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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 |