Chapter 12
Forecasting
Operations Management - 6th Edition
Roberta Russell & Bernard W. Taylor, III
Copyright 2009 John Wiley & Sons, Inc.
Beni Asllani
University of Tennessee at Chattanooga
่ ้นักศึกษา
Lecture Outline : เพือให
เข ้าใจหัวข ้อต่อไปนี ้
 Strategic Role of Forecasting in Supply
Chain Management
 Components of Forecasting Demand
 Time Series Methods
 Forecast Accuracy
 Time Series Forecasting Using Excel
 Regression Methods
Copyright 2009 John Wiley & Sons, Inc.
12-2
Forecasting : การพยากรณ์
 Predicting the future :ทานาย
อนาคต
 Qualitative forecast methods :
วิธเี ชิงคุณภาพ

subjective
 Quantitative forecast methods
: วิธเี ชิงปริมาณ

based on mathematical formulas
Copyright 2009 John Wiley & Sons, Inc.
12-3
Forecasting and Supply Chain
Management
 Accurate forecasting determines how much
inventory a company must keep at various points
along its supply chain
 Continuous replenishment




supplier and customer share continuously updated data
typically managed by the supplier
reduces inventory for the company
speeds customer delivery
 Variations of continuous replenishment




quick response
JIT (just-in-time)
VMI (vendor-managed inventory)
stockless inventory
Copyright 2009 John Wiley & Sons, Inc.
12-4
Forecasting
 Quality Management

Accurately forecasting customer demand is
a key to providing good quality service
 Strategic Planning

Successful strategic planning requires
accurate forecasts of future products and
markets
Copyright 2009 John Wiley & Sons, Inc.
12-5
Types of Forecasting Methods :
ชนิ ดของวิธก
ี ารพยากรณ์
้
 Depend on : จะเลือกชนิ ดใดขึนอยู
่กบั



time frame :ระบบเวลาในการพยากรณ์
demand behavior : ลักษณะความ
ต ้องการ
causes of behavior : สาเหตุของความ
ต ้องการ
Copyright 2009 John Wiley & Sons, Inc.
12-6
Time Frame : ระยะเวลา
 Indicates how far into the future is
forecast

้ กับระยะ
Short- to mid-range forecast :ระยะสัน
กลาง
typically encompasses the immediate future
 daily up to two years : ประจาวัน จนถึง 2 ปี


Long-range forecast : ระยะยาว

usually encompasses a period of time longer
than two years : มากกว่า 2 ปี
Copyright 2009 John Wiley & Sons, Inc.
12-7
Demand Behavior : พฤติกรรมของ
ความต ้องการ
 Trend : แนวโน้ม

a gradual, long-term up or down movement of
demand
 Random variations : ความแปรปรวนโดยสุ่ม

movements in demand that do not follow a pattern

an up-and-down repetitive movement in demand

an up-and-down repetitive movement in demand
occurring periodically
 Cycle : วัฏจักร
 Seasonal pattern : ฤดูกาล
Copyright 2009 John Wiley & Sons, Inc.
12-8
Demand
Demand
Forms of Forecast Movement
Random
movement
Time
(b) Cycle
Demand
Demand
Time
(a) Trend
Time
(c) Seasonal pattern
Copyright 2009 John Wiley & Sons, Inc.
Time
(d) Trend with seasonal pattern
12-9
Forecasting Methods : วิธก
ี าร
พยากรณ์
 Time series : อนุ กรมเวลา

statistical techniques that use historical demand data
to predict future demand : ใช ้ข ้อมูลในอดีตมาทานายความ
ต ้องการในอนาคต
 Regression methods : วิธก
ี ารถดถอย

attempt to develop a mathematical relationship
between demand and factors that cause its behavior
 Qualitative : วิธเี ชิงคุณภาพ

use management judgment, expertise, and opinion to
predict future demand : ใช ้ประสบการณ์ และความไตร่ตรองใน
การพยากรณ์
Copyright 2009 John Wiley & Sons, Inc.
12-10
Qualitative Methods : วิธเี ชิง
คุณภาพ
 Management, marketing, purchasing,
and engineering are sources for internal
qualitative forecasts: ใช ้ข ้อมูลทางการบริหาร
การตลาด การจัดซือ้ และการวิศวกรรม มาทานาย
 Delphi method : วิธเี ดลฟาย

