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{"sheet":"Regression","index":0,"n_rows":55,"n_cols":12,"rows_kept":55,"cut":false,"hidden":false,"merged":[]}
[null,"     Polynomial Regression",null,null,null,null,null,null,null,"Enter the data values in the cells below:"]
[null,null,null,null,null,null,null,null,null,null,"x","y"]
[null,"    This DIGMath module lets you find the",null,null,null,null,null,null,null,1,0,2]
[null,"    best polynomial fit of degree 1, 2, …, 6",null,null,null,null,null,null,null,2,1,7]
[null,null,"    to fit a set of (x,  y) data",null,null,null,null,null,null,3,2,14]
[null,"      using the least-squares approach.",null,null,null,null,null,null,null,4,4,26]
[null,null,null,null,null,null,null,null,null,5,5,17]
["How many data points, n, between 2 and 50?",null,null,null,null,null,null,null,null,6,7,11]
[null,"   n =",{"$f":"E9","v":8},null,8,null,null,null,null,7,10,31]
[null,null,null,null,null,null,null,null,null,8,12,63]
["What degree polynomial (1 to 6) do you want?",null,null,null,null,null,null,null,null,9,121,27]
[null,"   deg =",{"$f":"E12","v":4},null,4,null,null,null,null,10,135,37]
[null,null,null,null,null,null,null,null,null,11,152,41]
[null,null,null,null,null,null,null,null,null,12,196,48]
[null,null,null,null,null,null,null,null,null,13,213,55]
["Based on your data, the equation",null,null,null,null,null,null,null,null,14,227,51]
[{"$f":"\"   of the \"&IF(n=1,\"linear\",IF(n=2,\"quadratic\",IF(n=3,\"cubic\",IF(n=4,\"quartic\",IF(n=5,\"5th degree\",\"6th degree\")))))&\" regression function is\"","v":"   of the quartic regression function is"},null,null,null,null,null,null,null,null,15,244,63]
[null,null,null,null,null,null,null,null,null,16,258,69]
[{"$f":"IF(n=1,Sheet2!AA4,IF(n=2,Sheet2!AA5,IF(n=3,Sheet2!AA6,IF(n=4,Sheet2!AA7,IF(n=5,Sheet2!AA8,Sheet2!AA9)))))","v":"y = 0.003x^4 + 0.111x^3 - 2.396x^2 + 12.438x - 0.103"},null,null,null,null,null,null,null,null,17,274,75]
[null,null,null,null,null,null,null,null,null,18,288,80]
["    The coefficient of multiple determination R2 =",null,null,null,null,null,null,{"$f":"Sheet2!S11","v":0.96454496522755273},null,19,305,88]
[null,{"$f":"IF(n=1,\"so the correlation coefficient r = \"&TEXT(SQRT(H21),\"0.00\"),\"\")","v":""},null,null,null,null,null,null,null,20,319,93]
[{"$f":"\"    so the function explains \"&TEXT(100*H21,\"0.0\")&\"% of the variation in the data\"","v":"    so the function explains 96.5% of the variation in the data"},null,null,null,null,null,null,null,null,21,335,97]
[null,null,null,null,null,null,null,null,null,22,349,103]
["           and the Sum of the Squares =",null,null,null,null,null,{"$f":"sss","v":76708.507730319048},null,null,23]
[null,null,null,null,null,null,null,null,null,24]
[null,null,null,null,null,null,null,null,null,25]
