,11,70,67,41,54,80]
[null,"2011-04-06",9.1,11,70,64,41,53,76]
[null,"2011-05-06",9,11,68,69,41,57,89]
[null,"2011-06-06",9.1,11,69,72,44,60,90]
[null,"2011-07-06",9,12,66,70,49,56,85]
[null,"2011-08-06",9,12,67,76,73,58,87]
[null,"2011-09-06",9,11,70,69,77,54,76]
[null,"2011-10-06",8.8000000000000007,11,72,100,41,49,73]
[null,"2011-11-06",8.6,11,70,61,38,44,68]
[null,"2011-12-06",8.5,12,67,53,35,39,65]
[null,"2012-01-06",8.3000000000000007,14,75,67,39,49,90]
[null,"2012-02-06",8.3000000000000007,12,72,60,39,46,76]
[null,"2012-03-06",8.1999999999999993,10,70,60,38,45,77]
[null,"2012-04-06",8.1999999999999993,11,73,63,41,50,86]
[null,"2012-05-06",8.1999999999999993,10,71,67,41,51,98]
[null,"2012-06-06",8.1999999999999993,10,72,67,41,50,100]
[null,"2012-07-06",8.1999999999999993,11,71,67,49,49,93]
[null,"2012-08-06",8.1,10,71,67,82,48,95]
[null,"2012-09-06",7.8,10,75,64,73,45,84]
[null,"2012-10-06",7.8,10,72,62,37,43,76]
[null,"2012-11-06",7.7,11,71,56,35,38,70]
[null,"2012-12-06",7.9,11,72,49,33,34,64]
[null,"2013-01-06",8,12,76,66,37,46,92]
[null,"2013-02-06",7.7,9,74,59,36,41,75]
[null,"2013-03-06",7.5,9,73,61,36,41,83]
[null,"2013-04-06",7.6,9,76,64,39,45,89]
[null,"2013-05-06",7.5,8,74,65,42,45,96]
[null,"2013-06-06",7.5,8,74,66,41,45,99]
[null,"2013-07-06",7.3,9,74,69,54,46,97]
[null,"2013-08-06",7.2,8,73,72,91,44,93]
[null,"2013-09-06",7.2,8,78,65,72,42,84]
[null,"2013-10-06",7.2,9,80,62,37,41,77]
[null,"2013-11-06",6.9,8,77,57,33,37,70]
[null,"2013-12-06",6.7,10,73,53,32,33,62]
[null,"2014-01-06",6.6,14,80,68,38,43,91]
[null,"2014-02-06",6.7,11,79,62,39,39,78]
[null,"2014-03-06",6.7,10,79,61,36,40,81]
[null,"2014-04-06",6.2,10,79,66,40,42,80]
[null,"2014-05-06",6.3,9,78,68,42,42,85]
[null,"2014-06-06",6.1,7,77,67,39,42,87]
[null,"2014-07-06",6.2,7,78,70,49,42,86]
[null,"2014-08-06",6.1,6,75,67,94,40,80]
[null,"2014-09-06",5.9,6,79,66,60,39,75]
[null,"2014-10-06",5.7,6,79,63,34,37,69]
[null,"2014-11-06",5.8,6,77,54,31,32,61]
[null,"2014-12-06",5.6,6,75,52,31,30,59]
[null,"2015-01-06",5.7,7,80,65,34,37,75]
[null,"2015-02-06",5.5,6,81,60,34,35,67]
[null,"2015-03-06",5.4,6,80,62,35,37,70]
[null,"2015-04-06",5.4,6,80,62,36,39,72]
[null,"2015-05-06",5.6,5,80,65,37,37,75]
[null,"2015-06-06",5.3,5,79,68,39,39,82]
[null,"2015-07-06",5.2,6,79,68,48,39,82]
[null,"2015-08-06",5.0999999999999996,5,82,69,84,38,77]
[null,"2015-09-06",5,5,87,66,100,36,71]
[null,"2015-10-06",5,5,84,63,34,33,66]
[null,"2015-11-06",5.0999999999999996,5,82,55,32,30,60]
[null,"2015-12-06",5,6,81,51,30,28,54]
[null,"2016-01-06",4.9000000000000004,7,89,67,33,34,74]
[null,"2016-02-06",4.9000000000000004,6,97,61,34,34,70]
[null,"2016-03-06",5,5,95,62,35,35,71]
[null,"2016-04-06",5,5,93,63,35,36,77]
[null,"2016-05-06",4.8,5,89,65,36,34,82]
[null,"2016-06-06",4.9000000000000004,5,86,66,35,35,78]
[null,"2016-07-06",4.8,5,83,63,41,33,69]
[null,"2016-08-06",4.9000000000000004,5,83,65,71,34,72]
[null,"2016-09-06",5,4,87,61,90,31,62]
[null,"2016-10-06",4.9000000000000004,4,85,59,31,30,58]
[null,"2016-11-06",4.7,5,84,56,31,28,53]
[null,"2016-12-06",4.7,5,82,51,29,26,50]
[null,"2017-01-06",4.7,7,91,66,33,33,71]
[null,"2017-02-06",4.5999999999999996,5,90,61,36,32,64]
[null,"2017-03-06",4.4000000000000004,5,89,62,34,33,66]
[null,"2017-04-06",4.4000000000000004,5,87,63,34,34,66]
[null,"2017-05-06",4.4000000000000004,4,84,64,35,33,71]
[null,"2017-06-06",4.3,4,85,69,34,33,74]
[null,"2017-07-06",4.3,5,84,70,41,32,72]
[null,"2017-08-06",4.4000000000000004,4,85,70,71,32,71]
[null,"2017-09-06",4.2,4,86,64,79,29,61]
[null,"2017-10-06",4.0999999999999996,4,86,62,31,30,61]
[null,"2017-11-06",4.2,5,89,59,29,27,56]
[null,"2017-12-06",4.0999999999999996,5,86,53,28,25,51]
[null,"2018-01-06",4.0999999999999996,7,90,69,32,32,70]
[null,"2018-02-06",4.0999999999999996,5,91,62,32,30,64]
[null,"2018-03-06",4,4,89,63,32,31,63]
[null,"2018-04-06",4,5,90,64,34,32,68]
[null,"2018-05-06",3.8,4,88,67,34,32,70]