involves soliciting forecasts about
technological advances from experts :
่
รวมกลุม
่ ระดมความคิดจากผูเ้ ชียวชาญ
Copyright 2009 John Wiley & Sons, Inc.
12-11
Forecasting Process
1. Identify the
purpose of forecast
2. Collect historical
data
3. Plot data and identify
patterns
6. Check forecast
accuracy with one or
more measures
5. Develop/compute
forecast for period of
historical data
4. Select a forecast
model that seems
appropriate for data
7.
Is accuracy of
forecast
acceptable?
No
8b. Select new
forecast model or
adjust parameters of
existing model
Yes
8a. Forecast over
planning horizon
9. Adjust forecast based
on additional qualitative
information and insight
Copyright 2009 John Wiley & Sons, Inc.
10. Monitor results
and measure forecast
accuracy
12-12
Time Series : อนุ กรมเวลา
 Assume that what has occurred in the past will
่ ่
continue to occur in the future : สมมติวา่ สิงที
้
้
เกิดขึนในอดี
ตจะยังคงเกิดขึนในอนาคต
 Relate the forecast to only one factor - time
 Include :วิธก
ี ารมีดงั นี ้



moving average
exponential smoothing
linear trend line
Copyright 2009 John Wiley & Sons, Inc.
12-13
Moving Average : ค่าเฉลีย่
่
่
เคลือนที
 Naive forecast

demand in current period is used as next period’s
่ ดจิงในปัจจุบน
forecast :ใช ้ข ้อมูลทีเกิ
ั เป็ นค่าทานายในช่วง
ถัดไป
 Simple moving average


uses average demand for a fixed sequence of
่ าหนด
periods : ใช ้ค่าความต ้องการจากช่วงเวลาทีก
stable demand with no pronounced behavioral
patterns
 Weighted moving average

weights are assigned to most recent data : มีการ
่
กาหนดน้าหนักให ้กับข ้อมูลทีใหม่
ทสุ
ี่ ด
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12-14
Moving Average:
Naïve Approach
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
ORDERS
PER MONTH
120
90
100
75
110
50
75
130
110
90
-
Copyright 2009 John Wiley & Sons, Inc.
FORECAST
120
90
100
75
110
50
75
130
110
90
12-15
Simple Moving Average
n
 Di
i=1
MAn =
n
where
n = number of periods in
the moving average:
่ หา
ช่วงเวลาทีใช้
่
ค่าเฉลีย
Di = demand in period i :
ความต้องการในช่วงที ่ i
Copyright 2009 John Wiley & Sons, Inc.
12-16
3-month Simple Moving Average
3
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
ORDERS
PER MONTH
Di

i=1
MOVING
AVERAGE
120
90
100
75
110
50
75
130
110
90
-
Copyright 2009 John Wiley & Sons, Inc.
–
–
–
103.3
88.3
95.0
78.3
78.3
85.0
105.0
110.0
MA3 =
=
3
90 + 110 + 130
3
= 110 orders
for Nov
12-17
5-month Simple Moving Average
MONTH
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
ORDERS
PER MONTH
MOVING
AVERAGE
120
90
100
75
110
50
75
130
110
90
-
Copyright 2009 John Wiley & Sons, Inc.
–
–
–
–
–
99.0
85.0
82.0
88.0
95.0
91.0
5
Di

i=1
MA5 =
=
5
90 + 110 + 130+75+50
5
= 91 orders
for Nov
12-18
Smoothing Effects
150 –
5-month
125 –
Orders
100 –
75 –
50 –
3-month
Actual
25 –
0–
|
Jan
|
Feb
|
Mar
|
|
Apr May
|
|
June July
|
|
Aug Sept
|
Oct
|
Nov
Month
Copyright 2009 John Wiley & Sons, Inc.
12-19
Weighted Moving Average
n
 Adjusts
moving
average
method to
more closely
reflect data
fluctuations :
แสดงให ้เห็น
ความผันผวน
WMAn =
 Wi Di
i=1
where
Copyright 2009 John Wiley & Sons, Inc.
Wi = the weight for period i,
between 0 and 100
percent
 Wi = 1.00
12-20
Weighted Moving Average Example
MONTH
WEIGHT
DATA
17%
33%
50%
130
110
90
August
September
October
3
November Forecast
WMA3 =
Wi Di

i=1
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= 103.4 orders
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12-21
Exponential Smoothing :การปร ับ
เรียบแบบเอ็กซ ์โปรเนนเชียล
 Averaging method : วิธแี บบเฉลีย่
 Weights most recent data more strongly : ให ้
้
นาหนั
กมากกับข ้อมูลใหม่สด
ุ
 Reacts more to recent changes : ตอบสนองการ
่
เปลียนแปลงได
้เร็วกว่า
 Widely used, accurate method : แม่นยาสูง
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12-22
Exponential Smoothing (cont.)
Ft +1 = Dt + (1 - )Ft
where:
Ft +1 = forecast for next period : ค่าพยากรณ์
ในช่วงถัดไป
Dt = actual demand for present period:
ความต ้องการจริงในปัจจุบน
ั

