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["             Multivariate Linear Regression",null,null,null,null,null,null,null,null,null,null,"Enter the data values in the cells below:"]
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[null,"This DIGMath module lets you find the best",null,null,null,null,null,null,null,null,null,1,1,6,55]
[null," multivariate linear fit -- the regression plane --",null,null,null,null,null,null,null,null,null,2,15,8,53]
[null,null," to fit a set of (X1, X2, Y) data",null,null,null,null,null,null,null,null,3,32,11,56]
[null,null,"with 2 independent variables.",null,null,null,null,null,null,null,null,4,46,21,59]
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["How many data points, n, between 3 and 50?",null,null,null,null,null,null,null,null,null,null,6,74,25,67]
[null,"   n =",{"$f":"E9","v":18},null,18,null,null,null,null,null,null,7,91,29,72]
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["Based on your data,",null,null,null,null,null,null,null,null,null,null,10,135,37,84]
["      the equation of the multivariate regression equation is",null,null,null,null,null,null,null,null,null,null,11,152,41,89]
[null,null,null,null,null,null,null,null,null,null,null,12,196,48,98]
[null,null,"Y =",{"$f":"a","v":3.3815666975809648},"X1",{"$f":"IF(b>=0,\"+\",\"-\")","v":"+"},{"$f":"ABS(b)","v":1.200703445564443},"X2",{"$f":"IF(c0>=0,\"+\",\"-\")","v":"-"},{"$f":"ABS(c0)","v":83.099561772857669},null,13,213,55,99]
[null,null,null,null,null,null,null,null,null,null,null,14,227,51,98]
[null,null,null,null,null,null,null,null,null,null,null,15,244,63,94]
[null,"The Sum of the Squares =",null,null,null,null,{"$f":"Sheet2!J53","v":1602.7613569187331},null,null,null,null,16,258,69,90]
[null,null,null,null,null,null,null,null,null,null,null,17,274,75,85]
[null,null,null,null,null,null,null,null,null,null,null,18,288,80,80]
[null,"The coefficient of multiple determination =",null,null,null,null,null,null,null,{"$f":"Sheet2!C64","v":0.98938456156335286},null,19,305,88,72]
[null,null,"so that",{"$f":"100*J21","v":98.938456156335292},"% of the variation is  ",null,null,null,null,null,null,20,319,93,66]
[null,null,null,null,null,"explained by the linear function",null,null,null,null,null,21,335,97,61]
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["Click each item below for suggestions and investigations",null,null,null,null,null,null,null,null,null,null,26]
[null,null,"   Item 1",null,null,null,null,null,null,null,null,27]
[null,null,"   Item 2",null,null,null,null,null,null,null,null,28]
[null,null,"   Item 3",null,null,null,null,null,null,null,null,29]
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[null,"Created by:  Sheldon P. Gordon",null,null,null,null,null,null,null,null,null,35]
[null,"                     Farmingdale StateCollege",null,null,null,null,null,null,null,null,null,36]
[null,"Development of this module was supported by the ",null,null,null,null,null,null,null,null,null,37]
[null,"NSF's Division of Undergraduate Education  ",null,null,null,null,null,null,null,null,null,38]
[null,"under grants DUE-0310123 and DUE-0442160.",null,null,null,null,null,null,null,null,null,39]
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["             Multivariate Linear Regression",null,null,null,null,null,null,null,null,null,null,null,"Enter the data values in the cells below:"]
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[null,"    This DIGMath module lets you find the best",null,null,null,null,null,null,null,null,null,null,1,1,6,55,88]
[null," multivariate linear fit -- the regression \"plane\" --",null,null,null,null,null,null,null,null,null,null,2,15,8,53,84]
[null,null,"to fit a set of (X1, X2, X3, Y) data",null,null,null,null,null,null,null,null,null,3,32,11,56,77]
[null,null,"  with 3 independent variables.",null,null,null,null,null,null,null,null,null,4,46,21,59,72]
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["How many data points, n, between 3 and 50?",null,null,null,null,null,null,null,null,null,null,null,6,74,25,67,64]
[null,"   n =",{"$f":"E9","v":11},null,11,null,null,null,null,null,null,null,7,91,29,72,61]
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["Based on your data,",null,null,null,null,null,null,null,null,null,null,null,10,135,37,84,44]
["      the equation of the multivariate regression equation is",null,null,null,null,null,null,null,null,null,null,null,11,152,41,89,38]
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[null,"      Y =",{"$f":"aa","v":0.22317164548178425},"X1",{"$f":"IF(bb>=0,\"+\",\"-\")","v":"+"},{"$f":"ABS(bb)","v":1.092945085685642},"X2",{"$f":"IF(cc>=0,\"+\",\"-\")","v":"-"},{"$f":"ABS(cc)","v":2.1081878930247058},"X3",{"$f":"IF(dd>=0,\"+\",\"-\")","v":"+"},{"$f":"ABS(dd)","v":129.9289990743564},13,213,55,99,32]
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["           The Sum of the Squares =",null,null,null,null,{"$f":"sss","v":97.444739887190963},null,null,null,null,null,null,16,258,69,90,22]
[null,null,null,null,null,null,null,null,null,null,null,null,17,274,75,85,17]
[null,null,null,null,null,null,null,null,null,null,null,null,18,288,80,80,14]
[null,"The coefficient of multiple determination =",null,null,null,null,null,null,{"$f":"Sheet2!P64","v":0.99606896096159114},null,null,null,19,305,88,72,11]
[null,null,"so that",{"$f":"100*I21","v":99.606896096159119},"% of the variation is  ",null,null,null,null,null,null,null,20,319,93,66,10]
[null,null,null,null,null,"explained by the linear function",null,null,null,null,null,null,21,335,97,61,7]
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["Click each item below for suggestions and investigations",null,null,null,null,null,null,null,null,null,null,null,25]
[null,null,"   Item 1",null,null,null,null,null,null,null,null,null,26]
[null,null,"   Item 2",null,null,null,null,null,null,null,null,null,27]
[null,null,"   Item 3",null,null,null,null,null,null,null,null,null,28]
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[null,null,null,null,null,null,null,null,null,null,null,null,30]
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["Click each item below for suggestions and investigations",null,null,null,null,null,null,null,null,null,null,null,41]
[null,null,null,"   Item 1",null,null,null,null,null,null,null,null,42]
[null,null,null,"   Item 2",null,null,null,null,null,null,null,null,43]
[null,null,null,"   Item 3",null,null,null,null,null,null,null,null,44]
[null,null,null,"   Item 4",null,null,null,null,null,null,null,null,45]
[null,null,null,null,null,null,null,null,null,null,null,null,46]
[null,"Created by:  Sheldon P. Gordon",null,null,null,null,null,null,null,null,null,null,47]
[null,"                     Farmingdale StateCollege",null,null,null,null,null,null,null,null,null,null,48]
[null,"Development of this module was supported by the ",null,null,null,null,null,null,null,null,null,null,49]
[null,"NSF's Division of Undergraduate Education  ",null,null,null,null,null,null,null,null,null,null,50]
[null,"under grants DUE-0310123 and DUE-0442160."]

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