factor analysis in excel

7/25/2019 Factor Analysis in Excel

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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



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



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



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 ''



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!

+



#'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



(#'""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



!.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



e on 986!"7!598

factor analysis in excel

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