Ft =
previously determined forecast for
่ านมา
present period : ค่าพยากรณ์ในช่วงทีผ่
=
weighting factor, smoothing constant :
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12-23
Effect of Smoothing Constant
0.0  1.0
If = 0.20, then Ft +1 = 0.20 Dt + 0.80 Ft
If = 0, then Ft +1 = 0 Dt + 1 Ft = Ft
Forecast does not reflect recent data
If = 1, then Ft +1 = 1 Dt + 0 Ft = Dt
Forecast based only on most recent data
Copyright 2009 John Wiley & Sons, Inc.
12-24
Exponential Smoothing (α=0.30)
PERIOD
MONTH
DEMAND
1
2
3
4
5
6
7
8
9
10
11
12
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
37
40
41
37
45
50
43
47
56
52
55
54
Copyright 2009 John Wiley & Sons, Inc.
F2 = D1 + (1 - )F1
= (0.30)(37) + (0.70)(37)
= 37
F3 = D2 + (1 - )F2
เท่ากับ
D1
= (0.30)(40) + (0.70)(37)
= 37.9
F13 = D12 + (1 - )F12
= (0.30)(54) + (0.70)(50.84)
= 51.79
12-25
Exponential Smoothing (cont.)
PERIOD
MONTH
DEMAND
1
2
3
4
5
6
7
8
9
10
11
12
13
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
37
40
41
37
45
50
43
47
56
52
55
54
–
Copyright 2009 John Wiley & Sons, Inc.
FORECAST, Ft + 1
( = 0.3)
( = 0.5)
–
37.00
37.90
38.83
38.28
40.29
43.20
43.14
44.30
47.81
49.06
50.84
51.79
–
37.00
38.50
39.75
38.37
41.68
45.84
44.42
45.71
50.85
51.42
53.21
53.61
12-26
Exponential Smoothing (cont.)
70 –
60 –
 = 0.50
Actual
Orders
50 –
40 –
 = 0.30
30 –
20 –
10 –
0–
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
Month
Copyright 2009 John Wiley & Sons, Inc.
12-27
Adjusted Exponential Smoothing : การ
ปร ับค่าแบบ Exponential Smoothing โยมี
แนวโน้ม
AFt +1 = Ft +1 + Tt +1
where
แนวโน้ม
T = an exponentially smoothed trend factor : ปัจจัย
Tt +1 = (Ft +1 - Ft) + (1 - ) Tt
where
แนวโน้ม
Tt = the last period trend factor
่ าหร ับ
= a smoothing constant for trend : ค่าคงทีส
Copyright 2009 John Wiley & Sons, Inc.
12-28
Adjusted Exponential
Smoothing (β=0.30)
PERIOD
MONTH
DEMAND
1
2
3
4
5
6
7
8
9
10
11
12
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
37
40
41
37
45
50
43
47
56
52
55
54
T3
= (F3 - F2) + (1 - ) T2
= (0.30)(38.5 - 37.0) + (0.70)(0)
= 0.45
AF3 = F3 + T3 = 38.5 + 0.45
= 38.95
T13 = (F13 - F12) + (1 - ) T12
= (0.30)(53.61 - 53.21) + (0.70)(1.77)
= 1.36
AF13 = F13 + T13 = 53.61 + 1.36 = 54.97
Copyright 2009 John Wiley & Sons, Inc.
12-29
Adjusted Exponential Smoothing:
Example
PERIOD
MONTH
DEMAND
FORECAST
Ft +1
1
2
3
4
5
6
7
8
9
10
11
12
13
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
37
40
41
37
45
50
43
47
56
52
55
54
–
37.00
37.00
38.50
39.75
38.37
38.37
45.84