[null,"2018-06-06",4,4,88,70,33,31,75]
[null,"2018-07-06",3.8,5,88,69,41,31,75]
[null,"2018-08-06",3.8,4,89,72,80,31,74]
[null,"2018-09-06",3.7,4,88,65,78,28,62]
[null,"2018-10-06",3.8,4,91,65,31,28,59]
[null,"2018-11-06",3.7,4,90,60,29,25,53]
[null,"2018-12-06",3.9,5,87,55,27,23,48]
[null,"2019-01-06",4,6,95,69,31,29,64]
[null,"2019-02-06",3.8,5,95,65,31,28,61]
[null,"2019-03-06",3.8,4,89,64,31,29,60]
[null,"2019-04-06",3.6,4,91,66,32,30,62]
[null,"2019-05-06",3.6,4,89,69,33,29,68]
[null,"2019-06-06",3.7,4,88,72,31,29,69]
[null,"2019-07-06",3.7,4,86,72,40,28,66]
[null,"2019-08-06",3.7,4,87,72,82,29,65]
[null,"2019-09-06",3.5,4,89,68,71,27,63]
[null,"2019-10-06",3.6,4,92,66,30,26,63]
[null,"2019-11-06",3.5,4,89,59,28,23,55]
[null,"2019-12-06",3.5,5,88,57,26,22,51]
[null,"2020-01-06",3.6,6,96,74,30,28,71]
[null,"2020-02-06",3.5,5,94,65,31,27,65]
[null,"2020-03-06",4.4000000000000004,44,99,55,33,28,49]
[null,"2020-04-06",14.7,100,100,47,48,29,40]
[]
[null,"Data For the Update"]
[null,"2020-05-06",13.3,70,96,53,46,26,51]
[null,"2020-06-07",null,60,93,61,33,27,61]

{"sheet":"Compare2distributions Ex","index":3,"n_rows":290,"n_cols":18,"rows_kept":290,"cut":false,"hidden":false,"merged":[[0,0,0,12],[1,0,3,18],[17,0,17,4],[18,0,19,4],[28,1,28,3],[5,6,5,11],[5,13,5,18],[5,0,5,4],[32,12,32,13],[28,5,28,16],[29,5,31,16],[6,0,8,4],[6,6,8,11],[6,13,8,18],[14,0,15,4],[13,0,13,4],[9,0,9,4],[10,0,11,4]]}
["Example: Comparing Two Distributions"]
["This example shows the probability of sampling from one of two possible underlying distributions. The user can increase the number of observed samples and the probability will determine the true distribution.  The user can also explore different scenarios of sample points to confirm the true distribution. The user can also switch between the two distributions being the true distributions."]
[]
[]
[]
["Samples and Scenarios",null,null,null,null,null,"Distributions and Observed Samples",null,null,null,null,null,null,"Probability that Population 1 is the True Distribution"]
["Use the two slider bars as well as the distribution choice to view how many samples are needed to confirm or deny if the sample is from population 1 vs 2.",null,null,null,null,null,"In this graph the two hypothetical distributions are shown below. The green diamonds show the observed data as it is sampled.  One can increase the number of samples using the slider bar to the right.",null,null,null,null,null,null,"This graph shows the probability that population 1 is the true distribution. One will note how few samples it takes to get a reasonable estimate of the population."]
[]
[]
["Scenario"]
["Different scenarios will randomly changes the samples to show how different random samples could change the estimates."]
[]
[null,null,142]
["Number of Samples"]
["Enter number of samples or use slider bar below.  For a given scenario, increasing the number of samples improves estimates."]
[]
[null,null,6]
["Population Distributions"]
[]
[]
[null,null,"Pop1","Pop2","True Pop"]
[null,"The True, Hidden Population:",null,null,2]
[null,"Chance This is The True Population:",0.5,{"$f":"1-C23","v":0.5}]
[null,"Population Mean:",100,130,{"$f":"IF(E22=1,C24,D24)","v":130}]
[null,"Population Standard Deviation:",40,40,{"$f":"IF(E22=1,C25,D25)","v":40}]
[]
[]
[]
[null,"Distribution Chart Calcs",null,null,null,"Random Samples and Inferences"]
[null,null,"Chart minimum",{"$f":"MIN(C24-4*C25,D24-4*D25)","v":-60},null,"This table is used to generate random samples and make inferences for the chart on the right above.  For each sample, the probability of a sample in that bin for populations 1 and 2 are computed as p(O|Pop1) and p(O|Pop2), respectively. The cumulative set of  observations is shown as O1..On and the probability for that cumulative set is also computed for each population and in total.  Finally, the probability of Population 1 is computed given the cumulative samples."]
