MARKET PROJECTIONS
COMMON METHODS USED IN MARKET PROJECTION
ARITHMETIC STRAIGHT LINE METHOD ARITHMETIC GEOMETRIC CURVE STA ST ATISTICAL STRAIGHT LINE STA ST ATISTIC TISTICAL AL PARABOL ARABOLIC IC CURVE CU RVE
USING THE SAME HISTORICAL HIS TORICAL DATA, DATA, ONE MUST MUS T REMEMBER THAT THAT EACH E ACH OF THESE METHODS YIELDS DIFFERENT PROJEC PROJECTED TED FIGURES & TRENDS. TRENDS. WE MUST FIRST DETERMINE WHICH METHOD IS MOST APPROPRIATE FOR THE SET OF FIGURES ON HAND.
COMMON METHODS USED IN MARKET PROJECTION
ARITHMETIC STRAIGHT LINE METHOD ARITHMETIC GEOMETRIC CURVE STA ST ATISTICAL STRAIGHT LINE STA ST ATISTIC TISTICAL AL PARABOL ARABOLIC IC CURVE CU RVE
USING THE SAME HISTORICAL HIS TORICAL DATA, DATA, ONE MUST MUS T REMEMBER THAT THAT EACH E ACH OF THESE METHODS YIELDS DIFFERENT PROJEC PROJECTED TED FIGURES & TRENDS. TRENDS. WE MUST FIRST DETERMINE WHICH METHOD IS MOST APPROPRIATE FOR THE SET OF FIGURES ON HAND.
2 WAYS OF DETERMINING THE RIGHT METHOD OF PROJECTION
FIRST
DONE BY PLOTTING THE HISTORICAL DATA ALONG THE COORDI COORDINA NATES TES & VISUALL VISUALLY Y DETERMINING THE TREND TREND LINE. FROM THE THE SHAPE OF THE LINE, ONE CAN CAN MORE OR OR LESS DETERMINE WHICH METHOD WILL WILL DEVIA DEVI ATE FROM THE PAST TREND.
SECOND
IT INVOL INVOLVES VES MA MATHEMATICAL THEMATICAL COMPUTATIONS.
UNDER EACH OF THE METHODS, THE REGRESSION LINES ARE DERIVED AND THE STANDARD ST ANDARD DEVIATIONS OF EACH E ACH ARE COMPUTED FOR. THE ONE WHICH YIELDS THE SMALLEST STANDARD DEVIATION IS MOST LIKELY TO GIVE THE MOST RELIABLE FORECAST.
1. GRAPHICAL METHOD
CURVE Q
-PROGRESSIVELY INCREASING - ARITHMETIC GEOMETRIC CURVE IS THE RECOMMENDED PROJECTION METHOD
T Fig. 1
CURVE Q
-INCREASING - STATISTICAL PARABOLIC IS THE RECOMMENDED PROJECTION METHOD
T Fig. 2
STRAIGHT -CONSTANTLY - INCREASING - ARITHMETIC STRAIGHT LINE IS THE RECOMMENDED PROJECTION METHOD
Q
T Fig. 3
STRAIGHT -INCONSISTENTLY INCREASING -STATISTICAL STRAIGHT LINE IS THE RECOMMENDED PROJECTION METHOD
Q
T Fig. 4
MATHEMATICAL METHOD GIVEN THE FF DATA, WE CAN DETERMINE THE TREND LINE W/C WILL BEST FIT THE HISTORICAL DATA THROUGH THE GIVEN STEPS ON THE NEXT SLIDE. T
Q
2000
198.6
2001
214.9
2002
234.2
2003
353.7
2004
429.3
2005
340.8
2006
416.2
2007
351.6
2008
512.2
2009
471.2
STEP 1.
COMPUTE THE EXPECTED VALUES USING THE FOUR METHODS:
A. Arithmetic Straight Line: Yc = a + Yi - 1 B. Arithmetic Geometric Curve: Yc = Yi + 1 1+r C. Statistical Straight Line: Yc = a + bx D. Statistical Parabolic: Yc = a + bx +cX 2
STEP 2.
COMPUTE FOR THE STANDARD DEVIATIONS OF EACH METHOD USING THE FORMULA: σ= √ ∑ (y – yc)2 X
THE METHOD WHICH YIELDS THE LEAST STANDARD DEVIATION IS LIKELY TO COME UP WITH THE BEST ESTIMATES.
