From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001 From: priyanka Date: Wed, 24 Jun 2015 15:03:17 +0530 Subject: initial commit / add all books --- 331/CH11/EX11.2/Example_11_2.sce | 300 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 300 insertions(+) create mode 100755 331/CH11/EX11.2/Example_11_2.sce (limited to '331/CH11/EX11.2/Example_11_2.sce') diff --git a/331/CH11/EX11.2/Example_11_2.sce b/331/CH11/EX11.2/Example_11_2.sce new file mode 100755 index 000000000..d4baf58d9 --- /dev/null +++ b/331/CH11/EX11.2/Example_11_2.sce @@ -0,0 +1,300 @@ +//Caption: Factor Analysis +//Centroid Method +//Example11.2 +//Page439 +clear; +clc; +X1 = [6,4,4,1,4,4,3,7,5,5];// Fuel Efficiency +X2 = [8,4,1,2,3,4,3,7,3,4];//Life of the two-wheeler +X3 = [9,6,6,6,5,6,0,6,1,2];//Handling convenience +X4 = [9,8,5,3,5,8,9,9,8,3];//Quality of original spare +X5 = [1,2,1,2,2,2,1,9,1,1];//Breakdown rate +X6 = [2,1,2,3,3,3,3,2,2,0];//Price +n = 6;//number of variables +m = length(X1);//number of sets of observations +F = 3;//number of factors to be identified +f = 1;//current factor number +Xcorr1 = [1,0.742,0.168,0.496,0.484,-0.430;0.742,1,0.424,0.568,0.474,-0.204;0.168,0.424,1,0.050,0.238,0.092] +Xcorr2 = [0.496,0.568,0.050,1,0.29,0.196;0.484,0.474,0.238,0.290,1,0.037;-0.430,-0.204,0.092,0.196,0.037,1]; +Xcorr = [Xcorr1;Xcorr2] +Xcorr_ref = abs(Xcorr) +disp(Xcorr_ref,'Correlation Coefficient Matrix=') +for j = 1:n + S(j)= sum(Xcorr_ref(:,j)) +end +disp(S,'column totals S=') +T = sum(S); +disp(T,'Grand total of column totals T=') +Tsqrt = sqrt(T); +for j = 1:n + L1(j)= S(j)/Tsqrt; + if j ==n then + L1(j)=-L1(j); + end +end +disp(L1,'Loading values of factor1 L1=') +for i = 1:n + for j =1:n + P2(i,j)= L1(i)*L1(j); + R2(i,j) = Xcorr(i,j)-P2(i,j) + if (R2(i,j)<0) then + R2_ref(i,j)= -R2(i,j); + else + R2_ref(i,j)= R2(i,j); + end + end +end +disp(P2,'Cross-Product matrix P2=') +disp(R2,'Residual matrix R2=') +disp(R2_ref,'Reflected residual matrix R2=') +for j = 1:n + S1(j)= sum(R2_ref(:,j)) +end +disp(S1,'column totals S1=') +T1 = sum(S1); +disp(T1,'Grand total of column totals T1=') +Tsqrt1 = sqrt(T1); +for j = 1:n + L2(j)= S1(j)/Tsqrt1; + if S1(j)>1 then + L2(j)=-L2(j); + end +end +disp(L2,'Loading values of factor2 L2=') +for i = 1:n + for j =1:n + P3(i,j)= L2(i)*L2(j); + R3(i,j) = R2(i,j)-P3(i,j) + if (R3(i,j)<0) then + R3_ref(i,j)= -R3(i,j); + else + R3_ref(i,j)= R3(i,j); + end + end +end +disp(P3,'Cross-Product matrix P3=') +disp(R3,'Residual matrix R3=') +disp(R3_ref,'Reflected residual matrix R3=') +for j = 1:n + S2(j)= sum(R3_ref(:,j)) +end +disp(S2,'column totals S2=') +T2 = sum(S2); +disp(T2,'Grand total of column totals T2=') +Tsqrt2 = sqrt(T2); +for j = 1:n + L3(j)= S2(j)/Tsqrt2; + if S2(j)>0.8 then + L3(j)=-L3(j); + end +end +disp(L3,'Loading values of factor3 L3=') +for i = 1:n + for j = 1:F + h(i) = L1(i)^2+L2(i)^2+L3(i)^2; + end +end +disp(h,'Communality h^2 =') +EigenValueL1 = sum(L1.