[null,null,null,null,null,null,null,null,null,26]
[null,null,null,null,null,null,null,null,null,27]
[null,null,null,null,null,null,null,null,null,28]
[null,null,null,null,null,null,null,null,null,29]
[null,null,null,null,null,null,null,null,null,30]
[null,null,null,null,null,null,null,null,null,31]
[null,null,null,null,null,null,null,null,null,32]
[null,null,null,null,null,null,null,null,null,33]
[null,null,null,null,null,null,null,null,null,34]
[null,null,null,null,null,null,null,null,null,35]
[null,null,null,null,null,null,null,null,null,36]
[null,null,null,null,null,null,null,null,null,37]
[null,null,null,null,null,null,null,null,null,38]
[null,null,null,null,null,null,null,null,null,39]
[null,null,null,null,null,null,null,null,null,40]
[null,null,null,null,null,null,null,null,null,41]
["Click each item below for suggestions and investigations",null,null,null,null,null,null,null,null,42]
[null,null,"   Item 1",null,null,null,null,null,null,43]
[null,null,"   Item 2",null,null,null,null,null,null,44]
[null,null,"   Item 3",null,null,null,null,null,null,45]
[null,null,"   Item 4",null,null,null,null,null,null,46]
[null,null,null,null,null,null,null,null,null,47]
[null,null,null,null,null,null,null,null,null,48]
[null,"Created by:  Sheldon P. Gordon",null,null,null,null,null,null,null,49]
[null,"                     Farmingdale StateCollege",null,null,null,null,null,null,null,50]
[null,"Development of this module was supported by the "]
[null,"NSF's Division of Undergraduate Education  "]
[null,"under grants DUE-0310123 and DUE-0442160."]

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[3,{"$f":"IF(A4<=nn,Regression!L5,\"\")","v":14},{"$f":"IF($A4<=nn,Regression!K5,\"\")","v":2},4,8,16,32,64,15.936058150415253,{"$f":"I4-C4","v":13.936058150415253},{"$f":"IF($A4<=nn,C4,x0)","v":2},{"$f":"IF($A4<=nn,B4,y0)","v":14},"a =",{"$f":"SLOPE(C2:C51,B2:B51)","v":0.18798793045643949},"b  =",{"$f":"INTERCEPT(C2:C51,B2:B51)","v":1.1067579864936059},null,"d0 =",{"$f":"IF(n<3,0,IF(n=3,AA21,IF(n=4,AB26,IF(n=5,AC31,IF(n=6,AD36,0)))))","v":0.11063899748330372},null,null,"dx =",{"$f":"(xMax-xMin)/200","v":0.06},0.12,1.3550911602919349,"P1 =",{"$f":"\"y = \"&TEXT(a,\"0.000\")&\"x \"&IF(b<0,\"- \",\"+ \")&TEXT(ABS(b),\"0.000\")","v":"y = 0.188x + 1.107"},null,null,null,null,null,null,null,null,null,2,14,15.936058150415253,{"$f":"IF(AK4=\"\",\"\",(AL4-AM4)^2)","v":3.7483211617893293}]
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[5,{"$f":"IF(A6<=nn,Regression!L7,\"\")","v":17},{"$f":"IF($A6<=nn,Regression!K7,\"\")","v":5},25,125,625,3125,15625,10.610491368181235,5.6104913681812345,5,17,null,null,null,null,null,"f0 =",{"$f":"IF(n<5,0,IF(n=5,AA31,AB36))","v":0},null,null,null,null,0.24,2.7455087715898165,"P3 =",{"$f":"\"y = \"&TEXT(AA21,\"0.000\")&\"x^3 \"&IF(AB21<0,\"- \",\"+ \")&TEXT(ABS(AB21),\"0.000\")&\"x^2 \"&   IF(AC21<0,\"- \",\"+ \")&TEXT(ABS(AC21),\"0.000\") &\"x \"&  IF(AD21<0,\"- \",\"+ \")&TEXT(ABS(AD21),\"0.000\")","v":"y = 0.190x^3 - 2.982x^2 + 13.827x - 0.585"},null,null,null,null,null,null,null,null,null,5,17,10.610491368181235,40.825820556086512]
