appendix computation
TRANSCRIPT
PROJECTION OF DEMAND
I. Arithmetic Geometric Curve
In arithmetic geometric, the value of r which is the average rate of increase/decrease in demand of a particular product is given by:
r=
Σ(% increase /decrease)100N−1
Whereas the projected value (YC) is computed as:
Y C=Y i+1(1+r )
year Demand % increase or decrease
2004 1051039 0.002005 1623854 54.502006 1264139 -22.152007 2212636 75.032008 2059481 -6.922009 1524000 -26.00TOTAL 9735149 74.46
Sample computations:
% increase /decrease=Y i+1−Y iY i
x 100
%increasedecrease
=1623854−10510391051039
x100=54.50
r=
74.461006−1
=¿0.148912822
FOR THE PROJECTED VALUES
Y C=Y i+1(1+r )
year Yi +1 1+r Yc2009 1.148912822 1,524,0002010 1,524,000 1.148912822 1750943.142011 1,750,943 1.148912822 2011681.0242012 2,011,681 1.148912822 2311246.1222013 2,311,246 1.148912822 2655420.3032014 2,655,420 1.148912822 3050846.4342015 3,050,846 1.148912822 3505156.585
Sample computation:
Y C=1,524,000 (1.148912822 )=1750943.14
STANDARD DEVIATION FOR ARITHMETIC GEOMETRIC
Year Yc µ (Yc-µ) (Yc-µ)^22010 1750943.14 2547548.935 -796605.7944 6.34581E+
112011 2011681.024 2547548.935 -535867.9107 2.87154E+
112012 2311246.122 2547548.935 -236302.8129 558390194
032013 2655420.303 2547548.935 107871.3688 116362322
002014 3050846.434 2547548.935 503297.499 2.53308E+
112015 3505156.585 2547548.935 957607.6502 9.17012E+
11
To compute for Standard Deviation:
σ=√∑ ( yc−μ )2
n
σ=√ 2.15953 x10126=¿ 599934.8916
II. ARITHMETIC STRAIGHT LINE
In arithmetic straight, the value of a can be computed as:
a=yc− y1N−1
Whereas the projected value (YC) is computed as:
Y C=a+Y 1+i
year A Y1 + i Yc2009 15240002010 94,592 1,524,000 1,618,5922011 94,592 1,618,592 1,713,184
2012 94,592 1,713,184 1,807,7772013 94,592 1,807,777 1,902,3692014 94,592 1,902,369 1,996,9612015 94,592 1,996,961 2,091,553
Sample computation:
a=1524000−10510396−1
=94,592
Y C=94,592+1,524,000=1,618,592
STANDARD DEVIATION FOR ARITHMETIC STRAIGHT
Year Yc µ Yc-µ (Yc-µ)^22010 1,618,592 1855072.
7-236480.5 55923026880
2011 1,713,184 1855072.7
-141888.3 20132289677
2012 1,807,777 1855072.7
-47296.1 2236921075
2013 1,902,369 1855072.7
47296.1 2236921075
2014 1,996,961 1855072.7
141888.3 20132289677
2015 2,091,553 1855072.7
236480.5 55923026880
To compute for Standard Deviation:
σ=√∑ ( yc−μ )2
N
σ=√ 1.56584 E+116
=¿161546.936
III. STATISTICAL PARABOLIC CURVE
The projected value (YC) is computed as:
YC = A + Bx + Cx2
YEAR
A B x C x2 Yc
2010
374633.2 721410.2286
7 -84200.714
29
49 1298669.8
2011
374633.2 721410.2286
8 -84200.714
29
64 757069.3142
2012
374633.2 721410.2286
9 -84200.714
29
81 47067.39991
2013
374633.2 721410.2286
10 -84200.714
29
100 -831335.94
32014
374633.2 721410.2286
11 -84200.714
29
121 -1878140.7
142015
374633.2 721410.2286
12 -84200.714
29
144 -3093346.9
15
year Demand X 2004 1051039 12005 1623854 22006 1264139 32007 2212636 42008 2059481 52009 1524000 6
STANDARD DEVIATION FOR STATISTICAL PARABOLIC
year Yc µ Yc- µ (Yc- µ)^22010 1298669.8 -
616669.5097
1915339
3.66852E+12
2011 757069.3142 -616669.50
97
1373739
1.88716E+12
2012 47067.39991 -616669.50
97
663736.9
4.40547E+11
2013 -831335.943 -616669.50
97
