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