[null,null,"Chart maximum",{"$f":"MAX(C24+4*C25,D24+4*D25)","v":290}]
[null,null,"Chart increment size",{"$f":"(D31-D30)/200","v":1.75}]
[null,"X Values","Pop 1","Pop 2",null,"Y-axis for Sample","Sample Count","Random Number","Sample Value","Bin of Sample","p(O|Pop1)","p(O|Pop2)","p(O1..On|Pop1)",null,"p(O1..On|Pop2)","P(O1..On)","P(Pop1|O1..On)"]
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{"sheet":"ControlledExperiment Ws","index":4,"n_rows":121,"n_cols":14,"rows_kept":121,"cut":false,"hidden":false,"merged":[[13,0,13,1],[20,13,20,14],[0,0,0,13],[20,11,20,12],[1,0,1,9],[16,0,16,1],[17,0,17,1],[18,0,18,1],[12,0,12,2],[14,0,14,1],[15,0,15,1]]}
["Worksheet: A Controlled Experiment (The Difference Between Means)"]
["This is an example of a controlled experiment.  This compares the test group and the control group.  If the confidence in the difference is high, it is very unlikely that the difference is due to chance alone or due to factors other than the new training program.  (NOTE: This method uses z-test and therefore requires sample sizes greater than 30)"]
[]
[null,"Control","Test"]
["Sample Size",{"$f":"COUNT(B22:B112)","v":40},{"$f":"COUNT(C22:C111)","v":60}]
["Mean",{"$f":"AVERAGE(B22:B112)","v":8.7759200775005919},{"$f":"AVERAGE(C22:C111)","v":7.4405443719623001}]
["Variance",{"$f":"VAR(B22:B112)","v":8.1356397971792429},{"$f":"VAR(C22:C111)","v":6.0038063018993109}]
["Standard Deviation",{"$f":"B7^0.5","v":2.8523042960349168},{"$f":"C7^0.5","v":2.4502665777215569}]
["Standard Error of Estimate of Mean",{"$f":"B8/B5^0.5","v":0.45098890776767564},{"$f":"C8/C5^0.5","v":0.31632805497614103}]
["Upper Bound of 90% CI",{"$f":"B6+1.645*B9","v":9.5177968307784191},{"$f":"C6+1.645*C9","v":7.9609040223980525}]
["Lower Bound of 90% CI",{"$f":"B6-1.645*B9","v":8.0340433242227647},{"$f":"C6-1.645*C9","v":6.9201847215265477}]
[]
["Test vs. Control"]
["Difference Between Means",null,{"$f":"ABS(B6-C6)","v":1.3353757055382918}]
["Standard Error of the Estimate of Difference between means",null,{"$f":"(C7/C5+B7/B5)^0.5","v":0.55086698330401829}]
["Confidence in difference",null,{"$f":"1-NORMDIST(0,C14,C15,1)","v":0.99232754122570555}]
["90% Confidence Interval of difference"]
["Upper Bound",null,{"$f":"C14+1.645*C15","v":2.2415518930734017}]
["Lower Bound",null,{"$f":"C14-1.645*C15","v":0.42919951800318168}]
[]
["sample #","Control","Test","Std Error for Estimate of Mean (Normalized)","cpf for Control","Incremental P for Control","Control","cpf for Test","Incremental P for Test","Test","ND Test","Confidence Interval Bars",null,"For Plotting"]
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{"sheet":"UnivarReg Ex","index":5,"n_rows":40,"n_cols":5,"rows_kept":40,"cut":false,"hidden":false,"merged":[[6,0,6,3],[7,0,7,3],[8,0,8,3],[9,0,9,3],[5,0,5,3],[0,0,0,12],[1,0,1,4],[2,0,2,4],[3,0,3,3],[4,0,4,3]]}
["Example: Television Ratings Regression "]
["This is the television ratings regression example shown on page 156-160 of How to Measure Anything.  It shows how simple Excel formulas compare to Excel's regression wizard (see below).  These simple Excel formulas only work for situations where we are correlating a single variable to another.  The regression wizard, however, can work for multiple variables (as explained in the example in the book)."]