[6,{"$f":"IF(A7<=nn,Regression!L8,\"\")","v":11},{"$f":"IF($A7<=nn,Regression!K8,\"\")","v":7},49,343,2401,16807,117649,-13.261419364413644,-20.261419364413644,7,11,"xMin =",{"$f":"MIN(B2:B51)","v":2},"xMax =",{"$f":"MAX(B2:B51)","v":63},null,"g0 =",{"$f":"IF(n=6,AA$36,0)","v":0},"x^6",null,null,null,0.3,3.4156003853867363,"P4 =",{"$f":"\"y = \"&TEXT(AA26,\"0.000\")&\"x^4 \"&IF(AB26<0,\"- \",\"+ \")&TEXT(ABS(AB26),\"0.000\")&\"x^3 \"&IF(AC26<0,\"- \",\"+ \")&TEXT(ABS(AC26),\"0.000\")&\"x^2 \"&IF(AD26<0,\"- \",\"+ \")&TEXT(ABS(AD26),\"0.000\")&\"x \"&IF(AE26<0,\"- \",\"+\")&TEXT(ABS(AE26),\"0.000\")","v":"y = 0.003x^4 + 0.111x^3 - 2.396x^2 + 12.438x - 0.103"},null,null,null,null,null,null,null,null,null,7,11,-13.261419364413644,588.6164695759453]
[7,{"$f":"IF(A8<=nn,Regression!L9,\"\")","v":31},{"$f":"IF($A8<=nn,Regression!K9,\"\")","v":10},100,1000,10000,100000,1000000,-91.185772094863637,-101.18577209486364,10,31,null,null,null,null,null,null,null,null,null,null,null,0.36,4.0691231433526829,"P5 =",{"$f":"\"y = \"&TEXT(AA31,\"0.000\")&\"x^5 \"&IF(AB31<0,\"- \",\"+ \")&TEXT(ABS(AB31),\"0.000\")&\"x^4 \"&IF(AC31<0,\"- \",\"+ \")&TEXT(ABS(AC31),\"0.000\")&\"x^3 \"&IF(AD31<0,\"- \",\"+ \")&TEXT(ABS(AD31),\"0.000\")&\"x^2 \"&IF(AE31<0,\"- \",\"+\")&TEXT(ABS(AE31),\"0.000\") &\"x \"   &IF(AF31<0,\"- \",\"+\")&TEXT(ABS(AF31),\"0.000\")","v":"y = -0.009x^5 + 0.257x^4 - 2.454x^3 + 7.895x^2 - 1.298x +2.057"},null,null,null,null,null,null,null,null,null,10,31,-91.185772094863637,14929.362902417957]
[8,{"$f":"IF(A9<=nn,Regression!L10,\"\")","v":63},{"$f":"IF($A9<=nn,Regression!K10,\"\")","v":12},144,1728,20736,248832,2985984,-184.05433222441675,-196.05433222441675,12,63,null,{"$f":"N7","v":2},{"$f":"a*N9+b","v":1.4827338474064848},null,null,null,null,null,null,null,null,0.42,4.706205636573384,"P6 =",{"$f":"\"y = \"&TEXT(AA36,\"0.000\")&\"x^6 \"&IF(AB36<0,\"- \",\"+ \")&TEXT(ABS(AB36),\"0.000\")&\"x^5 \"&IF(AC36<0,\"- \",\"+ \")&TEXT(ABS(AC36),\"0.000\")&\"x^4 \"&IF(AD36<0,\"- \",\"+ \")&TEXT(ABS(AD36),\"0.000\")&\"x^3 \"&IF(AE36<0,\"- \",\"+\")&TEXT(ABS(AE36),\"0.000\") &\"x^2 \"   &IF(AF36<0,\"- \",\"+\")&TEXT(ABS(AF36),\"0.000\") &\"x \"   &IF(AG36<0,\"- \",\"+\")&TEXT(ABS(AG36),\"0.000\")","v":"y = 0.001x^6 - 0.038x^5 + 0.628x^4 - 4.596x^3 +13.321x^2 - 5.883x +2.274"},null,null,null,null,null,null,null,null,null,12,63,-184.05433222441675,61035.84307085249]
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