Data Analysis

1
Data Analysis
Chapter 8

• 
  

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In this chapter, we focus on 3 parts
Chapter 6
Data Analysis

• 1. Descriptive Analysis
• 2. Two-way Analysis of Variance
• 3. Forecasting

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1. Descriptive Analysis
Chapter 6
Data Analysis

• 1.1 Index Numbers
• 1.2 Exponential Smoothing

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1.1 Index Numbers
Chapter 6
Data Analysis

• Index Number a number that measures the change
  in a variable over time relative to the value of
  the variable during a specific base period
• Simple Index Number index based on the relative
  changes (over time) in the price or quantity of a
  single commodity

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1.1 Index Numbers
Chapter 6
Data Analysis

• Laspeyres and Paasche Indexes compared
• The Laspeyres Index weights by the purchase
  quantities of the baseline period
• The Paasche Index weights by the purchase
  quantities of the period the index value
  represents.
• Laspeyres Index is most appropriate when baseline
  purchase quantities are reasonable approximations
  of purchases in subsequent periods.
• Paasche Index is most appropriate when you want
  to compare current to baseline prices at current
  purchase levels

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1.1 Index Numbers
Chapter 6
Data Analysis

• Calculating a Laspeyres Index
• Collect price info for the k price series (the
  basket) to be used, denoted as P1t, P2tPkt
• Select a base period t0
• Collect purchase quantity info for base period,
  denoted as Q1t0, Q2t0..Qkt0
• Calculate weighted totals for each time period
  using the formula
• Calculate the index using the formula

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1.1 Index Numbers
Chapter 6
Data Analysis

• Calculating a Paasche Index
• Collect price info for the k price series to be
  used, denoted as P1t, P2tPkt
• Select a base period t0
• Collect purchase quantity info for every period,
  denoted as Q1t, Q2t..Qkt
• Calculate the index for time t using the formula

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1.2 Exponential Smoothing
Chapter 6
Data Analysis

• Exponential smoothing is a type of weighted
  average that applies a weight w to past and
  current values of the time series. (Yi actual
  value)
• Exponential smoothing constant (w) lies between 0
  and 1, and smoothed series Et is calculated as
• How much influence
• does the past have when w 0 and
  when w 1?

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1.2 Exponential Smoothing
Chapter 6
Data Analysis

• Selection of smoothing constant w is made by
  researcher.
• Small values of w give less weight to current
  value, yield a smoother series
• Large values of w give more weight to current
  value, yield a more variable series

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2 Two-way Analysis of Variance
Chapter 6
Data Analysis

• Two-way ANOVA is a type of study design with one
  numerical outcome variable and two categorical
  explanatory variables.
• Example In a completely randomised design we
  may wish to compare outcome by age, gender or
  disease severity. Subjects are grouped by one
  such factor and then randomly assigned one
  treatment.
• Technical term for such a group is block and the
  study design is also called randomised block
  design

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2 Two-way Analysis of Variance
Chapter 6
Data Analysis

• 2.1 Randomised Block Design
• 2.2 Analysis in Two-way ANOVA 1
• 2.3 Analysis of Two-way ANOVA by the regression
  method

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2.1 Randomised Block Design
Chapter 6
Data Analysis

• Blocks are formed on the basis of expected
  homogeneity of response in each block (or group).
• The purpose is to reduce variation in response
  within each block (or group) due to biological
  differences between individual subjects on
  account of age, sex or severity of disease.

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2.1 Randomised Block Design
Chapter 6
Data Analysis

• Randomised block design is a more robust design
  than the simple randomised design.
• The investigator can take into account
  simultaneously the effects of two factors on an
  outcome of interest.
• Additionally, the investigator can test for
  interaction, if any, between the two factors.

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Steps in Planning a Randomised Block Design
Chapter 6
Data Analysis
2.1 Randomised Block Design

1. Subjects are randomly selected to constitute a
   random sample.
2. Subjects likely to have similar response
   (homogeneity) are put together to form a block.
3. To each member in a block intervention is
   assigned such that each subject receives one
   treatment.
4. Comparisons of treatment outcomes are made within
   each block

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2.2 Analysis in Two-way ANOVA - 1
Chapter 6
Data Analysis

• The variance (total sum of squares) is first
  partitioned into WITHIN and BETWEEN sum of
  squares. Sum of Squares BETWEEN is next
  partitioned by intervention, blocking and
  interaction

