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7/25/2019 Factor Analysis in Excel
http://slidepdf.com/reader/full/factor-analysis-in-excel 1/12
Factor Analysis
Identify 3 factors
Variables X1 Seeds
X2 fertilizer
X3 management
X4 Pesticide
X5 waterX6 cost
Data
Score given X1 X2 X3
1 6 !
2 4 4 6
3 4 1 6
4 1 2 6
5 4 3 5
6 4 4 6
" 3 3 # " " 6
! 5 3 1
1# 5 4 2
$orrelation %atri&
X1 X2 X3
X1 1'### #'"42 #'16
$orrelation %atri& X2 #'"42 1'### #'424
X3 #'16 #'424 1'###X4 #'4!6 #'56 #'#5#
X5 #'44 #'4"4 #'23
X6 (#'43# (#'2#4 #'#!2
$orrelation wit)o*t negative sig
X1 X2 X3
X1 1'### #'"42 #'16
$orrelation wit)o*t negative sign X2 #'"42 1'### #'424
X3 #'16 #'424 1'###
X4 #'4!6 #'56 #'#5#X5 #'44 #'4"4 #'23
X6 #'43# #'2#4 #'#!2
Total(T) 3.320 3.412 1.972
Square root of T = 3.97
+oading
S ,+ - S .s/rt 0
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X1 3'32# #'35614
S*m X S and + X2 3'412 #'523
X3 1'!"2 #'4!6434
X4 2'5!! #'654224
X5 2'523 #'634!53
X6 1'!5! #'4!3121
$ross Prod*ct %atri&
X1 X2 X3
X1 #'6! #'"1 #'415
X2 #'"1 #'"3 #'426
X3 #'415 #'426 #'246
X4 #'54" #'562 #'325
X5 #'531 #'545 #'315
X6 (#'412 (#'424 (#'245
esid*al matri& X1 X2 X3
X1 #'3#2 #'#24 (#'24"
X2 #'#24 #'262 (#'##2
X3 (#'24" (#'##2 #'"54
X4 (#'#51 #'##6 (#'2"4
X5 (#'#46 (#'#"1 (#'#""
X6 (#'#1 #'21! #'33"
esid*al %atri& wit)o*t negative
X1 X2 X3
X1 #'3#2 #'#24 #'24"
X2 #'#24 #'262 #'##2
X3 #'24" #'##2 #'"54
X4 #'#51 #'##6 #'2"4
X5 #'#46 #'#"1 #'#""
X6 #'#1 #'21! #'33"
Total(T) 0.!9 0."!" 1.91
Square root of T = 2.!2
+oading
S ,+ - S .s/rt 0
X1 #'6! #'24316
X2 #'55 #'2#"222
X3 1'6!1 #'5!"45
X4 1'54" #'54"15
X5 1'26" #'4451
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X6 2'1!! #'""5"3
$ross Prod*ct %atri&
X1 X2 X3
X1 #'#5! #'#51 (#'146
X2 #'#51 #'#43 (#'124
X3 (#'146 (#'124 #'35X4 (#'134 (#'114 #'32
X5 (#'1#! (#'#!3 #'26!
X6 (#'1!# (#'161 #'466
esid*al %atri&
X1 X2 X3
X1 #'242 (#'#26 (#'1#1
X2 (#'#26 #'21! #'122
X3 (#'1#1 #'122 #'3!5
X4 #'#3 #'11! (#'6#2X5 #'#63 #'#22 (#'346
X6 #'1"2 #'3# (#'12!
esid*al %atri& wit)o*t negative
X1 X2 X3
X1 #'242 #'#26 #'1#1
X2 #'#26 #'21! #'122
X3 #'1#1 #'122 #'3!5
X4 #'#3 #'11! #'6#2
X5 #'#63 #'#22 #'346
X6 #'1"2 #'3# #'12!