-214666
46081677606
2014 -1878140.714 -616669.50
97
-126147
1
1.59131E+12
2015 -3093346.915 -616669.50
97
-247667
7
6.13393E+12
σ=√∑ ( yc−μ )2
N
σ=√ 1 .37676 x10136=¿ 1514791.072
IV. STATISTICAL GEOMETRIC CURVE
For statistical geometric curve, values of of a and b can be computed by:
log a=Σ log y−log b Σ xn
log b=nΣ xlog y−Σx Σ log ynΣ x2−(Σ x )2
Whereas the projected value (YC) is computed as:
log YC = log a + log x * log b
Year Demand
x x2 log x log y xlogy
2004
1051039 1 1 0 6.021618831
6.021618831
2005
1623854 2 4 0.602059991
6.210546979
12.42109396
2006
1264139 3 9 0.954242509
6.10179483
18.30538449
2007
2212636 4 16 1.204119983
6.344909974
25.3796399
2008
2059481 5 25 1.397940009
6.31375779
31.56878895
200 1524000 6 36 1.5563025 6.1829849 37.097909
9 01 67 8TOTAL
9,735,149
21 91 5.714664993
37.17561337
130.7944359
log b=6(21)(130.7944359 )−(21 )(37.17561)
6 (91 )−(21)2=¿0.038845093¿
log a=37.17561−(0.038845093)(21)
6=6.059977737
YEAR
log a x Logx log b log Yc Yc
2010
6.059977737
7 0.84509804
0.038845093
6.092805649
1238242.336
2011
6.059977737
8 0.903089987
0.038845093
6.095058351
1244681.834
2012
6.059977737
9 0.954242509
0.038845093
6.097045376
1250389.666
2013
6.059977737
10 1 0.038845093
6.09882283
1255517.671
2014
6.059977737
11 1.041392685
0.038845093
6.100430732
1260174.63
2015
6.059977737
12 1.079181246
0.038845093
6.101898632
1264441.183
Sample computation:
log YC = 6.059977737+ (log 7)* (0.84509804)
YC = 1238242.336
STANDARD DEVIATION FOR STATISTICAL GEOMETRIC
YEAR Yc µ Yc- µ (Yc- µ)^22010 1238242.336 1252241.22 -
13998.8842195968759
.1
12011 1244681.834 1252241.22 -
7559.385953
57144315.98
2012 1250389.666 1252241.22 -1851.55436
6
3428253.571
2013 1255517.671 1252241.22 3276.450849
10735130.16
2014 1260174.63 1252241.22 7933.410582
62939003.46
2015 1264441.183 1252241.22 12199.9631 148839099.6
To compute for Standard Deviation:
σ=√∑ ( yc−μ )2
N
σ=√ 479054561.96=¿ 8935.458969
V. STATISTICAL STRAIGHT LINE
For statistical straight line, values of a and b can be computed by:
b=nΣ xy−Σ x Σ yn Σ x2−(Σ x )2
a= y−bx
Whereas the projected value (YC) is computed as:
Y C=a+bx
Year Demand x x2 xy2004 1051039 1 1 10510392005 1623854 2 4 32477082006 1264139 3 9 37924172007 2212636 4 16 88505442008 2059481 5 25 102974052009 1524000 6 36 9144000TOTA
L9,735,149 21 91 36383113
b=6 (36383113)−(21)(9,735,149)
6(91)−(21)2=132005.2286
a=(9,735,149)−(132005.2286)(21)
6=1160506.533
YEAR a b x Yc2010 1160506.533 132005.2286 7 2084543.1
332011 1160506.533 132005.2286 8 2216548.3
622012 1160506.533 132005.2286 9 2348553.5
92013 1160506.533 132005.2286 10 2480558.8
192014 1160506.533 132005.2286 11 2612564.0
482015 1160506.533 132005.2286 12 2744569.2
76
Sample computation:
Y C=1160506.533+132005.2286 (7 )=2084543.133
STANDARD DEVIATION FOR STATISTICAL STRAIGHT
YEAR Yc µ Yc- µ (Yc- µ)^22010 2084543.133 2414556.205 -
330013.0714
1.08909E+11
2011 2216548.362 2414556.205 -198007.842
9
39207105833
2012 2348553.59 2414556.205 -66002.6142
9
4356345093
2013 2480558.819 2414556.205 66002.61429
4356345093
2014 2612564.048 2414556.205 198007.8429
39207105833
2015 2744569.276 2414556.205 330013.0714
1.08909E+11
To compute for Standard Deviation:
σ=√∑ ( yc−μ )2
N
σ=√ 3.04944 x 10116=¿225441.8463
PROJECTION OF SUPPLY
I. Arithmetic Geometric Curve
In arithmetic geometric, the value of r which is the average rate of increase/decrease in demand of a particular product is given by:
r=
Σ(% increase /decrease)100N−1
Whereas the projected value (YC) is computed as:
Y C=Y i+1(1+r )
year Supply % increase or decrease
2004 992353 0.002005 764541 -22.962006 1229219 60.782007 2138652 73.982008 1875456 -12.312009 1307268 -30.30
TOTAL 69.20
Sample computations:
%
increasedecrease
increase
decrease=764541−992353
992353x 100=−22.96
r= 69.20(6−1 )∗100
=¿0.138407872
FOR THE PROJECTED VALUES
Y C=Y i+1(1+r )
year Yi +1 1+r Yc2009 1.138407872 1,307,2682010 1,307,268 1.138407872 1488204.1822011 1,488,204 1.138407872 1694183.3572012 1,694,183 1.138407872 1928671.672013 1,928,672 1.138407872 2195615.0122014 2,195,615 1.138407872 2499505.4152015 2,499,505 1.138407872 2845456.641
Sample computation:
Y C=1307268 (1.138407872 )=1488204.182
STANDARD DEVIATION FOR ARITHMETIC GEOMETRIC
Year Yc µ (Yc-µ) (Yc-µ)^22010 1488204.182 2108606.046 -620401.8638 3.84898E+
112011 1694183.357 2108606.046 -414422.6895 1.71746E+
11
2012 1928671.67 2108606.046 -179934.3759 32376379622
2013 2195615.012 2108606.046 87008.96626 7570560210
2014 2499505.415 2108606.046 390899.3684 1.52802E+11
2015 2845456.641 2108606.046 736850.5945 5.42949E+11
To compute for Standard Deviation:
σ=√∑ ( yc−μ )2
n
σ=√ 1.29234E+126=¿464101.7656
II. ARITHMETIC STRAIGHT LINE
In arithmetic straight, the value of a can be computed as:
a=yc− y1N−1
Whereas the projected value (YC) is computed as:
Y C=a+Y 1+i
year a Y1 + i Yc2009 13072682010 62,983 1,307,268 1,370,2512011 62,983 1,370,251 1,433,2342012 62,983 1,433,234 1,496,2172013 62,983 1,496,217 1,559,2002014 62,983 1,559,200 1,622,1832015 62,983 1,622,183 1,685,166
Sample computation:
a=1307268−9923536−1
=62983
Y C=62983+1,307,268=1,370,251
STANDARD DEVIATION FOR ARITHMETIC STRAIGHT
Year Yc µ Yc-µ (Yc-µ)^22010 1,370,251 1527708.
5-157457.5 24792864306
2011 1,433,234 1527708.5
-94474.5 8925431150
2012 1,496,217 1527708.5
-31491.5 991714572.3
2013 1,559,200 1527708.5
31491.5 991714572.3
2014 1,622,183 1527708.5
94474.5 8925431150
2015 1,685,166 1527708.5
157457.5 24792864306
To compute for Standard Deviation:
σ=√∑ ( yc−μ )2
N
σ=√ 6.942 E+106
=¿107563.95
III. STATISTICAL PARABOLIC CURVE
The projected value (YC) is computed as:
YC = A + Bx + Cx2
year Supply X 2004 992353 12005 764541 22006 1229219 32007 2138652 42008 1875456 52009 1307268 6
YEAR
A B X C x2 Yc
2010
34010.2 742864.9429
7 -82381.714
29
49 1197360.8
2011
34010.2 742864.9429
8 -82381.714
29
64 704500.0286
2012
34010.2 742864.9429
9 -82381.714
29
81 46875.82861
2013
34010.2 742864.9429
10 -82381.714
29
100 -775511.8
2014
34010.2 742864.9429
11 -82381.714
29
121 -1762662.8
572015
34010.2 742864.9429
12 -82381.714
29
144 -2914577.3
43
STANDARD DEVIATION FOR STATISTICAL PARABOLIC
year Yc µ Yc- µ (Yc- µ)^22010 1197360.8 -
584002.5571
1781363
3.17326E+12
2011 704500.0286 -584002.55
71
1288503
1.66024E+12
2012 46875.82861 -584002.55
71
630878.4
3.98008E+11
2013 -775511.8 -584002.55
71
-191509
36675790103