["Excel Formulas for Simple (one variable) regression"]
["Correlation of ratings to promotion period",null,null,null,{"$f":"CORREL(B13:B40,A13:A40)","v":0.70295213663438982}]
["Slope: Additional ratings points for one extra week of promotion",null,null,null,{"$f":"SLOPE(B13:B40,A13:A40)","v":0.21545340272911928}]
["Intercept: Estimated ratings points if no time was spent on promotion",null,null,null,{"$f":"INTERCEPT(B13:B40,A13:A40)","v":0.87733114434826964}]
["Enter X to estimate Y",null,null,null,3]
["Upper bound of y estimate",null,null,null,{"$f":"E9+1.645*STEYX(B13:B40,A13:A40)","v":2.417092834203415}]
["Mean of y estimate",null,null,null,{"$f":"E7*E5+E6","v":1.5236913525356275}]
["Lower bound of y estimate",null,null,null,{"$f":"E9-1.645*STEYX(B13:B40,A13:A40)","v":0.63028987086784016}]
[]
["Duration of Promotion Period (weeks)","Ratings Points","Model"]
[2.4799907254559801,0.3,{"$f":"$E$6+$E$5*A13","v":1.4116535848844176}]
[0.7,1.2899999999999998,{"$f":"$E$6+$E$5*A14","v":1.0281485262586532}]
[1.2,0.98999999999999988,1.1358752276232127]
[0.5,0.89999999999999991,0.98505784571282928]
[3.24093076471154,1.5678599333659111,1.5756007056148575]
[2,1.3193128762131072,1.3082379498065082]
[3.6650885762427872,1.8540765934252874,1.6669869494034013]
[0.5,0.3,0.98505784571282928]
[4.0586434030968794,2.2046527283141666,1.7517796760095847]
[2.5,2.1229720170100657,1.415964651171068]
[4.3552560569618191,1.2,1.8156858815773005]
[4.9015479318771451,2.1422481160551983,1.9333863249110779]
[3,2.52,1.5236913525356275]
[5.1347294390232454,1.8403452676633203,1.9836260740792098]
[5.182378324790931,2.3408019577336057,1.9938921886541086]
[5.5782074536242359,2.5402655184239618,2.079174921360547]
[5.6008041265800612,2.3825736938118456,2.0840434514392365]
[5.9148155719013129,1.912173491685679,2.151698285829589]
[6.0805310061062716,1.5496954071869937,2.1874022400137809]
[6.1840667654117736,2.6097878488273798,2.2097093716602947]
[8,2.1,2.6009583661812239]
[6.3838768351383548,2.4538333764562532,2.2527591310824291]
[6.5772688066045468,3.3,2.294426089395313]
[6.6492770507414836,1.32,2.3099405106191648]
[6.6610949954465575,1.7999999999999998,2.312486727019138]
[7.0521352478358752,2.4,2.39673768000047]
[8.7532888493102128,3.0426758764100699,2.7632570120030122]
[9.1374977732463911,2.6999999999999997,2.8460361320239551]

{"sheet":"MutivarReg Ws","index":6,"n_rows":10005,"n_cols":31,"rows_kept":2250,"cut":true,"hidden":false,"merged":[[3,25,3,27],[0,0,0,17],[1,0,1,8],[1,10,1,17],[2,0,3,0],[2,1,3,1],[2,2,2,7],[2,11,2,17],[1,19,1,30]],"bounds":{"rows_first":1000,"rows_last":250,"rows_between":1000,"halvings":1}}
["Worksheet: Multivariate Regression Using Linest (10,000 Row Max)"]
["Excel's regression wizard can be used for multivariate regression models, but there is a simpler, dynamic way that doesn't require any add-ins. This example shows how the LINEST() function in Excel allows you to build a dynamic regression model with a single dependent variable and multiple independent variables. Independent variables can be included or excluded on the fly to see how the model changes. Input your data in the yellow cells below and select or deselect independent variables by entering a 1 or 0 in row 4.   The current formulas are made for data up to 10,000 rows long.  If you require more rows, you will need to change range references in all formulas.",null,null,null,null,null,null,null,null,null,"The LINEST() function outputs coefficients for each independent variable, but note that the order of variables is reversed from the input. Headers here are dynamic and are linked to the input headers in columns C:H. Linest can also output regression statistics, just like the regression wizard in the analysis toolpak. Two charts are shown below. The first shows both the actual and estimated depdendent variables on the same axis (defined in column A) for direct comparison. The second shows the actual values VS the estimates, so you can see how the fit more clearly. ",null,null,null,null,null,null,null,null,"This table uses the \"include\" flags to include or exclude an independent variable from the regression calculation. If a flag is turned off, the values below that variable will default to 0. it also contains a dynamic table using the offsett function that alows the user to choose how many rows to include in the regression. The user can also find the calculation for computing the 90% confidence interval for the model."]
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[null,1927,6.35474906699584,6.3888446202437388E-2,1.9530550297005456E-2,0.23855426179111239,0.12564438728331961,0.18019345629571126,0.68876531736903657]
[null,1928,7.0273646055874357,0.23606711471717645,0.70188496851551752,3.1828487225107005E-2,5.7527495563684972E-2,0.51149593961867257,0.41740873530263345]
[null,1929,10.049657609832863,0.2214258579256515,0.28064131251594893,0.30503023831424148,0.87053608232136481,0.80222375606083496,0.14309921705715911]