Total(T) 0.!7 0.!!9 1.9"
Square root of T = 2.3
+oading
S ,+ - S .s/rt 0
X1 #'6" #'26#"52
X2 #'! #'33"51
X3 1'6!5 #'643"63
X4 1'54# #'54"""
X5 1'1! #'454!52
X6 #'!25 #'3511!6
Factor-1 Factor-2 Factor-3
)ig)est in row X1 0.!3 #'244 #'261
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X2 0.!"9 #'2#" #'33
X3 #'4!6 (#'5!! #0.44
X4 0."4 (#'54 (#'55
X5 0.3" (#'44! (#'455
X6 (#'4!3 #0.779 (#'351
ig)en val*e 2.757 1.568 1.269
#'6! #'#5! #'#6
#'"3 #'#43 #'114
#'246 #'35 #'414
#'42 #'3## #'342
#'4#3 #'2#1 #'2#"
#'243 #'6#6 #'123
Proortion of total variance #'45! #'261 #'211
Proortion of common variance #'4!3 #'2# #'22"
X1 Seeds
X2 fertilizer
X4 Pesticide
X5 water
X6 cost '
X3 management ''
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Note: 1)If any doubt in calculation, contact Dr Sangita ara
X4 X5 X6
! 1 2
2 1
5 1 2
3 2 3
5 2 3
2 3
! 1 3! ! 2
1 2
3 1 #
7eig)t
X4 X5 X6
#'4!6 #'44 (#'43# 1'###
#'56 #'4"4 (#'2#4 1'###
#'#5# #'23 #'#!2 1'###1'### #'2!# #'1!6 1'###
#'2!# 1'### #'#3" 1'###
#'1!6 #'#3" 1'### (1'###
X4 X5 X6
#'4!6 #'44 #'43#
#'56 #'4"4 #'2#4
#'#5# #'23 #'#!2
1'### #'2!# #'1!6#'2!# 1'### #'#3"
#'1!6 #'#3" 1'###
2."99 2."23 1.9"9 1".7!
+
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#'35614
#'523
#'4!6434
#'654224
#'634!53
(#'4!3121becas*e weig)t is negative
X4 X5 X6
#'54" #'531 (#'412
#'562 #'545 (#'424
#'325 #'315 (#'245
#'42 #'415 (#'323
#'415 #'4#3 (#'313
(#'323 (#'313 #'243
X4 X5 X6
(#'#51 (#'#46 (#'#1
#'##6 (#'#"1 #'21!
(#'2"4 (#'#"" #'33"
#'5"2 (#'126 #'51!
(#'126 #'5!" #'35#
#'51! #'35# #'"5"
sign
X4 X5 X6
#'#51 #'#46 #'#1
#'##6 #'#"1 #'21!
#'2"4 #'#"" #'33"
#'5"2 #'126 #'51!
#'126 #'5!" #'35#
#'51! #'35# #'"5"
1."47 1.27 2.199 7.979
+
#'24316
#'2#"222
(#'5!"45
(#'54"15
(#'4451
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(#'""5"3
X4 X5 X6
(#'134 (#'1#! (#'1!#
(#'114 (#'#!3 (#'161
#'32 #'26! #'466#'3## #'246 #'42"
#'246 #'2#1 #'34!
#'42" #'34! #'6#6
X4 X5 X6
#'#3 #'#63 #'1"2
#'11! #'#22 #'3#
(#'6#2 (#'346 (#'12!
#'2"2 (#'3"1 #'#!2(#'3"1 #'3!6 #'##1
#'#!2 #'##1 #'151
sign
X4 X5 X6
#'#3 #'#63 #'1"2
#'11! #'#22 #'3#
#'6#2 #'346 #'12!
#'2"2 #'3"1 #'#!2
#'3"1 #'3!6 #'##1
#'#!2 #'##1 #'151
1."40 1.19! 0.92" .932
+
#'261
#'33
(#'644
(#'55
(#'455
(#'351
community h2
!.826 #'6! #'#5! #'#6
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!.89" #'"3 #'#43 #'114
1.!19 #'246 #'35 #'414
1.!7! #'42 #'3## #'342
!.811 #'4#3 #'2#1 #'2#"
!.97# #'243 #'6#6 #'123
5.59"
8ig) variance wit) factor 1
%edi*m variance wit) factor 2
+ow variance wit) factor 3
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e on 986!"7!598
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