The document discusses four common methods used to project market values: the arithmetic straight line method, arithmetic geometric curve, statistical straight line, and statistical parabolic curve. It explains that each method yields different projected figures and trends when using the same historical data. The best method is determined by either visually plotting the historical data to see the trend line shape, or through mathematical computations to find the method with the smallest standard deviation between actual and projected values. Examples of applying each method to a sample data set are provided.

1. MARKET PROJECTIONS

2. COMMON METHODS USED IN MARKET
PROJECTION
 ARITHMETIC STRAIGHT LINE METHOD
 ARITHMETIC GEOMETRIC CURVE
 STATISTICAL STRAIGHT LINE
 STATISTICAL PARABOLIC CURVE
 USINGTHE SAME HISTORICAL DATA, ONE MUST
REMEMBERTHAT EACH OFTHESE METHODS
YIELDS DIFFERENT PROJECTED FIGURES &TRENDS.
WE MUST FIRST DETERMINE WHICH METHOD IS
MOST APPROPRIATE FORTHE SET OF FIGURES ON
HAND.

3. 2 WAYS OF DETERMINING THE
RIGHT METHOD OF PROJECTION

4. FIRST
 DONE BY PLOTTINGTHE HISTORICAL DATA
ALONGTHE COORDINATES &VISUALLY
DETERMININGTHETREND LINE. FROMTHE
SHAPEOFTHE LINE, ONE CAN MORE OR
LESS DETERMINEWHICH METHODWILL
DEVIATE FROMTHE PASTTREND.

5. SECOND
 IT INVOLVES MATHEMATICAL
COMPUTATIONS.
 UNDER EACH OFTHE METHODS,THE
REGRESSION LINES ARE DERIVED ANDTHE
STANDARD DEVIATIONS OF EACH ARE
COMPUTED FOR.
 THE ONEWHICHYIELDSTHE SMALLEST
STANDARD DEVIATION IS MOST LIKELYTO GIVE
THE MOST RELIABLE FORECAST.

6. 1. GRAPHICAL METHOD

7. CURVE
Q
T
Fig. 1
-PROGRESSIVELY
INCREASING
- ARITHMETIC
GEOMETRIC CURVE IS
THE RECOMMENDED
PROJECTION METHOD

8. CURVE
Q
T
Fig. 2
-INCREASING
- STATISTICAL
PARABOLIC ISTHE
RECOMMENDED
PROJECTION METHOD

9. STRAIGHT
Q
T
Fig. 3
-
-CONSTANTLY
INCREASING
- ARITHMETIC STRAIGHT
LINE ISTHE
RECOMMENDED
PROJECTION METHOD

10. STRAIGHT
Q
T
Fig. 4
-INCONSISTENTLY
INCREASING
-STATISTICAL STRAIGHT
LINE ISTHE
RECOMMENDED
PROJECTION METHOD

11. MATHEMATICAL METHOD
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
GIVENTHE FF DATA,WE CAN DETERMINETHETREND LINEW/C WILL BEST FIT
THE HISTORICAL DATATHROUGH THE GIVEN STEPSONTHE NEXT SLIDE.

12. STEP 1.
 COMPUTETHE EXPECTEDVALUES USING
THE FOUR METHODS:
 A. Arithmetic Straight Line: Yc = a +Yi - 1
 B. ArithmeticGeometricCurve: Yc = Yi + 1
1 + r
 C. Statistical Straight Line: Yc = a + bx
 D. Statistical Parabolic: Yc = a + bx +cX2

13. STEP 2.
 COMPUTE FORTHE STANDARD
DEVIATIONSOF EACH METHOD USINGTHE
FORMULA:
σ= √ ∑ (y –yc)2
 THE METHODWHICHYIELDSTHE LEAST
STANDARD DEVIATION IS LIKELYTO COME UP
WITHTHE BEST ESTIMATES.
X

14. METHODS OF PROJECTION

15. 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

16. HISTORICAL VALUES
STEP 1 STEP 2
Y a + Yi - 1 = Yc Y -Yc (Y-Yc)2
2000 198.6 - - 0 0.00
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

17. 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

18. 2. ARITHMETIC GEOMETRIC
CURVE
 Yc = Yi + 1
1 + r
Where: Yi + 1 = value for the year ahead
r = average rate of increases

19. HISTORICAL VALUES
STEP 1 STEP 2
Y % increase
(decrease)
Yi + 1 + (1 + r) Yc Y -Yc (Y-Yc)2
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 = 103 = 11.44
N – 1 9
σ= 51,666.33
10
= 71.9

20. PROJECTED VALUES
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
Yc =Yi – 1 (1 + r)

21. 3. STATISTICAL STRAIGHT LINE
 Yc = a + bx
 Where: a = ∑Y - b ∑x
n n
b = n ∑ XY - ∑X ∑Y
n ∑ X2 – (∑ X)2

22. HISTORICAL VALUES
STEP 1
Y X X2 XY a + b (x)
2000 198.6 1 1 198.6 160.92 + 36.61 (1)
2001 214.9 2 4 429.8 160.92 + 36.61 (2)
2002 234.2 3 9 702.6 160.92 + 36.61 (3)
2003 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

23. HISTORICAL VALUES
STEP 2
Yc Y -Yc (Y-Yc)2
= 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 = 38.5
10

24. PROJECTED VALUES
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
Yc =Yi – 1 (1 + r)

25. 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

26. HISTORICAL VALUES
STEP 1
Y X X2 X4 XY X2Y
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
3,622.7 330 19,338 5,720.5 114,725.9