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[null,1932,5.6947972431705445,0.73315394220949348,0.17057234751983419,0.75643315734497774,0.28784835547073806,0.16422710347697655,6.3111699103102437E-2]
[null,1933,11.287071030533999,0.48619051882627395,9.4379925191995229E-2,0.63498199193753446,0.94045971792409089,0.52858886299338814,0.38373191647463789]
[null,1934,11.232897881982765,0.87654994393624519,0.67630819018771493,0.29485183114590552,1.2158181766128595E-2,0.87644185549639053,0.61472234328115105]
[null,1935,13.272788201406293,0.21181035311349528,0.53604008458983432,0.1247698289582716,{"$f":"RAND()","v":0.80019350796390598},0.80236341233415787,0.73366618311865039]
[null,1936,8.2433825214174306,0.49447253001142688,0.32503349119917779,0.90165333041044882,0.46890427689321346,0.38532659426975036,9.8605489809116098E-2]
[null,1937,8.1547476275926556,0.94251221030260224,0.12047531229331732,0.43469108508683785,7.3589968650524695E-2,0.14139284312377987,0.7776479078703179]
[null,1938,12.985547632440902,0.44025626497931081,0.5356649554335976,0.39430757142242023,0.92315635928751372,0.56126679000551449,0.63201322585825115]
[null,1939,8.7741854278464455,0.5201340515618148,0.51614517622794431,0.38694844029293762,0.42962938939988415,0.1428549542877996,0.60468722898523242]
[null,1940,10.537000962009914,0.90987993020354341,7.7801686353490163E-2,0.1694189996228711,0.8903497011707765,0.21081189943662104,0.7246337263940944]
[null,1941,14.974269263426381,0.46942672500683191,0.61825234802756335,0.28994904137413136,0.55588307168924,0.96508292525529094,0.89159063420143547]
[null,1942,8.1050864220039429,9.4510022604826771E-3,0.5848625700440877,9.9303059988407938E-2,0.72039456692033843,0.44073725209439329,0.25712276192279016]
[null,1943,10.828515848096604,0.89669153706976445,9.966863184605268E-3,0.39415187740306912,0.5743793182962752,0.16473331932575586,0.93470851377242359]
[null,1944,15.058561439858066,0.33355654967805537,0.92274909190887511,0.7600850171596184,0.62664478119861933,0.64443540427481638,0.81174925145247445]
[null,1945,11.922123153081063,6.5282412048984662E-2,0.73227706889570132,0.42220545418342981,0.86943812216754413,0.24189542698509814,0.73974010284911973]
[null,1946,8.0897621003420408,0.29941578668253532,0.43108446705254533,7.8993811058360675E-2,0.71702846702692347,0.59593286248987665,0.14056962763704273]
[null,1947,10.688577439674434,0.24832330704488026,0.20152655273044673,0.62001122485571236,0.39889363638608333,0.92394333127262185,0.32697935844901338]
[null,1948,10.565875502700463,0.49634517113933307,0.81734830573530981,0.7847787762230134,0.62629000683372216,0.54473647122009994,0.14194250133101349]
[null,1949,7.7960681753900047,0.1803524981514768,0.40015971657916893,0.30047575611560451,0.54092195763455053,6.2966686486717549E-2,0.57257461879359783]
[null,1950,8.7312691878299802,5.7880423822202931E-2,0.35187542535372807,0.36148738694726879,6.6762134519393834E-2,0.80435426586789138,0.43272598084024694]
[null,1951,9.321310901012577,0.47442326424984349,0.1269201075672064,0.94069860892983093,0.47329619503707809,0.13939627209264727,0.53013090903787974]
[null,1952,9.9779072454129096,8.4127036653073084E-2,0.78394400644032003,0.53897759114230503,0.28026817769893309,0.98268701705193506,0.11240860439947886]
[null,1953,11.051803457046081,0.33180340729904834,0.11991221270486496,0.79559810918018625,0.50830957826719902,0.4219056663244467,0.65843577535095255]
[null,1954,7.0791681632243755,0.4848100173126989,0.40468372188896318,0.57396714533092674,0.17093312170435437,6.3592071336789013E-2,0.51023273710660133]
[null,1955,8.6709591707891978,7.7940406540714546E-2,0.65235813679751831,0.23588712867958161,0.65845079062755085,0.24908370536617219,0.45023656921227295]
[null,1956,7.8985879119140376,{"$f":"RAND()","v":0.62332787539617118},0.62118022961405317,4.4861453972469434E-2,0.16450470699281494,0.36063532697046341,0.57285329209146252]
[null,1957,7.4445199060268159,0.19656612711464783,0.21407206149960856,0.16076248062625631,0.17702190464129197,0.6050957614842063,0.43399263134133048]
[null,1958,12.762709329206658,0.96458889689453908,0.86948363088361236,0.27714489703264489,0.30838471540355594,0.96105476441466953,0.53148429929323115]
[null,1959,15.208901172399832,0.89798922703524864,0.36958115487577192,0.2695096085138019,0.77314580963551238,0.87443758178567355,0.88307494376686935]
[null,1960,9.580979980587351,0.49755065815652677,0.23928355799772538,0.14295669939430977,0.77981346143287877,0.5518867052158245,0.38288412274030115]
[null,1961,12.472173929958299,0.63903018591877947,0.53872992892500138,0.98992701515567916,0.67625119871778983,0.21349998965591821,0.66889968292862101]
[null,1962,13.890126758638429,0.82285803372272037,0.51929141865738648,0.93074986408269977,0.71664595263873798,0.59387984767390323,0.56674220773806128]