SS TOTAL
SS BETWEEN
SS WITHIN
SS INTERVENTION
SS BLOCKING
SS INTERACTION
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Chapter 6
Data Analysis
2.2 Analysis in Two-way ANOVA - 1
method. And an interaction between gender and
teaching method is being sought. Analysis of
Two-way ANOVA is demonstrated in the slides that
follow. The study is about a n experiment
involving a teaching method in which professional
actors were brought in to play the role of
patients in a medical school. The test scores of
male and female students who were taught either
by the conventional method of lectures, seminars
and tutorials and the role-play method were
recorded. The hypotheses being tested
are Role-play method is superior to conventional
way of teaching. Female students in general have
better test scores than male students. Role-play
method makes a better impact on students of a
particular gender. Thus, there are two factors
gender and teaching method. And an interaction
between teaching method and gender is being
sought.
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Chapter 6
Data Analysis
2.2 Analysis in Two-way ANOVA - 2

• Each Sum of Squares (SS) is divided by its degree
  of freedom (df) to get the Mean Sum of Squares
  (MS).
• The F statistic is computed for each of the three
  ratios as
• MS INTERVENTION MS WITHIN
• MS BLOCK MS WITHIN
• MS INTERVENTION MS WITHIN

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2.2 Analysis of Two-way ANOVA - 3
Chapter 6
Data Analysis

• Analysis of Variance for score
• Source DF SS MS F
  P
• sex 1 2839 2839 22.75
  0.000
• Tchmthd 1 1782 1782 14.28
  0.001
• Error 29 3619 125
• Total 31 8240

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2.2 Analysis of Two-way ANOVA - 4
Chapter 6
Data Analysis

• Individual 95 CI
• Sex Mean -------------------------
  -------------
• 0 58.5
  (------------)
• 1 39.6 (-------------)
• -------------------------
  -------------
• 40.0 48.0
  56.0 64.0
• Individual 95 CI
• Tchmthd Mean -------------------------
  -------------
• 0 56.5
  (--------------)
• 1 41.6 (---------------)
• -------------------------
  -------------
• 42.0 49.0
  56.0 63.0

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2.2 Analysis of Tw0-way ANOVA - 5
Chapter 6
Data Analysis
Analysis of Variance for SCORE Source
DF SS MS F
P SEX 1 2839
2839 22.64 0.000 TCHMTHD 1
1782 1782 14.21 0.001 INTERACTN
1 108 108 0.86
0.361 Error 28 3511
125 Total 31 8240
Interaction is not significant P 0.361
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2.2 Analysis of Two-way ANOVA - 6
Chapter 6
Data Analysis
Individual 95 CI SEX Mean
-------------------------------------- 0
58.5
(------------) 1 39.6
(-------------)
--------------------------------------
40.0 48.0 56.0
64.0 Individual 95
CI TCHMTHD Mean ----------------------
---------------- 0 56.5
(--------------) 1
41.6 (---------------)
--------------------------------------
42.0 49.0 56.0
63.0
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2.3 Analysis of Two-way ANOVA by the regression
method (reference coding)
Chapter 6
Data Analysis
The regression equation is SCORE 65.9 - 18.8
SEX - 14.9 TCHMTHD Predictor Coef
SE Coef T P Constant
65.913 3.420 19.27 0.000 SEX
-18.838 3.950 -4.77
0.000 TCHMTHD -14.925 3.950
-3.78 0.001 S 11.17 R-Sq 56.1
R-Sq(adj) 53.1 Analysis of Variance Source
DF SS MS F
P Regression 2 4620.9
2310.4 18.51 0.000 Residual Error 29
3619.0 124.8 Total 31
8239.8
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2.3 Analysis of Two-way ANOVA by the regression
method (effect coding)
Chapter 6
Data Analysis
The regression equation is SCORE 49.0 - 9.42
EFCT-Sex - 7.46 EFCT-Tchmthd - 1.84
Interaction Predictor Coef SE
Coef T P Constant 49.031
1.980 24.77 0.000 EFCT-Sex
-9.419 1.980 -4.76 0.000 EFCT-Tch
-7.463 1.980 -3.77
0.001 Interact -1.838 1.980
-0.93 0.361 S 11.20 R-Sq 57.4
R-Sq(adj) 52.8
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Reference Coding and Effect Coding - 1
Chapter 6
Data Analysis

• In both methods, for k explanatory variables k-1
  dummy variables are created.
• In reference coding the value 1 is assigned to
  the group of interest and 0 to all others (e.g.
  Female 1 Male 0).
• In effect coding the value -1 is assigned to
  control group 1 to the group of interest (e.g.
  new treatment), and 0 to all others (e.g. Female
  1 Male (control group) -1 Role Play 1
  conventional teaching (control) -1).

