Page 290 - DMGT404 RESEARCH_METHODOLOGY

Research Methodology

Notes ( X )( X ) ´
å
å
åx x = S X X – 2 3 = 11500 – 385 210 = –50
2 3 2 3 n 7
å
( X ) 2 385 2
å x = S X 2 – 2 = 23975 – = 2800
2
2 2 n 7
å
( X ) 2 210 2
å X = S X 2 – 3 = 6324 – = 24
2
3
3
n 7
Substituting these values in equations (10) and (11), we get
´
-
-
-
´
1900 24 ( 20) ( 50) =
b = 2 0.689
-
´
-
12.3 2800 24 ( 50)
-
-
´
´
-
( 20) 2800 1900 ( 50)
b = = 0.603
-
-
´
13.2 2800 24 ( 50) 2
455 385 210
Also X =  65,X   55,X   30
1 7 2 7 3 7
´
´
-
-
Thus a = X - b X - b X = 65 0.689 55 0.603 30 = 9.015
1.23 1 12.3 2 13.2 3
 The fitted regression of X on X and X is X = 9.015 + 0.689X + 0.603X
1 2 3 1c 2 3
The estimate of yield (X ) when X = 60 and X = 25 is
1c 2 3
X = 9.015 + 0.689 × 60 + 0.603 × 25 = 65.43 quintals.
1c
Alternatively to simplify calculation work, we change origin of the three variable as
U = X – 65, U = X – 55 and U = X – 30.
1 1 2 2 3 3
2
U U U U U U U U U U U U
2
2
1 2 3 1 2 1 3 2 3 1 2 3
– 20 – 30 1 600 – 20 – 30 400 900 1
– 15 – 20 – 2 300 30 40 225 400 4
– 10 – 10 2 100 – 20 – 20 100 100 4
5 0 2 0 10 0 25 0 4
10 10 – 1 100 – 10 – 10 100 100 1
10 20 – 3 200 – 30 – 60 100 400 9
20 30 1 600 20 30 400 900 1
0 0 0 1900 – 20 – 50 1350 2800 24

Note: Since SU = 0,  u = U – U = U , i = 1, 2, 3. ( U = ) 0
i i i i i
´
1900 24 - ( 20- )( 50- )
Hence b = ) 2 = 0.689
´
12.3 2800 24 - ( 50-
( 20- ) 2800 1900´ - ´ ( 50- )
b = ) 2 = 0.603
´
13.2 2800 24 - ( 50-
284 LOVELY PROFESSIONAL UNIVERSITY