[null,1963,4.8580435787971776,0.43079077035309654,0.72321861022697109,0.36897859034292424,0.29473020608278155,9.102756565623904E-2,3.9970194058174036E-2]
[null,1964,11.042644763215996,0.68048990164563139,0.46235919510086898,0.9607282684740921,0.71914657022937356,0.1477010789926011,0.49002666501097536]
[null,1965,13.965540176780403,0.55018630556137094,0.75411139121722448,0.76258366118391285,0.92240409281804236,0.81208807215115053,0.3115538955341538]
[null,1966,9.651776103389885,0.43440022254450461,0.24651439936552066,0.69982246879399068,6.5279103931415783E-2,0.20385567675491145,0.89074747937202448]
[null,1967,12.004668258191007,0.82910478262489884,0.61753696313762585,0.67506125769634484,0.60340711522463153,8.4184721654311345E-2,0.84679228450528965]
[null,1968,6.3816258370480421,0.78672994730142232,0.94961253692168612,0.65660303756896821,0.31080740177567623,8.0396036620334566E-2,1.3441985498660824E-2]
[null,1969,11.60071782145242,0.74051572993044423,0.71891863020508218,0.22422341267252111,6.8681266444209355E-3,0.99621369376278579,0.62352560295043935]
[null,1970,7.8044007547024563,0.75641993465925361,0.78952826401897336,0.84908364549885795,0.4829028917950311,1.9446123761445944E-2,0.14880519492022137]
[null,1971,9.7748409537965841,5.4582225517648686E-3,0.50483223923104315,0.57483939014674446,0.63091784046409627,0.5205063169354005,0.31816618930151863]
[null,1972,10.256588383338997,0.74193375783662185,2.5136176853521097E-2,0.70953234581664015,0.45715487801559329,0.76699079792014502,0.27870195544705223]
[null,1973,10.568459563015546,0.27481822332262418,0.56580801388427415,0.81739067730182713,0.63880369722434982,0.45128732458870968,0.3163669780296573]
[null,1974,11.870622236769252,6.707859961281426E-3,0.39886389257574006,0.97352650413379416,0.57884643475618958,0.57629239874318394,0.4914598910857384]
[null,1975,3.2072889737668899,0.32081378429567409,0.72570593914854253,9.3065524952634648E-2,0.12272778787846939,3.2093301049633816E-3,0.10815148904625538]
[null,1976,10.980986364152908,0.25869923090785329,1.679856191636242E-2,0.90759726172158472,0.35207030438305442,0.93784247198883597,0.31140077446186298]
[null,1977,7.7117613840027364,0.94121854226999335,8.4288472960048377E-2,0.21439375647010539,0.54946344168922978,0.40950989000959748,0.2855635682662373]
[null,1978,13.003159963055687,0.98374887142813783,0.78833998547035988,0.66429737382491372,0.57520514275011536,0.91315582564672448,0.26387321666300079]
[null,1979,15.851073948693983,0.84591938310919801,0.71756089460018391,0.42481537633100619,0.7000411372756522,0.83372489043330533,0.88779960768704358]
[null,1980,10.025311983996271,0.53662693632684555,0.25772552677675276,0.65713206921841483,0.50720281051131821,0.52622157473954034,0.39031977845295018]
[null,1981,8.3878492489519445,0.52753415820469285,0.94278185571543327,0.14888459016539757,0.11471647139513785,0.97917489964280124,2.8892870837605833E-2]
[null,1982,11.088888161500709,0.94949514100929477,0.17275495661048446,0.83599419760856408,0.55702184084160422,0.97577910784478517,2.9819601975734966E-2]
[null,1983,11.734595382847328,0.63897787927996008,0.50682722196546148,0.77854726046595757,0.33060938727609646,9.4248889895830912E-2,0.99210654660917175]
[null,1984,8.3955685551869266,0.86083239654693411,0.43190980120885847,0.29694649378596971,0.45420196686341974,0.40776588517546741,0.32073996358889145]
[null,1985,14.719364287470372,0.29100994886021925,0.20577193480441813,0.74329259410880999,0.92004860063713234,0.7816884354265734,0.69971601783224813]
[null,1986,{"$f":"D1989+2*E1989+3*F1989+4*G1989+5*H1989+6*I1989","v":11.087879006610448},0.30019278581275255,0.45911178150609977,0.89995483565800993,{"$f":"RAND()","v":0.28404918044401029},0.46153992539670807,0.62095030034198084]
[null,1987,5.5042791553610355,0.12803188145299527,0.93334592569162511,0.78986797746165549,9.4388596420836857E-2,5.5670351711584964E-2,8.0674224316425236E-2]
[null,1988,10.936276821218982,5.9657963753309673E-2,0.95203274258164117,0.83997183516381824,0.95329495088174554,5.3324613507848007E-2,0.39547249929078576]
[null,1989,15.856516001339461,0.67559688599065981,0.99507154460596536,0.47590291125993378,0.69234030700748039,0.84217978260403137,0.79713452521783168]
[null,1990,9.7306983611891607,0.64217701510244007,8.3584440756606648E-2,0.30135420076472019,0.26370765116248196,0.90039866243362621,0.41007765757688142]
[null,1991,12.499771525377389,0.9758585698432235,0.83747810706103898,0.64426620561327708,0.86028007313103205,0.66911342629005088,0.1882451167663125]
[null,1992,15.431695128821183,0.96565679175097985,0.49887239887949542,0.57208450726398019,0.62544069553252601,0.86720988454359493,0.81903796877853197]
[null,1993,5.3591590227358434,0.89557535900937513,0.62260595920606032,0.3156883561444872,6.0242440001466391E-2,1.0643535778777635E-2,0.32951987299685526]
[null,1994,10.124934788000035,0.57673450463456655,0.61777430688249468,0.9264655991743258,0.35399313012070022,0.50663130566958081,0.2640209705411326]