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Reference Coding and Effect Coding - 2
Chapter 6
Data Analysis

• In reference coding the ß coefficients of the
  regression equation provide estimates of the
  differences in means from the control (reference)
  group for various treatment groups.
• In effect coding the ß coefficients provide the
  differences from the overall mean response for
  each treatment group.

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Chapter 6
Data Analysis

• 3 Marketing Forecasting

3.1 The concept of market forecast 3.2 The
theoretical bases of forecast 3.3 The
classification of forecast methods 3.4
Qualitative Forecast Methods 3.5 Quantitative
Forecast Methods
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3.1 The concept of market forecast
Chapter 6
Data Analysis

• Based on market surveys and by applying
  scientific methods, to estimate the development
  situation of objects-forecasted in a certain
  period in future in order to help managers to
  improve decisions-making qualify. The process is
  generally called as market forecast.
• In this chapter, objects-forecasted mainly are
  need quantities of products, sometime may also be
  product prices, competitive situations,
  environmental factors, and so on.

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3.2 The theoretical bases of forecast
Chapter 6
Data Analysis

• (1)The continuity principle
• ?It is also called as inertia principle. Because
  of existing inertia, any system doesn't change
  its basic characteristics in the short run.
• Attention all time series analysis methods
  are based on this principle.

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Chapter 6
Data Analysis
3.2 The theoretical bases of forecast

• (2)The analogy principle
• ?time analogy to make an inference in future
  from the past and the present. When two things
  and more things have characteristic similarity
  (structure, mode, property, and develop
  tendency), we can forecast the developing things
  and the ready-to-develop things by studying the
  developed or advanced things. Attention analogy
  is suitable to the homogeneous things, also to
  inhomogeneous things.

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Chapter 6
Data Analysis
3.2 The theoretical bases of forecast

• (2)The analogy principle
• ?(continual to front page) sampling analogy to
  make an inference about the whole from the part.
  When the whole and the part have characteristic
  similarity, we can forecast the whole by studying
  the part.
• Attention the similarity is the key point either
  between the things with difference in advance
  time, or between the whole and the part.

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Chapter 6
Data Analysis
3.2 The theoretical bases of forecast

• (3)The relevancy principle
• ?the theory considers that there is relativity
  among things, especially between two relevance
  things or causal things. All statistical
  regression analysis methods are based on this
  principle.

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3.3 The classification of forecast methods
Chapter 6
Data Analysis

• Although there are many theoretical forecast
  methods, in general forecast can be classified as
  two types
• qualitative forecast
• quantitative forecast.

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3.3.1 Qualitative forecast
Chapter 6
Data Analysis

• Qualitative forecast emphasizes the development
  tendencies (maybe essential characteristics), and
  is suitable to cases which there are a fewer and
  lack of data, such as science and technology
  forecast, development forecast of infant
  industries, long-term forecast, and forecasting
  things with uncertainty, etc.

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Chapter 6
Data Analysis
3.3.2 Quantitative forecast

• Quantitative forecast emphasizes the quantitative
  relationships of developing things. Essentially
  it is a kind of methods based on quantitative
  trend extrapolation, and is suitable to cases
  which there are many data.

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Chapter 6
Data Analysis
3.3.3 The comparison of two methods

• Qualitative forecast might contribute to the
  analysis of the basic trends, development
  inflection point, and the essence of things.
  Quantitative forecast can draw us numeral
  development concepts, and bring us conveniences
  of applying forecast results. None of two methods
  should be our preference, otherwise we probably
  abuse forecast methods.

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3.4 Qualitative Forecast Methods
Chapter 6
Data Analysis

• Delphi method
• Social investigation or consumer survey
• Colligating sellers opinions
• having an informal discussion of a team
• Integration of experts forecasts
• The method of subjective probabilities
• above methods all belong to non-models.

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Exponential Smoothing
• ?mathematical model
• ?signs and meanings to explain every sign and
  its meaning
• ?avalue ais greater, means that the more late
  sample observations, the more its influence on
  forecast results. Vice versa. Recommendation a
  2/(n1)

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Exponential Smoothing
• ?mathematical model----horizontal trend
• ? mathematical model----lineal trend

39
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Exponential Smoothing
• ?mathematical model---- quadratic curve trend

40
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Exponential Smoothing
• ?how to choose mathematical models according to
  the trend of sample observations on coordinate
  diagram.