METHODS OF PROJECTION
1. ARITHMETIC STRAIGHT LINE
Yc = a + Yi – 1
Where a = Yn – Yc = 471.2 – 198.6 = 30.29 N – 1 9
Yc = initial value (1st year) Yn = final value (last year) N = number of years Yi = value for the year past
HISTORICAL VALUES STEP 1
STEP 2 +
Yi - 1
=
Yc
Y - Yc
(Y-Yc)2
0
0.00
Y
a
2000
198.6
-
2001
214.9
30.29
+
198.6
=
228.89
-
13.99
195.72
2002
234.2
30.29
+
288.89
=
259.18
-
24.98
624.00
2003
353.7
30.29
+
259.18
=
289.47
64.23
4,125.49
2004
429.3
30.29
+
289.47
=
319.76
109.05
11,999.01
2005
340.8
30.29
+
319.79
=
350.05
9.25
85.16
2006
416.2
30.29
+
350.05
=
380.24
35.86
1,285.94
2007
451.6
30.29
+
380.24
=
410.63
40.97
1,678.54
2008
512.2
30.29
+
410.63
=
440.92
71.28
5,080.94
2009
471.2
30.29
+
440.92
=
471.20
0.01
0.00
-
-
-
∑ =22,110.62 σ= 22,110.62 10
= 47
PROJECTED VALUES a
+
Yi - 1
=
Yc
2010
30.29
+
471.21
=
501.50
2011
30.29
+
501.50
=
531.79
2012
30.29
+
531.79
=
562.08
2013
30.29
+
562.08
=
592.37
2014
30.29
+
592.37
=
622.26
2015
30.29
+
622.66
=
652.95
2016
30.29
+
652.95
=
683.24
2017
30.29
+
683.24
=
713.53
2018
30.29
+
713.53
=
743.82
2019
30.29
+
743.81
=
774.11
2. ARITHMETIC GEOMETRIC CURVE
Yc = Yi + 1 1+r
Where: Yi + 1 = value for the year ahead r = average rate of increases
HISTORICAL VALUES STEP 1
STEP 2 Yc
Y - Yc
(Y-Yc) 2
Y
% increase (decrease)
Yi + 1
+ (1 + r)
2000
198.6
-
204.46
+
1.11
=
184.20
14.40
207.36
2001
214.9
8
226.95
+
1.11
=
204.46
10.44
108.99
2002
234.2
9
251.92
+
1.11
=
226.95
7.25
52.56
2003
353.7
51
279.63
+
1.11
=
251.92
101.78
10,359.17
2004
429.3
21
310.39
+
1.11
=
279.63
149.67
22,401.11
2005
340.8
(21)
344.53
+
1.11
=
310.39
30.41
924.77
2006
416.2
22
382.43
+
1.11
=
344.53
71.69
5,136.59
2007
451.6
8
424.50
+
1.11
=
382.43
69.17
4,754.49
2008
512.2
13
471.20
+
1.11
=
424.50
87.70
7,691.29
2009
471.2
(8)
0
103 r = ∑ % increase N – 1
= 103 9
= 11.44
σ= 51,666.33 10
PROJECTED VALUES Yc = Yi – 1 (1 + r) Yi -1x(1+r)
=
Yc
2010
471.20
X
1.11
=
523.03
2011
523.03
X
1.11
=
580.56
2012
580.56
X
1.11
=
644.42
2013
644.42
X
1.11
=
715.31
2014
715.31
X
1.11
=
793.99
2015
793.99
X
1.11
=
881.33
2016
881.33
X
1.11
=
978.28
2017
978.28
X
1.11
=
1,085.89
2018
1,085.89
X
1.11
=
1,205.34
2019
1,205.34
X
1.11
=
1,337.93
3. STATISTICAL STRAIGHT LINE
Yc = a + bx Where: a = ∑Y - b ∑x n n b = n ∑ XY - ∑X ∑Y n ∑ X2 – (∑ X)2
HISTORICAL VALUES STEP 1 Y
X
X2
2000
198.6
1
1
2001
214.9
2
2002
234.2
2003
XY
+
b
(x)
198.6 160.92
+
36.61
(1)
4
429.8 160.92
+
36.61
(2)
3
9
702.6 160.92
+
36.61
(3)
353.7
4
16
1,414.8 160.92
+
36.61
(4)
2004
429.3
5
25
2,146.5 160.92
+
36.61
(5)
2005
340.8
6
36
2,044.8 160.92
+
36.61
(6)
2006
416.2
7
49
2,193.4 160.92
+
36.61
(7)
2007
451.6
8
64
3,612.8 160.92
+
36.61
(8)
2008
512.2
9
81
4,609.8 160.92
+
36.61
(9)
2009
471.2
10
100
4,712.0 160.92
+
36.61
(10)
3,622.7
55
386
22,785.1
a
HISTORICAL VALUES STEP 2 Yc
(Y-Yc)2
Y - Yc
=
197.53
1.07
1.14
=
234.14
