Factor AnalysisIdentify 3 factors

Variables X1 SeedsX2 fertilizerX3 managementX4 PesticideX5 waterX6 cost

DataScore given X1 X2 X3

1 6 8 92 4 4 63 4 1 64 1 2 65 4 3 56 4 4 67 3 3 08 7 7 69 5 3 1

10 5 4 2

Correlation MatrixX1 X2 X3

X1 1.000 0.742 0.168Correlation Matrix X2 0.742 1.000 0.424

X3 0.168 0.424 1.000X4 0.496 0.568 0.050X5 0.484 0.474 0.238X6 -0.430 -0.204 0.092

Correlation without negative signX1 X2 X3

X1 1.000 0.742 0.168Correlation without negative sign X2 0.742 1.000 0.424

X3 0.168 0.424 1.000X4 0.496 0.568 0.050X5 0.484 0.474 0.238X6 0.430 0.204 0.092

Total(T) 3.320 3.412 1.972

Square root of T = 3.97Loading

S UL = S /sqrt (T)

X1 3.320 0.835614Sum X S and L X2 3.412 0.858823

X3 1.972 0.496434X4 2.599 0.654224X5 2.523 0.634953X6 1.959 0.493121

Cross Product MatrixX1 X2 X3

X1 0.698 0.718 0.415X2 0.718 0.738 0.426X3 0.415 0.426 0.246X4 0.547 0.562 0.325X5 0.531 0.545 0.315X6 -0.412 -0.424 -0.245

Residual matrixX1 X2 X3

X1 0.302 0.024 -0.247X2 0.024 0.262 -0.002X3 -0.247 -0.002 0.754X4 -0.051 0.006 -0.274X5 -0.046 -0.071 -0.077X6 -0.018 0.219 0.337

Residual Matrix without negative signX1 X2 X3

X1 0.302 0.024 0.247X2 0.024 0.262 0.002X3 0.247 0.002 0.754X4 0.051 0.006 0.274X5 0.046 0.071 0.077X6 0.018 0.219 0.337

Total(T) 0.689 0.585 1.691

Square root of T = 2.82LoadingS UL = S /sqrt (T)

X1 0.689 0.243816X2 0.585 0.207222X3 1.691 0.598745X4 1.547 0.547815X5 1.267 0.448518

X6 2.199 0.778573

Cross Product MatrixX1 X2 X3

X1 0.059 0.051 -0.146X2 0.051 0.043 -0.124X3 -0.146 -0.124 0.358X4 -0.134 -0.114 0.328X5 -0.109 -0.093 0.269X6 -0.190 -0.161 0.466

Residual Matrix X1 X2 X3

X1 0.242 -0.026 -0.101X2 -0.026 0.219 0.122X3 -0.101 0.122 0.395X4 0.083 0.119 -0.602X5 0.063 0.022 -0.346X6 0.172 0.380 -0.129

Residual Matrix without negative signX1 X2 X3

X1 0.242 0.026 0.101X2 0.026 0.219 0.122X3 0.101 0.122 0.395X4 0.083 0.119 0.602X5 0.063 0.022 0.346X6 0.172 0.380 0.129

Total(T) 0.687 0.889 1.695

Square root of T = 2.63LoadingS UL = S /sqrt (T)

X1 0.687 0.260752X2 0.889 0.33751X3 1.695 0.643763X4 1.540 0.584777X5 1.198 0.454952X6 0.925 0.351196

Factor-1 Factor-2 Factor-3highest in row X1 0.836 0.244 0.261

X2 0.859 0.207 0.338X3 0.496 -0.599 -0.644X4 0.654 -0.548 -0.585X5 0.635 -0.449 -0.455X6 -0.493 -0.779 -0.351

Eighen value 2.757 1.568 1.2690.698 0.059 0.0680.738 0.043 0.1140.246 0.358 0.4140.428 0.300 0.3420.403 0.201 0.2070.243 0.606 0.123

Proportion of total variance 0.459 0.261 0.211

Proportion of common variance 0.493 0.280 0.227

X1 SeedsX2 fertilizer ………X4 PesticideX5 water

X6 cost ……….

X3 management …………..

X4 X5 X69 1 28 2 15 1 23 2 35 2 38 2 39 1 39 9 28 1 23 1 0

WeightX4 X5 X60.496 0.484 -0.430 1.0000.568 0.474 -0.204 1.0000.050 0.238 0.092 1.0001.000 0.290 0.196 1.0000.290 1.000 0.037 1.0000.196 0.037 1.000 -1.000

Correlation without negative signX4 X5 X60.496 0.484 0.4300.568 0.474 0.2040.050 0.238 0.0921.000 0.290 0.1960.290 1.000 0.0370.196 0.037 1.000

2.599 2.523 1.959 15.786

L

0.8356140.8588230.4964340.6542240.634953

-0.493121 becasue weight is negative

X4 X5 X60.547 0.531 -0.4120.562 0.545 -0.4240.325 0.315 -0.2450.428 0.415 -0.3230.415 0.403 -0.313

-0.323 -0.313 0.243

X4 X5 X6-0.051 -0.046 -0.0180.006 -0.071 0.219

-0.274 -0.077 0.3370.572 -0.126 0.519

-0.126 0.597 0.3500.519 0.350 0.757

Residual Matrix without negative signX4 X5 X60.051 0.046 0.0180.006 0.071 0.2190.274 0.077 0.3370.572 0.126 0.5190.126 0.597 0.3500.519 0.350 0.757

1.547 1.267 2.199 7.979

L0.2438160.207222

-0.598745-0.547815-0.448518

-0.778573

X4 X5 X6-0.134 -0.109 -0.190-0.114 -0.093 -0.1610.328 0.269 0.4660.300 0.246 0.4270.246 0.201 0.3490.427 0.349 0.606

X4 X5 X60.083 0.063 0.1720.119 0.022 0.380

-0.602 -0.346 -0.1290.272 -0.371 0.092

-0.371 0.396 0.0010.092 0.001 0.151

Residual Matrix without negative signX4 X5 X60.083 0.063 0.1720.119 0.022 0.3800.602 0.346 0.1290.272 0.371 0.0920.371 0.396 0.0010.092 0.001 0.151

1.540 1.198 0.925 6.932

L0.2610.338

-0.644-0.585-0.455-0.351

community h20.826 0.698 0.059 0.068

0.894 0.738 0.043 0.1141.019 0.246 0.358 0.4141.070 0.428 0.300 0.3420.811 0.403 0.201 0.2070.973 0.243 0.606 0.1235.594

High variance with factor 1

Medium variance with factor 2

Low variance with factor 3