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Exponential Smoothing
• ?how to determine initial values of smoothing
  parameters in general, the first observation
  value instead of them.
• ?superiorities of exponential smoothing the
  storage data only is a fewer and it is suitable
  to forecast in short run.
• ?application cases reference to another teaching
  materials.

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• The growth curve
• ?mathematical model
• Logistic curve
• Gompertz curve

43
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• The growth curve
• ?mathematical processing of initial observations
• For Logistic curve
• 2. For Gompertz curve

The processed data of observations can be used
for calculation of parameters k, a and b. The
calculation formulas are as following
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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Calculation of k, a, and b

Attention the processed data of observations
must be blacked into 3 groups, thus we can obtain
3 sum values
When the number of initial data is not integer
multiple of 3, we must add or cut down data of
initials.
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Chapter 6
Data Analysis
3.5 Quantitative Forecast Methods

• Linear regression
• ?An independent variable and a dependent variable
  are chosen on the model, and the varied relation
  of y and x is linear. This model is widely
  applied in quantitative forecasts.
• ?the standard model
• yabx
• to non-standard equation, it is must
  transferred as standard model.

46
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression
• ?determination of the coefficient a and b
• by means of method of minimum squares, let
  the variance minimization, and the calculation
  of is as following
• and let derivatives of Q to a and b are equal
  to 0, then

47
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression

We can get a and b
48
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression
• ?then the forecast model is

It is necessary to check if the model the built
model is of high quality, the checking methods
are 1. standards error analysis
49
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression
• in general, the following is required

2. correlation coefficient and test of
significance. The calculation of correlation
coefficient is
50
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression
• ?discussion of correlation coefficient R
• ?when R0, means y doesn't have the correlation
  with x, the case is called 0- correlation, so the
  built model cant be applied to forecast.
• ?when R1, means y has the direct correlation
  with x.
• ?in general, R is required to meet Rgt0.7. when
  Rlt0.3, means the built model can not be applied.
  When 0.3ltRlt0.7, means the model is not good and
  worthless.

51
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression
• ? The quality of regression model is also tested
  by significance.
• if , the built model is good and
  worth to application. on the contrary, if
  , the built model is worthless.
• is the critical value of
  correlation coefficient R. It is known by looking
  up the given table. Theais given level of
  significance such as 0.05. The (n-m) is the
  degree of freedom such as n-2, m is the number of
  variables.

52
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression
• ?the application of model if the future value of
  x is known as x?, the interval value of forecast
  variable is

Here, s?is determined by the formula
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Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression
• and is T-distribution with
  significance level aand freedom degree n-m-1,
  here n is the number of observations, m is the
  number of variables.
• ?In addition, many non-linear equation can be
  transferred as linear regression. For example

54
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Linear regression

Then we can get the equation , the
same work is suitable to exponential function,
logarithm function, reciprocal function, etc.
Those functions are called as allowed linear
regression with single variable.
Application case to see another teaching
materials.
55
3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• analogy forecasting method a case of
  application
• ?We can forecast an object variable by
  researching the relationship between the variable
  and an economic indicator (for example, per
  capita national income, NI, or gross national
  product, GNP)
• ?The relationship between vehicle population and
  NI is given in page 78 of textbook.

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Elastic coefficient method
• ?For example, we can get the average growth rate
  of vehicle sales quantity by observing selling in
  the past years, but the rate is only an image. If
  we analyzes growth rate of sales together with
  growth rate of an economic indicator, we can
  improve forecast quality. Detail case is given in
  textbook.

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• Combination forecasting method
• ?Concept of combination forecasting it is called
  as combination forecasting to get a final
  forecast conclusion based on colligating multi
  intermediate forecast results gained by adopting
  multi-models, or on same model adopting multi
  independent variables.
• ?The core idea combination is benefit to clear
  up the chanciness of single mode or independent
  variable.

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• talking about forecast experience
• ?policy variables it is very difficult to
  forecast changes of policy, but we can strengthen
  monitoring of environmental factors, especially
  paying attention to the running condition of the
  national economy. Establishing the monitoring and
  early warning system of the national economy is
  very necessary.

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• talking about forecast experience
• ?predicting accuracy and goodness of fit in
  model.
• ?simple model and complexity model
• ?single predicting result and many results
• ?reliability of forecast conclusions three pints
  are very important----reality initial data
  (authoritativeness), accuracy of mathematical
  models, and correctness of forecast procedures.

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3.5 Quantitative Forecast Methods
Chapter 6
Data Analysis

• talking about forecast experience
• ?data processing, actual cases and researchers
  imagination.
• to improve forecast, establishing information
  system is very important.