-19.24
370.80
=
270.75
-36.55
1,335.90
=
307.36
46.34
2,147.40
=
343.97
85.33
7,281.21
=
380.53
-9.78
95.65
=
417.19
-0.99
0.98
=
453.80
-2.20
4.84
=
490.41
21.79
474.80
527.02
-55.82
3,115.87
10 (22,785.1) – (55) (3,622.7) b= 10 (385) – (55)2 = 36.61 a = 3,622.7 – 36.61 (55) = 160.92 10 10
14,827.97
σ= 14,827.97 10
= 38.5
PROJECTED VALUES Yc = Yi – 1 (1 + r)
a
+
b
=
Yc
2010
160.92
+
36.61 (11)
=
563.63
2011
160.92
+
36.61 (12)
=
600.24
2012
160.92
+
36.61 (13)
=
636.85
2013
160.92
+
36.61 (14)
=
673.46
2014
160.92
+
36.61 (15)
=
710.07
2015
160.92
+
36.61 (16)
=
746.68
2016
160.92
+
36.61 (17)
=
783.29
2017
160.92
+
36.61 (18)
=
819.90
2018
160.92
+
36.61 (19)
=
856.51
2019
160.92
+
36.61 (20)
=
893.12
4. STATISTICAL PARABOLIC
Y = a + bx + cx2 Where:
“a” = (∑X4) (∑Y) – (∑X2) (∑X2Y) n(∑X4) - (∑X2)2 “b” = ∑XY ∑X2 ”c” = n(∑X2Y) - (∑X2) (∑Y) n(∑X4) - (∑X2)2
HISTORICAL VALUES STEP 1 Y
X
X2
2000
198.6
-9
81
6,561
-1,787.4
16,086.6
2001
214.9
-7
49
2,401
-1,504.3
10,530.1
2002
234.2
-5
25
625
-1,171.0
5,855.0
2003
353.7
-3
9
81
-1,061.1
3,183.3
2004
429.3
-1
1
1
-429.3
429.3
2005
340.8
1
1
1
340.8
340.8
2006
416.2
3
9
81
1,284.6
3,745.8
2007
451.6
5
25
625
2,258.0
11,290.0
2008
512.2
7
49
2,401
3,585.8
25,097.8
2009
471.2
9
81
6,561
4,240.8
38,167.2
330
19,338
5,720.5
114,725.9
3,622.7
X4
XY
X2Y
HISTORICAL VALUE STEP 1
STEP 2 X2
=
Yc
(-57)
(-9 2)
=
178.97
+
(-57)
(-72)
=
17.33 (-5)
+
(-57)
(-5 2)
+
17.33 (-3)
+
(-57)
381.11
+
17.33 (-1)
+
381.11
+
17.33 (1)
381.11
+
381.11
a
+
B
x
+
381.11
+
17.33 (-9)
+
381.11
+
17.33 (-7)
381.11
+
381.11
c
Y - Yc
(Y-Yc)2
19.63
385.34
231.87
-16.97
287.98
=
280.21
-46.01
2,116.92
(-3 2)
=
323.99
29.71
882.68
(-57)
(-1 2)
=
363.21
-66.09
4,367.89
+
(-57)
(1 2)
=
397.87
-57.07
3,256.98
17.33 (3)
+
(-57)
(3 2)
=
427.97
-11.77
138.53
+
17.33 (5)
+
(-57)
(5 2)
=
453.51
-1.91
3.65
381.11
+
17.33 (7)
+
(-57)
(72)
=
474.49
37.71
1,422.04
381.11
+
17.33 (9)
+
(-57)
(9 2)
490.91
-19.71
388.48 13,250.49 σ= 13,250.49 10
= 36.3
PROJECTED VALUES Yc = Yi – 1 (1 + r) a
+
b
X
+
c
X2
=
Yc
2010
381.11 +
17.33
(11)
+
(-57)
(11 2)
=
502.77
2011
381.11 +
17.33
(13)
+
(-57)
(13 2)
=
510.07
2012
381.11 +
17.33
(15)
+
(-57)
(15 2)
=
512.81
2013
381.11 +
17.33
(17)
+
(-57)
(172)
=
510.99
2014
381.11 +
17.33
(19)
+
(-57)
(19 2)
=
504.61
2015
381.11 +
17.33
(21)
+
(-57)
(21 2)
=
493.67
2016
381.11 +
17.33
(23)
+
(-57)
(23 2)
=
478.17
2017
381.11 +
17.33
(25)
+
(-57)
(252)
=
458.11
2018
381.11 +
17.33
(27)
+
(-57)
(272)
=
433.49
2019
381.11 +
17.33
(29)
+
(-57)
(29 2)
=
404.31
Remarks on the Mathematical Methods of Projection
1. Based on the standard deviations derived:
A. Arithmetic straight line = 47 B. Arithmetic geometric curve = 71.9 C. Statistical Straight line = 38.5 D. Statistical Parabolic = 36.3
The statistical parabolic curve is bound to be favored by the statistician as the best method in projecting the future.