2014 -1762662.857 -584002.55
71
-117866
0
1.38924E+12
2015 -2914577.343 -584002.55
-233057
5.43158E+12
71 5
σ=√ 1.2089E+136=¿1419448.049
IV. STATISTICAL GEOMETRIC CURVE
For statistical geometric curve, values of of a and b can be computed by:
log a=Σ log y−log b Σ xn
log b=nΣ xlog y−Σx Σ log ynΣ x2−(Σ x )2
Whereas the projected value (YC) is computed as:
log YC = log a + xlog b
Year Supply x x2 log x log y xlogy2004
992353 1 1 0 5.996666187
5.996666187
2005
764541 2 4 0.301029996
5.88340078
11.76680156
2006
1229219 3 9 0.477121255
6.089629265
18.26888779
2007
2138652 4 16 0.602059991
6.330140122
25.32056049
2008
1875456 5 25 0.698970004
6.27310688
31.3655344
2009
1307268 6 36 0.77815125
6.11636463
36.69818778
TOT 8,307,489 21 91 2.8573324 36.689307 129.41663
AL 96 86 82
log b=6 (129.41663827 )−(21 )(36.68930786)
6 (91 )−(21)2=0.057374896
log a=36.68930786−(0.057374896 )(21)
6=5.914072507
YEAR
log a x Logx log b log Yc Yc
2010
5.914072507
7 0.84509804
0.057374896
5.962559919
917402.4997
2011
5.914072507
8 0.903089987
0.057374896
5.965887201
924458.0341
2012
5.914072507
9 0.954242509
0.057374896
5.968822072
930726.4835
2013
5.914072507
10 1 0.057374896
5.971447403
936369.8103
2014
5.914072507
11 1.041392685
0.057374896
5.973822304
941504.2918
2015
5.914072507
12 1.079181246
0.057374896
5.975990419
946216.2863
Sample computation:
log YC = 5.914072507+ (log7)* 0.057374896
YC = 917402.4997
STANDARD DEVIATION FOR STATISTICAL GEOMETRIC
YEAR Yc µ Yc- µ (Yc- µ)^22010 917402.4997 932779.5676 -
15377.0679236454217
.12011 924458.0341 932779.5676 -
8321.533477
69247919.4
2012 930726.4835 932779.5676 -2053.08413
7
4215154.474
2013 936369.8103 932779.5676 3590.24266 12889842.36
2014 941504.2918 932779.5676 8724.724211
76120812.55
2015 946216.2863 932779.5676 13436.71864
180545407.8
To compute for Standard Deviation:
σ=√∑ ( yc−μ )2
N
σ=√ 5.794733536E+86=¿9827.456043
V. STATISTICAL STRAIGHT LINE
For statistical straight line, values of a and b can be computed by:
b=nΣ xy−Σ x Σ yn Σ x2−(Σ x )2
a= y−bx
Whereas the projected value (YC) is computed as:
Y C=a+bx
Year Supply Unsaturated
x x2 xy
2004 992353 1 1 9923532005 764541 2 4 15290822006 1229219 3 9 36876572007 2138652 4 16 85546082008 1875456 5 25 93772802009 1307268 6 36 7843608TOTA
L8,307,489 21 91 31984588
b=6 (31984588 )−(21)(8307489)
6 (91)−(21)2=166192.9429
a=8,307,489−(166192.9429)(21)
6=802906.2
YEAR a b x Yc2010 802906.2 166192.9429 7 1966256.82011 802906.2 166192.9429 8 2132449.7
432012 802906.2 166192.9429 9 2298642.6
862013 802906.2 166192.9429 10 2464835.6
292014 802906.2 166192.9429 11 2631028.5
712015 802906.2 166192.9429 12 2797221.5
14
Sample computation:
Y C=802906.2+166192.9429 (7 )=1966256.8
STANDARD DEVIATION FOR STATISTICAL STRAIGHT
YEAR Yc µ Yc- µ (Yc- µ)^22010 1966256.8 2381739.157 -
415482.3571
1.72626E+11
2011 2132449.743 2381739.157 -249289.414
3
62145212075
2012 2298642.686 2381739.157 -83096.4714
3
6905023564
2013 2464835.629 2381739.157 83096.47143
6905023564
2014 2631028.571 2381739.157 249289.4143
62145212075
2015 2797221.514 2381739.157 415482.3571
1.72626E+11
To compute for Standard Deviation:
σ=√∑ ( yc−μ )2
N
σ=√ 4.83352E+116=¿283828.4839