44.42
45.71
50.85
51.42
53.21
53.61
Copyright 2009 John Wiley & Sons, Inc.
TREND
Tt +1
ADJUSTED
FORECAST AFt +1
–
0.00
0.45
0.69
0.07
0.07
1.97
0.95
1.05
2.28
1.76
1.77
1.36
–
37.00
38.95
40.44
38.44
38.44
47.82
45.37
46.76
58.13
53.19
54.98
54.96
12-30
Adjusted Exponential Smoothing
Forecasts
70 –
Adjusted forecast ( = 0.30)
60 –
Actual
Demand
50 –
40 –
Forecast ( = 0.50)
30 –
20 –
10 –
0–
|
1
|
2
|
3
|
4
|
5
Copyright 2009 John Wiley & Sons, Inc.
|
|
6
7
Period
|
8
|
9
|
10
|
11
|
12
|
13
12-31
Linear Trend Line
y = a + bx
where
a = intercept
b = slope of the line
x = time period
y = forecast for
demand for period x
xy - nxy
b =
x2 - nx2
a = y-bx
where
n = number of periods
x
x =
= mean of the x values
n
y
y = n = mean of the y values
Copyright 2009 John Wiley & Sons, Inc.
12-32
Least Squares Example
x(PERIOD)
y(DEMAND)
xy
x2
1
2
3
4
5
6
7
8
9
10
11
12
73
40
41
37
45
50
43
47
56
52
55
54
37
80
123
148
225
300
301
376
504
520
605
648
1
4
9
16
25
36
49
64
81
100
121
144
78
557
3867
650
Copyright 2009 John Wiley & Sons, Inc.
12-33
Least Squares Example
(cont.)
78
x =
= 6.5
12
557
y =
= 46.42
12
xy - nxy
b =
=
2
2
x - nx
3867 - (12)(6.5)(46.42)
=1.72
2
650 - 12(6.5)
a = y - bx
= 46.42 - (1.72)(6.5) = 35.2
Copyright 2009 John Wiley & Sons, Inc.
12-34
Linear trend line y = 35.2 + 1.72x
Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units
70 –
60 –
Actual
Demand
50 –
40 –
Linear trend line
30 –
20 –
10 –
|
1
|
2
|
3
|
4
|
5
0–
Copyright 2009 John Wiley & Sons, Inc.
|
|
6
7
Period
|
8
|
9
|
10
|
11
|
12
|
13
12-35
Seasonal Adjustments
 Repetitive increase/ decrease in demand :
่ น/ลดลง
้
้
ความต ้องการเพิมขึ
เป็ นแบบซาๆเดิ
ม
 Use seasonal factor to adjust forecast
Seasonal factor = Si =
Copyright 2009 John Wiley & Sons, Inc.
Di
D
12-36
Seasonal Adjustment (cont.)
YEAR
2002
2003
2004
Total
DEMAND (1000’S PER QUARTER)
1
2
3
4
Total
12.6
14.1
15.3
42.0
8.6
10.3
10.6
29.5
6.3
7.5
8.1
21.9
17.5
18.2
19.6
55.3
45.0
50.1
53.6
148.7
D1
42.0
S1 =
=
= 0.28
D 148.7
D3
21.9
S3 =
=
= 0.15
D 148.7
D2
29.5
S2 =
=
= 0.20
D 148.7
D4
55.3
S4 =
=
= 0.37
D 148.7
Copyright 2009 John Wiley & Sons, Inc.
12-37
Seasonal Adjustment (cont.)
กาหนดให ้สมการเส ้นตรงของปี 2005
For 2005
เป็ นดังนี ้
y = 40.97 + 4.30x = 40.97 + 4.30(4) = 58.17
SF1 = (S1) (F5) = (0.28)(58.17) = 16.28
SF2 = (S2) (F5) = (0.20)(58.17) = 11.63
SF3 = (S3) (F5) = (0.15)(58.17) = 8.73
SF4 = (S4) (F5) = (0.37)(58.17) = 21.53
Copyright 2009 John Wiley & Sons, Inc.
12-38
Forecast Accuracy
 Forecast error