Remarks..
2. However, it is advisable to reconsider the projected trend the statistical parabolic would yield in the light of other factors which may or may not make the projection realistic.
A. If, for instance, the historical data refer to demand for heavy automobiles, then the down-sloping curve of the statistical parabolic method would be logical since continually increasing oil prices will presumably cause demand to taper off or even decline in the future. B. However, if the data refer to the demand for cement which has not been doing well lately, but is expected to fare much better in the future, then the downward-sloping curve would seem unrealistic. In this case, the statistical straight line method, which also gives a small standard deviation, might give a more realistic approximation of the future demand.
Remarks..
3. In general, if the method yielding the smallest standard deviation appears to be unrealistic, then the one which yields the next smallest deviation may be favored.
DATA GATHERING & DERIVATION
A PROBLEM COMMONLY ENCOUNTERED BY THE RESEARCHER IN UNDERTAKING THE MARKET STUDY IS THE UNAVAILABILITY OF THE DATA REQUIRED. VERY OFTEN, HE WILL RESORT TO DIFFERENT METHODOLOGIES TO DETERMINE THE FIGURES NEEDED TO ESTABLISH A PARTICULAR ASPECT OF HIS STUDY. MAKING USE OF OTHER DATA WHICH ARE AVAILABLE AND SIGNIFICANTLY CORRELATED WITH THE DESIRED BUT UNAVAILABLE ONES, HE CAN DERIVE FIGURES WITH WHICH, HE CAN WORK ON.
SAMPLE CASES & REMEDIES
CASE 1.
PROBLEM: THE PROJECT INVOLVES PRODUCTION AND SALE OF HOGS. A PROJECTION OF THE SUPPLY OF HOGS IS NEEDED AS PART OF THE MARKET STUDY. SOLUTION: THE BUREAU OF AGRICULTURAL ECONOMICS CAN PROVIDE A CENSUS ON THE HOG POPULATION WHICH COVERS THE PERIOD 2000-2009.
SAMPLE CASES
CASE 2.
PROBLEM: THE PROJECT PROPOSES TO PRODUCE HOG FEEDS, BUT NO CENSUS RECORDING THE DEMAND FOR THE PRODUCT IS AVAILABLE. SOLUTION: HERE, THE DEMAND FIGURES WILL REPRESENT THE ESTIMATED TOTAL HOG FEED REQUIREMENTS. SINCE, THE QUANTITY OF HOG FEEDS AND THE NUMBER OF HOGS ARE HIGHLY CORRELATED, THE DEMAND FOR HOG FEEDS CAN BE DERIVED THROUGH THE FOLLOWING DATA GATHERED BY THE
BUREAU OF AGRI’L ECONOMICS:
AN ANNUAL HOG POPULATION CENSUS COVERING AT LEAST 10 YEARS. AN ESTIMATED ANNUAL CONSUMPTION, 298 KG, OG HOG FEEDS BY THE AVERAGE HOG.
SAMPLE CASES
CASE 3.
THE PROJECT CONCERNS THE PLANTING OF SOYBEANS TO MEET THE PROTEIN REQUIREMENTS OF THE HOG POPULATION. FOR SOME REASONS, NO RECORD OF PAST SOYBEAN PURCHASES BY FEED MILLERS IS AT HAND. SOLUTION: BASED ON THE CORRELATIONS:
1. BETWEEN THE QUANTITY OF SOYBEANS AND HOG FEEDS REQUIRED. BETWEEN THE QUANTITY OF HOG FEEDS REQUIRED AND THE HOG POPULATION, THE DEMAND FOR SOYBEANS BY THE HOG FEED INDUSTRY CAN BE ESTABLISHED BY MAKING USE OF THE FOLLOWING AVAILABLE DATA:
AN ANNUAL HOG POPULATION CENSUS COVERING AT LEAST 10 YEARS AN ESTIMATED ANNUAL CONSUMPTION, 298 KG, OF HOG FEEDS BY THE AVERAGE HOG. THE QUANTITY, 5.6 KG OF SOYBEANS, A 40 KG BAG OF HOG MASH CONTAINS:
LET’S TWIST YOUR MINDS A
LITTLE BIT
Pulsing Vortex
If you stare at this one long enough you’ll notice a fast and pulsing multicolored vortex.