[null,1995,11.281789816540055,9.655133522758419E-2,0.42136143050572061,0.94862632958448079,0.60268541931132791,0.98320696325148338,2.8310023007476426E-2]
[null,1996,9.4653612364943331,0.22119648903126576,0.22049620713416218,0.23310804398568119,0.79262859409343456,8.800239309960356E-2,0.74888697656099068]
[null,1997,8.0849011989803508,0.48248908239207822,0.14092728807438915,0.41183372634058657,0.19537376824484787,0.71594847623088476,0.28730315121398653]
[null,1998,9.0763541362744142,0.37104282232097052,0.92440573817817906,0.60443540768490145,0.84318714672770101,0.2905578300304994,3.627597957984674E-2]
[null,1999,10.828929978285311,0.80012960002170108,0.66710436595601241,3.3820309343163268E-2,0.49223732789131214,0.70815386241181166,0.51390201578296468]
[null,2000,11.746404759110336,0.37684460833602273,0.92552082255405899,0.25663346834000833,0.83680325002187739,0.22868169806644245,0.70966610170440803]
[null,2001,8.0673788492021803,0.29284522614011765,0.58690168367889051,0.75869674788241104,0.24978451857581752,0.4445303812368111,0.18380833859495371]
[null,2002,5.4238602710101071,0.9339857149165528,0.87106935651859718,2.6299144255531037E-2,0.10393217895303919,0.21515485631457465,0.19622256881745603]
[null,2003,5.5064186400385982,0.53763601905511871,0.46250352198014533,0.47236214359167339,0.10398284128339874,6.1115895730397662E-2,0.31752971707709765]
[null,2004,12.416711824418172,0.43885423914606014,0.51086720055059098,0.50321738603229371,0.80852465511237726,0.13487110568710425,0.92300281286483643]
[null,2005,5.6356000481402386,0.11075529836332532,2.4085849001314719E-2,0.70275361649200907,6.3282168263235294E-2,0.12484627771107093,0.41517535678166007]
[null,2006,15.267682914097474,0.10919726263837715,1.9269822095644207E-2,0.94440270842616902,0.65800938834937428,0.93978090802470915,0.82596596474470974]
[null,2007,12.799424493152186,0.51044506247514843,0.58314198367756975,0.7082322224436457,0.68741843494023336,0.57383202975542946,0.56319415124214667]
[null,2008,8.7517443802068442,0.7755338851100565,0.33327389864819446,0.94858541596820301,0.73420400349596482,0.19982412255186577,8.7994970525433369E-2]
[null,2009,11.586776306209867,0.99061764890682269,0.53200729543238157,0.9373794762994605,0.44693316213915679,0.65107897173524676,0.27947968838450643]
[null,2010,9.5049214530239858,0.1963778592136104,0.27834273199896598,0.92945753257727715,0.91276689335933303,0.14411303209473159,0.26530879969493715]
[null,2011,8.8722406508130547,0.52699290752328853,0.27181633630489632,0.23844484857126325,0.68932728098736507,0.52906041207099619,0.28061155677695693]
[null,2012,7.3504353084043004,0.6420912496371971,0.21026298323691406,0.25114562668374019,3.1252964180151999E-2,0.34367628039938247,0.61516465892075567]
[null,2013,10.343035439317378,0.33328404106243026,0.74116970823652473,0.47225996338568876,0.89450468862423482,0.48926564124814453,0.18104752181452832]
[null,2014,16.577468802917036,0.57695169738867857,8.5795134962611153E-2,0.77268866210841791,0.87471632823013579,0.99223641706526977,0.84180224183849817]
[null,2015,14.663271016350112,0.17708846822655233,0.97204097337280593,0.7707645521340174,0.68776418061658384,0.66903087789068449,0.68893263884268974]
[null,2016,7.6536621603165056,0.64377050183334594,0.72287362664567789,0.52585733241136257,0.59124513392366163,0.21657911184334089,8.9782718841060705E-2]
[null,2017,7.1612362434576982,0.66918093694884428,0.82497310771520238,0.81139268258384012,0.32996836902613946,8.1279546235437761E-2,0.11360997267419692]
[null,2018,11.094261267264063,0.48390510052446989,0.59111654618556142,0.20415105373526676,0.87726173160000975,0.27316725501753014,0.65679778527916344]
[null,2019,5.9658522310511097,7.2868567991541955E-3,0.38649566910988542,0.82714800184222104,0.2445241240967565,0.16414064589383581,0.15088838410821948]
[null,2020,8.8359496876212233,{"$f":"RAND()","v":0.64059308787691549},0.1791205203525138,4.7912193806659231E-2,0.7030993268697362,0.3719419822235932,0.50354529317039864]
[null,2021,14.743817637740285,0.30032295915057117,0.9764436100959718,0.79071461101863016,0.99937490164314868,0.56615694036179764,0.54836321949338318]
[null,2022,11.832054756733797,0.22289118736055058,0.93931857035643218,0.22706004796504786,0.47946241242632215,0.47946482552299652,0.78902875124082783]
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{"sheet":"LOR Estimates Ws","index":8,"n_rows":40,"n_cols":12,"rows_kept":40,"cut":false,"hidden":false,"merged":[[1,1,3,8],[30,0,33,0],[36,0,38,0],[4,0,7,0],[9,2,9,8],[11,0,14,0],[16,0,19,0],[21,0,24,0]]}
[null,"Worksheet: Log Odds Ratio "]
[null,"This spreadsheet shows an example of how to use the Log Odds Ratios (LOR) to apply several conditions to a single probability.  This spreadsheet will estimate the conditional probability of a cybersecurity event  given the aggregate effect of several conditions.  Further details are given in the areas to the left below."]