27. HISTORICAL VALUE
STEP 1 STEP 2
a + B x + c X2 = Yc Y -Yc (Y-Yc)2
381.11 + 17.33 (-9) + (-57) (-92) = 178.97 19.63 385.34
381.11 + 17.33 (-7) + (-57) (-72) = 231.87 -16.97 287.98
381.11 + 17.33 (-5) + (-57) (-52) = 280.21 -46.01 2,116.92
381.11 + 17.33 (-3) + (-57) (-32) = 323.99 29.71 882.68
381.11 + 17.33 (-1) + (-57) (-12) = 363.21 -66.09 4,367.89
381.11 + 17.33 (1) + (-57) (12) = 397.87 -57.07 3,256.98
381.11 + 17.33 (3) + (-57) (32) = 427.97 -11.77 138.53
381.11 + 17.33 (5) + (-57) (52) = 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) (92) 490.91 -19.71 388.48
13,250.49
σ= 13,250.49
10
= 36.3

28. PROJECTED VALUES
a + b X + c X2 = Yc
2010 381.11 + 17.33 (11) + (-57) (112) = 502.77
2011 381.11 + 17.33 (13) + (-57) (132) = 510.07
2012 381.11 + 17.33 (15) + (-57) (152) = 512.81
2013 381.11 + 17.33 (17) + (-57) (172) = 510.99
2014 381.11 + 17.33 (19) + (-57) (192) = 504.61
2015 381.11 + 17.33 (21) + (-57) (212) = 493.67
2016 381.11 + 17.33 (23) + (-57) (232) = 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) (292) = 404.31
Yc =Yi – 1 (1 + r)

29. 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.

30. 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.

31. 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.

32. DATA GATHERING & DERIVATION
 A PROBLEM COMMONLY ENCOUNTERED BYTHE
RESEARCHER IN UNDERTAKINGTHE MARKET
STUDY ISTHE UNAVAILABILITYOFTHE DATA
REQUIRED.
 VERY OFTEN, HEWILL RESORTTO DIFFERENT
METHODOLOGIESTO DETERMINETHE FIGURES
NEEDEDTO ESTABLISHA PARTICULAR ASPECT OF
HIS STUDY.
 MAKING USE OF OTHER DATAWHICH ARE
AVAILABLE AND SIGNIFICANTLY CORRELATED
WITHTHE DESIRED BUT UNAVAILABLEONES, HE
CAN DERIVE FIGURESWITHWHICH, HE CAN
WORK ON.

33. SAMPLE CASES & REMEDIES
 CASE 1.
 PROBLEM:THE PROJECT INVOLVES
PRODUCTIONAND SALE OF HOGS. A
PROJECTION OFTHE SUPPLY OF HOGS IS
NEEDEDAS PART OFTHE MARKET STUDY.
 SOLUTION:THE BUREAU OF AGRICULTURAL
ECONOMICS CAN PROVIDEA CENSUS ONTHE
HOG POPULATIONWHICH COVERSTHE PERIOD
2000-2009.

34. SAMPLE CASES
 CASE 2.
 PROBLEM:THE PROJECT PROPOSESTO PRODUCE HOG
FEEDS, BUT NO CENSUS RECORDINGTHE DEMAND FOR
THE PRODUCT IS AVAILABLE.
 SOLUTION: HERE,THE DEMAND FIGURES WILL
REPRESENTTHE ESTIMATEDTOTAL HOG FEED
REQUIREMENTS. SINCE,THE QUANTITY OF HOG FEEDS
ANDTHE NUMBER OF HOGS ARE HIGHLY CORRELATED,
THE DEMAND FOR HOG FEEDS CAN BE DERIVED
THROUGHTHE FOLLOWING DATA GATHERED BYTHE
BUREAU OF AGRI’L ECONOMICS:
 ANANNUAL HOG POPULATIONCENSUSCOVERING AT
LEAST 10YEARS.
 AN ESTIMATEDANNUAL CONSUMPTION, 298 KG, OG HOG
FEEDS BYTHE AVERAGE HOG.

35. SAMPLE CASES
 CASE 3.
 THE PROJECTCONCERNSTHE PLANTING OF SOYBEANSTO MEET
THE PROTEIN REQUIREMENTSOFTHE HOG POPULATION. FOR SOME
REASONS, NO RECORD OF PAST SOYBEAN PURCHASES BY FEED
MILLERS ISAT HAND.
 SOLUTION: BASED ONTHE CORRELATIONS:
 1. BETWEENTHE QUANTITY OF SOYBEANS AND HOG FEEDS
REQUIRED.
 BETWEENTHE QUANTITY OF HOG FEEDS REQUIREDANDTHE HOG
POPULATION,THE DEMAND FOR SOYBEANS BYTHE HOG FEED
INDUSTRYCAN BE ESTABLISHED BY MAKING USE OFTHE FOLLOWING
AVAILABLE DATA:
 AN ANNUAL HOG POPULATION CENSUS COVERING AT LEAST 10YEARS
 AN ESTIMATED ANNUAL CONSUMPTION, 298 KG, OF HOG FEEDS BYTHE
AVERAGE HOG.
 THE QUANTITY, 5.6 KG OF SOYBEANS, A 40 KG BAG OF HOG MASH
CONTAINS:

36. LET’S TWIST YOUR MINDS A
LITTLE BIT

37. Pulsing Vortex
If you stare at this one long enough you’ll notice a fast and pulsing
multicolored vortex.

38. Waves
The blue almond-shaped objects look as if they’re all passing over three separate
columns.

39. 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

40. Kaleidoscopes

41. 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.

42. 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.

43. 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.

44. 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.

45. 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.

46. 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.)

47. 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.)

49. 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??

50. 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?

51. 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...

52. 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 " ...

53. 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.

54. 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!!!!

55. 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

56. Thank you