^2); +EigenValueL2 = sum(L2.^2); +EigenValueL3 = sum(L3.^2); +EigenValueh = sum(h); +disp(EigenValueL1,'Eigen Value of L1 =') +disp(EigenValueL2,'Eigen Value of L2 =') +disp(EigenValueL3,'Eigen Value of L3 =') +disp(EigenValueh,'Eigen Value of h =') +disp([EigenValueL1/n,EigenValueL2/n,EigenValueL3/n],'Proportion of total variance=') +disp([EigenValueL1/EigenValueh,EigenValueL2/EigenValueh,EigenValueL3/EigenValueh],'Proportion of common variance=') +disp(round(EigenValueL1*100/n),'The proportion of total variance of the factor-1=') +disp(round(EigenValueL2*100/n),'The proportion of total variance of the factor-1=') +disp(round(EigenValueL3*100/n),'The proportion of total variance of the factor-1=') +disp(round(EigenValueL1*100/EigenValueh),'The proportion of common variance=') +disp(round(EigenValueL2*100/EigenValueh),'The proportion of common variance=') +disp(round(EigenValueL3*100/EigenValueh),'The proportion of common variance=') +//Result + +// Correlation Coefficient Matrix= +// +// 1. 0.742 0.168 0.496 0.484 0.43 +// 0.742 1. 0.424 0.568 0.474 0.204 +// 0.168 0.424 1. 0.05 0.238 0.092 +// 0.496 0.568 0.05 1. 0.29 0.196 +// 0.484 0.474 0.238 0.29 1. 0.037 +// 0.43 0.204 0.092 0.196 0.037 1. +// +// column totals S= +// +// 3.32 +// 3.412 +// 1.972 +// 2.6 +// 2.523 +// 1.959 +// +// Grand total of column totals T= +// +// 15.786 +// +// Loading values of factor1 L1= +// +// 0.8356069 +// 0.8587623 +// 0.4963304 +// 0.6543910 +// 0.6350109 +// - 0.4930584 +// +// Cross-Product matrix P2= +// +// 0.6982389 0.7175877 0.4147371 0.5468136 0.5306195 - 0.4120030 +// 0.7175877 0.7374727 0.4262298 0.5619663 0.5453235 - 0.4234200 +// 0.4147371 0.4262298 0.2463438 0.3247941 0.3151752 - 0.2447199 +// 0.5468136 0.5619663 0.3247941 0.4282275 0.4155454 - 0.3226530 +// 0.5306195 0.5453235 0.3151752 0.4155454 0.4032389 - 0.3130975 +// - 0.4120030 - 0.4234200 - 0.2447199 - 0.3226530 - 0.3130975 0.2431066 +// +// Residual matrix R2= +// +// 0.3017611 0.0244123 - 0.2467371 - 0.0508136 - 0.0466195 - 0.0179970 +// 0.0244123 0.2625273 - 0.0022298 0.0060337 - 0.0713235 0.2194200 +// - 0.2467371 - 0.0022298 0.7536562 - 0.2747941 - 0.0771752 0.3367199 +// - 0.0508136 0.0060337 - 0.2747941 0.5717725 - 0.1255454 0.5186530 +// - 0.0466195 - 0.0713235 - 0.0771752 - 0.1255454 0.5967611 0.3500975 +// - 0.0179970 0.2194200 0.3367199 0.5186530 0.3500975 0.7568934 +// +// Reflected residual matrix R2= +// +// 0.3017611 0.0244123 0.2467371 0.0508136 0.0466195 0.0179970 +// 0.0244123 0.2625273 0.0022298 0.0060337 0.0713235 0.2194200 +// 0.2467371 0.0022298 0.7536562 0.2747941 0.0771752 0.3367199 +// 0.0508136 0.0060337 0.2747941 0.5717725 0.1255454 0.5186530 +// 0.0466195 0.0713235 0.0771752 0.1255454 0.5967611 0.3500975 +// 0.0179970 