difference between forecast and actual demand
MAD


MAPD



mean absolute deviation
mean absolute percent deviation
Cumulative error
Average error or bias
Copyright 2009 John Wiley & Sons, Inc.
12-39
Mean Absolute Deviation
(MAD)
 Dt - Ft 
MAD =
n
where
t = period number
Dt = demand in period t
Ft = forecast for period t
n = total number of periods
 = absolute value
Copyright 2009 John Wiley & Sons, Inc.
12-40
MAD Example
PERIOD
1
2
3
4
5
6
7
8
9
10
11
12
DEMAND, Dt
37
40
41
37
MAD
45
50
43
47
56
52
55
54
=
=
=
Ft ( =0.3)
(Dt - Ft)
|Dt - Ft|
37.00
–
37.00
3.00
37.90
3.10
 D
t - Ft  -1.83
38.83
n
38.28
6.72
40.29
9.69
53.39
43.20
-0.20
43.14
3.86
11
44.30
11.70
4.19
4.8547.81
49.06
5.94
50.84
3.15
–
3.00
3.10
1.83
6.72
9.69
0.20
3.86
11.70
4.19
5.94
3.15
49.31
53.39
557
Copyright 2009 John Wiley & Sons, Inc.
12-41
Other Accuracy Measures
Mean absolute percent deviation (MAPD)
|Dt - Ft|
MAPD =
Dt
Cumulative error
E = et
Average error
et
E= n
Copyright 2009 John Wiley & Sons, Inc.
12-42
Comparison of Forecasts
FORECAST
MAD
MAPD
E
(E)
Exponential smoothing (= 0.30)
Exponential smoothing (= 0.50)
Adjusted exponential smoothing
(= 0.50, = 0.30)
Linear trend line
4.85
4.04
3.81
9.6%
8.5%
7.5%
49.31
33.21
21.14
4.48
3.02
1.92
2.29
4.9%
–
–
Copyright 2009 John Wiley & Sons, Inc.
12-43
Forecast Control
 Tracking signal

monitors the forecast to see if it is biased
high or low
Tracking signal =


(Dt - Ft)
E
=
MAD
MAD
1 MAD ≈ 0.8 б
Control limits of 2 to 5 MADs are used most
frequently
Copyright 2009 John Wiley & Sons, Inc.
12-44
Tracking Signal Values
PERIOD
DEMAND
Dt
1
2
3
4
5
6
7
8
9
10
11
12
37
40
41
37
45
50
43
47
56
52
55
54
FORECAST,
Ft
ERROR
Dt - Ft
E =
(Dt - Ft)
37.00
–
–
37.00
3.00
3.00
37.90
3.10
6.10
38.83
-1.83
4.27
38.28
6.72 for period
10.99 3
Tracking
signal
40.29
9.69
20.68
43.20
-0.20
6.10 20.48
43.14
TS3 = 3.86 =24.34
2.00
3.05
44.30
11.70
36.04
47.81
4.19
40.23
49.06
5.94
46.17
50.84
3.15
49.32
Copyright 2009 John Wiley & Sons, Inc.
MAD
–
3.00
3.05
2.64
3.66
4.87
4.09
4.06
5.01
4.92
5.02
4.85
TRACKING
SIGNAL
–
1.00
2.00
1.62
3.00
4.25
5.01
6.00
7.19
8.18
9.20
10.17
12-45
Tracking Signal Plot
Tracking signal (MAD)
3 –
2 –
Exponential smoothing ( = 0.30)
1 –
0 –
-1 –
-2 –
Linear trend line
-3 –
|
0
|
1
|
2
|
3
|
4
|
5
Copyright 2009 John Wiley & Sons, Inc.
|
6
Period
|
7
|
8
|
9
|
10
|
11
|
12
12-46
Statistical Control Charts
=
(Dt - Ft)2
n-1
 Using  we can calculate statistical
control limits for the forecast error
 Control limits are typically set at  3
Copyright 2009 John Wiley & Sons, Inc.
12-47
Statistical Control Charts
18.39 –
UCL = +3
12.24 –
Errors
6.12 –
0–
-6.12 –
-12.24 –
-18.39 –
|
0
LCL = -3
|
1
|
2
|
3
|
4
|
5
Copyright 2009 John Wiley & Sons, Inc.
|
6
Period
|
7
|
8
|
9
|
10
|
11
|
12
12-48
Time Series Forecasting using Excel
 Excel can be used to develop forecasts:




Moving average
Exponential smoothing
Adjusted exponential smoothing
Linear trend line
Copyright 2009 John Wiley & Sons, Inc.
12-49
Exponentially Smoothed and Adjusted
Exponentially Smoothed Forecasts
 Insert Exhibit 12.1
Copyright 2009 John Wiley & Sons, Inc.
12-50
Demand and exponentially
smoothed forecast
 Insert Exhibit 12.2
Copyright 2009 John Wiley & Sons, Inc.
12-51
Data Analysis option
 Insert Exhibit 12.3
 Insert Exhibit 12.4
Copyright 2009 John Wiley & Sons, Inc.
12-52
Computing a Forecast with
Seasonal Adjustment
 Insert Exhibit 12.5
Copyright 2009 John Wiley & Sons, Inc.
12-53
OM Tools
 Insert Exhibit 12.6
Copyright 2009 John Wiley & Sons, Inc.
12-54
Regression Methods : วิธก
ี าร
ถดถอย
 Linear regression : ถดถอยแบบเส ้นตรง

a mathematical technique that relates a
dependent variable to an independent
variable in the form of a linear equation
 Correlation : สหสัมพันธ ์

a measure of the strength of the relationship
between independent and dependent
variables
Copyright 2009 John Wiley & Sons, Inc.
12-55
Linear Regression
y = a + bx
a = y-bx
xy - nxy
b =
x2 - nx2
where
a = intercept
b = slope of the line
x
= mean of the x data
n
y
y = n = mean of the y data
x =
Copyright 2009 John Wiley & Sons, Inc.
12-56
Linear Regression Example
x
(WINS)
y
(ATTENDANCE)
xy
x2
4
6
6
8
6
7
5
7
36.3
40.1
41.2
53.0
44.0
45.6
39.0
47.5
145.2
240.6
247.2
424.0
264.0
319.2
195.0
332.5
16
36
36
64
36
49
25
49
49
346.7
2167.7
311
Copyright 2009 John Wiley & Sons, Inc.
12-57
Linear Regression Example (cont.)
49
= 6.125
8
346.9
y=
= 43.36
8
x=
xy - nxy2
b=
x2 - nx2
(2,167.7) - (8)(6.125)(43.36)
=
(311) - (8)(6.125)2
= 4.06
a = y - bx
= 43.36 - (4.06)(6.125)
= 18.46
Copyright 2009 John Wiley & Sons, Inc.
12-58
Linear Regression Example (cont.)
Regression equation
Attendance forecast for 7 wins
y = 18.46 + 4.06x
y = 18.46 + 4.06(7)
= 46.88, or 46,880
60,000 –
Attendance, y
50,000 –
40,000 –
30,000 –
Linear regression line,
y = 18.46 + 4.06x
20,000 –
10,000 –
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
Wins, x
Copyright 2009 John Wiley & Sons, Inc.
12-59
Correlation and Coefficient of
Determination
 Correlation, r : วัดระดับความสาคัญของตัวแปรว่า
มากหรือน้อย
 Measure of strength of relationship
 Varies between -1.00 and +1.00
 Coefficient of determination, r2 : เปอร ์เซนของ
 Percentage of variation in dependent
variable resulting from changes in the
independent variable
ความแปรปรวนในตัวแปรตาม ยังเกิดจาการ
Copyright 2009 John Wiley & Sons, Inc.
12-60
Computing Correlation
r=
n xy -  x y
[n x2 - ( x)2] [n y2 - ( y)2]
(8)(2,167.7) - (49)(346.9)
r=
[(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2]
r = 0.947
Coefficient of determination
r2 = (0.947)2 = 0.897
Copyright 2009 John Wiley & Sons, Inc.
12-61
Regression Analysis with Excel
 Insert Exhibit 12.7
Copyright 2009 John Wiley & Sons, Inc.
12-62
Regression Analysis with Excel
(cont.)
 Insert Exhibit 12.8 &12.9
Copyright 2009 John Wiley & Sons, Inc.
12-63
Regression Analysis with Excel
(cont.)
 Insert Exhibit 12.10
Copyright 2009 John Wiley & Sons, Inc.
12-64
Multiple Regression
Study the relationship of demand to two or
more independent variables
y = 0 + 1x1 + 2x2 … + kxk
where
0 = the intercept
1, … , k = parameters for the
independent variables
x1, … , xk = independent variables
Copyright 2009 John Wiley & Sons, Inc.
12-65
Multiple Regression with Excel
 Insert Exhibit 12.11
 Insert Exhibit 12.12
Copyright 2009 John Wiley & Sons, Inc.
12-66
Copyright 2009 John Wiley & Sons, Inc.
All rights reserved. Reproduction or translation of this work beyond that
permitted in section 117 of the 1976 United States Copyright Act without
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Sons, Inc. The purchaser may make back-up copies for his/her own use only and
not for distribution or resale. The Publisher assumes no responsibility for
errors, omissions, or damages caused by the use of these programs or from the
use of the information herein.
Copyright 2009 John Wiley & Sons, Inc.
12-67