Waves
The blue almond-shaped objects look as if they’re all passing over three separate columns.
Hypnosis
Although this image is comprised of simple purple and green squares outlined in black, it looks like it is bulging out in the center
Kaleidoscopes
Wormhole
The black and white circular lines make this illusion seem as if there are various depths in the image, creating different entryways and tunnels.
Bull’s-Eye
If you stare at the center of the image, it looks as if the outer rings are rotating in alternating directions —an effect meant to mesmerize the viewer.
Starbursts
These bright purple and green star-like shapes appear to be moving, which can be a little nauseating if you stare at it for too long.
WARNING!!!
The phenomena on this page rely on your eye movements. You will be moving them anyway (you can never keep your eyes really still), but the demonstrations are aided by moving your display (if possible), or by scrolling the page in small steps.
The sample on the right is
the “Ouchi Illusion” (Ouchi 1977, Spillmann et al 1986). When you shake your head rapidly, or better shake the display, a central disk will segregate as a distinct object, which in addition seems to be floating atop the background.
Akiyoshi Kitaoka’s image on the left is called “Out of Focus”. It also leads to a seeming shift of the central disk with respect to the surroundings. It is very effectively provoked by the eye movements occurring during reading. So, while you are
reading this cast your “inner eye” to the left and watch for a seeming decoupling of disk and background. You may also observe that the disk floats above the background. (Image reproduced with kind permission.)
This sample called “Floating Motion” from Pinna & Spillmann (2002) also often appears very strong to me. I do not need to shake the screen, or the saccades from reading, just by exploratory eye movements over the image
the centre square “decouples”. Here the background seems to move, while the central square remains in place, and seems to float on top. (Image redrawn with kind permission.)
JOKES LANG…
FVR: ERAP, may gift ako for you. Galing sa India and it's a 10 feet snake. ERAP: Ows, niloloko mo naman ako eh! 10 feet? Hoy, di ako ganoon katanga, snake walang feet. di ba??
JOKES LANG…
Stewardess: Sir, chewing gum po para di sumakit ang tenga nyo during d flight. Pasahero: Tenk u! (aftr 1 hr) Pasahero: Ms. pano ba tanggalin tong chewing gum sa tenga ko?
JOKES LANG…
Secretary: IDEDEMANDA KO ANG BOSS KO NG SEXUAL HARASSMENT Attorney: Bakit anong ginawa sa iyo? Secretary: Kasi sabi nya na mabango daw ang buhok ko e. Attorney: Para ganoon lang ay magdedemanda ka na, Bakit? Secretary: Kasi unano siya e...
JOKES LANG…
Mrs. Tanoy is a very kuripot Ilocana (no offense meant to all Ilocanos. When her husband died, she inquired with the newspaper, asking the price for the obituary. The ad taker said: "300 pesos for 5 words. She said: "Pwede ba 2 words lang? Eto lang naman yun... "Tanoy Dead" Ad taker said: "No mam. 5 words is the minimum." After thinking for a while, Mrs. Tanoy said: "Ok, para sulit, ilagay mo, "TANOY DEAD, TOYOTA FOR SALE " ...
JOKES LANG…
Pablo: Father, patawarin po ninyo ako. Pari: Ano ang kasalanan mo? Pablo: Nagnakaw ako ng limang manok. Pari: Magdasal ka ng limang Ama Namin. Pablo: Father, walong Ama Namin na po ang dadasalin ko. Babalikan ko pan yung naiwan kong tatlong manok.
JOKES LANG…
Pari: Iho, nakita ko ang kuya mo na naglalaro ng tong-its sa kanto. Pinapabayaan na niya ang kanyang pag-aaral. Sana di mo siya tularan at pagbutihin mo ang pag-aaral mo. Juan: Wag po kayong mag-alala father, di ko naman po pinapabayaan ang pag-aaral ko eh. Pari: Talaga! Alam mo bang magbilang? Juan: Opo! Pari: Umpisahan mo nga Juan:
One…Two…Three…Four…Five…Six…Seven…Eight…Nine… Ten! Pari: Magaling! Kaya mo bang ituloy? Juan: Opo! Pari: Very Good! Sige nga. (Tuwang-tuwa)
Juan: Jack…Queen..King!!!!
JOKES LANG…
Quiapo Church : MRS: Lord, bigyan ninyo ako ng P1,000 kasi anak ko nasa hospital. Narinig ng pulis, naawa, binigyan ng P500. MRS: Lord, next time huwag padaan sa pulis, nabawasan agad