0.2194200 0.3367199 0.5186530 0.3500975 0.7568934 +// +// column totals S1= +// +// 0.6883406 +// 0.5859465 +// 1.6913123 +// 1.5476123 +// 1.2675222 +// 2.1997807 +// +// Grand total of column totals T1= +// +// 7.9805146 +// +// Loading values of factor2 L2= +// +// 0.2436621 +// 0.2074161 +// - 0.5986988 +// - 0.5478312 +// - 0.4486835 +// - 0.7786888 +// +// Cross-Product matrix P3= +// +// 0.0593712 0.0505394 - 0.1458802 - 0.1334857 - 0.1093272 - 0.1897369 +// 0.0505394 0.0430215 - 0.1241798 - 0.1136290 - 0.0930642 - 0.1615126 +// - 0.1458802 - 0.1241798 0.3584402 0.3279858 0.2686263 0.4662000 +// - 0.1334857 - 0.1136290 0.3279858 0.3001190 0.2458028 0.4265900 +// - 0.1093272 - 0.0930642 0.2686263 0.2458028 0.2013169 0.3493849 +// - 0.1897369 - 0.1615126 0.4662000 0.4265900 0.3493849 0.6063563 +// +// Residual matrix R3= +// +// 0.2423899 - 0.0261272 - 0.1008569 0.0826720 0.0627076 0.1717400 +// - 0.0261272 0.2195058 0.1219500 0.1196627 0.0217408 0.3809326 +// - 0.1008569 0.1219500 0.3952159 - 0.6027800 - 0.3458015 - 0.1294801 +// 0.0826720 0.1196627 - 0.6027800 0.2716535 - 0.3713482 0.0920630 +// 0.0627076 0.0217408 - 0.3458015 - 0.3713482 0.3954442 0.0007126 +// 0.1717400 0.3809326 - 0.1294801 0.0920630 0.0007126 0.1505371 +// +// Reflected residual matrix R3= +// +// 0.2423899 0.0261272 0.1008569 0.0826720 0.0627076 0.1717400 +// 0.0261272 0.2195058 0.1219500 0.1196627 0.0217408 0.3809326 +// 0.1008569 0.1219500 0.3952159 0.6027800 0.3458015 0.1294801 +// 0.0826720 0.1196627 0.6027800 0.2716535 0.3713482 0.0920630 +// 0.0627076 0.0217408 0.3458015 0.3713482 0.3954442 0.0007126 +// 0.1717400 0.3809326 0.1294801 0.0920630 0.0007126 0.1505371 +// +// column totals S2= +// +// 0.6864936 +// 0.8899191 +// 1.6960844 +// 1.5401794 +// 1.1977549 +// 0.9254655 +// +// Grand total of column totals T2= +// +// 6.935897 +// +// Loading values of factor3 L3= +// +// 0.2606665 +// - 0.3379086 +// - 0.6440153 +// - 0.5848170 +// - 0.4547960 +// - 0.3514058 +// +// Communality h^2 = +// +// 0.8255572 +// 0.8946764 +// 1.0195397 +// 1.0703575 +// 0.8113952 +// 0.9729489 +// +// Eigen Value of L1 = +// +// 2.7566285 +// +// Eigen Value of L2 = +// +// 1.568625 +// +// Eigen Value of L3 = +// +// 1.2692212 +// +// Eigen Value of h = +// +// 5.5944748 +// +// Proportion of total variance= +// +// 0.4594381 0.2614375 0.2115369 +// +// Proportion of common variance= +// +// 0.4927413 0.2803883 0.2268705 +// +// The proportion of total variance of the factor-1= +// +// 46. +// +// The proportion of total variance of the factor-1= +// +// 26. +// +// The proportion of total variance of the factor-1= +// +// 21. +// +// The proportion of common variance= +// +// 49. +// +// The proportion of common variance= +// +// 28. +// +// The proportion of common variance= +// +// 23. \ No newline at end of file -- cgit