[]
[]
["In the yellow cells to the right, enter time period of your estimates in years and the initial probability of a cybersecurity event occurring  in the that time period. For example, you might estimate the likelihood of an event over a 5 year period at 5%. You are given no information about the event other than it is one of your applications.  This is then converted to a baseline log odds ratio that the adjustments below will be applied to.  It also computes a total number of combinations of the attributes (just for reference).","Time Period for Estimates (years):",5]
[null,"Initial Probability of Event per Time Period: P(E)",0.1]
[null,"Baseline Log Odds",{"$f":"IFERROR(LN(C6/(1-C6)),\"\")","v":-2.1972245773362191}]
[null,"Condition Combinations",{"$f":"IFERROR(PRODUCT(C29:I29),\"\")","v":864}]
[]
[null,null,"Conditions"]
["Each column represnts a unique \"class\" of attributes that affect the likelihood of a cybersecurity event. Make sure the classes are non-overlapping and non-redundant. ",null,"Web","Platform","Pen Results","Server/ Vendor","Age","Users","Data"]
["Enter the possible attributes for each class. There is space for 4 attributes, but it is not neceesary to fill out all 4. Some classes may have 2 attributes, others may have 3 or 4, etc. These attributes should be orthogonal; i.e., they should not overlap with each other. They should also cover all possible states of a class. For example, whether or not an app is on the web is either a \"yes\" or a \"no\". There is no overlap between those attributes and they cover all possible states of being on the web. For a continuous variable, such as age, you should define bins of logical sizes. For example, the bins might be: \"<1 yr\", \"1-5 yrs\", or \"5+ yrs\"","X1","Web","MS","Pos Pen","Internal","<1 Year","Less than 5","PHI, PII, PCI, $"]
[null,"X2","No Web","Not MS","Neg Pen","External US","1 to 5 Years","5 to 200","Critical IP"]
[null,"X3",null,null,null,"Foreign","5+ Years","200 to 2000","No Critical Data"]
[null,"X4",null,null,null,null,null,"Over 2000"]
[]
["Enter the conditional probability of a cybersecurity event given each of the attributes listed above. \nAnother way to phrase this question is, \"Given a random application, the baseline probability of a cybersecurity event in the next T years is X%. If you learn one thing about that application, whether or not it is externally accessible, how does that affect the probability of an event?","P(E|X1)",0.15,0.2,0.3,7.0000000000000007E-2,0.15,0.05,0.32]
[null,"P(E|X2)",0.05,0.09,0.05,0.09,0.1,0.08,0.12]
[null,"P(E|X3)",null,null,null,0.13,0.05,0.15,0.02]
[null,"P(E|X4)",null,null,null,null,null,0.36]
[]
["In this section, enter how frequently the attributes listed above occur. In other words, enter the percentage of applications that fall into that category. If this information is readily available, fill it out with actual values. Otherwise, provide calibrated estimates based on your knowledge of the environment.","P(X1)",0.5,0.09,0.2,0.4,0.33300000000000002,0.15,0.15]
[null,"P(X2)",0.5,0.91,0.8,0.3,0.33300000000000002,0.18,0.35]
[null,"P(X3)",null,null,null,0.3,0.33300000000000002,0.42,0.5]
[null,"P(X4)",null,null,null,null,null,0.25]
[]
["The sum of the probabilities of each attribute should equal 100%. In other words, the attributes should reflect all possible states for a given class.","Sum Check P(X) =100%",{"$f":"IF(SUM(C22:C25)=1, \"Good\", SUM(C22:C25))","v":"Good"},{"$f":"IF(SUM(D22:D25)=1, \"Good\", SUM(D22:D25))","v":"Good"},"Good","Good",0.99900000000000011,"Good","Good"]
["The weighted average of the conditional probabilities should be close to the baseline probability. If the weighted average is close to the baseline, this row will return \"Good\". Otherwise, you will see the actual weighted average and you need to adjust the conditional probabilities or frequency of attributes until this row reads \"Good\" all the way across.","Test P( E) Computed=Stated",{"$f":"IF(AND(SUMPRODUCT(C17:C20,C22:C25)>initialP-0.0005,SUMPRODUCT(C17:C20,C22:C25)<initialP+0.0005), \"Good\", SUMPRODUCT(C17:C20,C22:C25))","v":"Good"},"Good","Good",9.4E-2,"Good",0.1749,"Good"]
["This simply counts the attributes for each class.","Count of Possible States",{"$f":"IF(COUNTA(C12:C15)=0,\"\",COUNTA(C12:C15))","v":2},{"$f":"IF(COUNTA(D12:D15)=0,\"\",COUNTA(D12:D15))","v":2},2,3,3,4,3]
[]
["This is where the change in Log Odds Ratio is computed. \n\nYou do not need to edit anything in this range of cells.","Log Odds change|X1",{"$f":"IF(C17=\"\",\"\",LN(C17/(1-C17))-$C$7)","v":0.46262352194811274},{"$f":"IF(D17=\"\",\"\",LN(D17/(1-D17))-$C$7)","v":0.81093021621632855},1.3499267169490157,-0.38946476676172326,0.46262352194811274,-0.74721440183022114,1.4434527749598391]
[null,"Log Odds change|X2",-0.74721440183022114,-0.11641035184441151,-0.74721440183022114,-0.11641035184441151,0,-0.24512245803298516,0.20479441264601284]
[null,"Log Odds change|X3","","","",0.29626581614317216,-0.74721440183022114,0.46262352194811274,-1.6945957207744073]
[null,"Log Odds change|X4","","","","","",1.6218604324326573,""]
[]
["Choose combinations of attributes to see how the conditional probability of an event changes (below).","Condition State that Applies","Web","Not MS","Pos Pen","Internal","1 to 5 Years","5 to 200","Critical IP"]
["Each attribute contributes to the likelihood of a cybersecurity event. The change in Log Odds Ratio is referenced from the rows above, then the sum of the changes is added to the baseline log odds ratio. Finally, the updated log odds ratio is converted back to a probability.","Attribute Contribution to Likelihood",{"$f":"IF(C36=\"\",\"\",INDEX(C31:C34, MATCH(C36, C12:C15, 0)))","v":0.46262352194811274},-0.11641035184441151,1.3499267169490157,-0.38946476676172326,0,-0.24512245803298516,0.20479441264601284]
[null,"Total Adjustment",{"$f":"SUM(C37:I37)","v":1.2663470749040213}]
[null,"Conditional Probability",{"$f":"1/(1+1/EXP(C7+C38))","v":0.28274672220353503}]
[null,null,null,null,null,null,null,null,null,null,null,"No"]