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# Demand assessment elementary methods

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Demand assessmentelementary methods

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2 directions in demand assessmentstatistical analysis

market intelligence

При

Задача

отсутствии

статистического

надежной

экспериментальной

анализа: определение

информации

параметров необходимо

функции спроса

предпринять

посредствомисследование

использования

рынка

эмпирических данных

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Statistical analysisSteps:

1) Collection, validation and

assessment of data

2) The choice of the information curve

3) Verification and evaluation of the

selected curve

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Statistical analysis1) Collection, validation and

assessment of data

time series

cross-sectional data

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Statistical analysis1) Collection, validation and assessment of data

time series

Examine time changes in the demand for certain types of goods

or services and the corresponding time changes in pricing,

sales volume and other independent variables that affect the

demand

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time seriesLong time period

Adjustment of necessary information

in order to avoid effects such as inflation

Deflationary correction: divide all nominal figures by the consumer

price index and multiplied by 100. Get "regular money" base

period

And also it is necessary to take into account changes in

population, accounting for seasonal and cyclical fluctuations

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Statistical analysis1) Collection, validation and

assessment of data

cross-sectional data

Considered changing the variables from some set in a

particular time

A snapshot of the many variables in

one certain time

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Ex: In order to determine the effect of prices ondemand, as a variable can be selected volume of

sales for a particular month,

while the set may include a list of firms producing the

product

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Statistical analysis2) The choice of the information curve

The results of the observations are used to

estimate the parameters of demand function

This function can then be used to predict values for the

dependent variable for known values of the independent

variables

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When choosing a curve there are two main questions:1. What type of equation it is necessary to use?

2. How the selected function fits and predicts the

demand?

The choice of the equation depends on two conditions:

а) the number of independent variables and б) the distribution of

the data, i.e. linear or nonlinear distribution

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If the trend of the experimental values of the dependentvariable is approximately linear, and there are many

independent variables, the estimated equation is:

constant value

The coefficients of the

independent variables

˄

Q

b

b

X

b

X

...

b

X

0

1

1

2

2

X

X

The estimated demand

for the product

The value of the independent

variable

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## 12.

If the data can be reduced to a single independent variable (e.g. price)and the trend is almost linear than to find the formula for this straight

line we can use simple (pair) regression analysis

The equation thus is:

A constant value (which determines the point of

intersection of the graph of the function with the Y

axis)

QX a bP

x

The quantity X,

(dependent variable)

The unit price of X

(independent variable)

The regression coefficient for Px

(defining the slope of a line on the graph

of a function)

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## 13.

If the trend of the dependent variable is nonlinear and thefunction has a single independent variable, it is described

by the equation:

Q x aP

b

x

This equation can be written as the logarithm, if you find

the logarithm of both parts

logQ x log a b log Px

This logarithmic function is linear and can be estimated

using simple regression analysis

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simple linear regressionSTEP 1. Data collection

Collect time series data

Period

Observation X

Observation Y

TASK: TO FIND THE REGRESSION FUNCTION for THESE DATA!

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simple linear regressionSTEP 2. Organization variables in time

There is a direct relationship between X and Y,

Причины: визуализация;

определение

линейности

with an increase of

X, Y also increases

and if или нелинейности

для выбора

соответствующей

формы кривой

X falls,

Y falls too

X

and

Y

There are no obvious links of the lag-lead between them

(no need to move forward or back in time)

the trend, allocated to each

series, is linear

Period

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simple linear regressionSTEP 3. Organization of a scatter plot

Database for simple linear regression is a set of

ordered pairs (X, Y), which represent the values of X

and Y for the reviewed period

If we assume that the true distribution function

Y = f(X) is linear, then we must check the validity

of this assumption

As between the variables does not exist relations of the lag lead,purpose

one can contrast

values

for eachdata

year,inthe

values of X for

For this

we put the

available

a scatter

chartthe same period without the need to move the rows

Visual inspection confirms that the selected function can be linear

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simple linear regressionSTEP 4. Evaluation of the regression line

In

Minimizing

When

ordermaking

to estimate

the the

sumregression

the

of quadratic

true regression

analysis

deviations

we

lineuse

of

Уi =the

а + b Хi,

parameters

calculated

method ofYleast

avalues

andsquares

b should

from itsbe

observed

calculated

values

for the estimated

regression

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simple linear regressionSTEP 4. Evaluation of the regression line

Y 13 2,6 X i

i

Period

Observa

Observa

-tion

-tionXX

Observa

-tion Y

Sum

Average

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simple linear regressionSTEP 5. Comparison of calculated and actual values

How well our estimated regression equation describes Y as a function

Compare the actual and estimated value

of X?

Initial X

Initial Y

Estimated function

Deviation

The deviation of the actual values from the calculated

values: the results of all observations do not fit on the

regression line

The fact that the observations deviate from the regression line

indicates that the magnitude of Y is effected also by forces

different from X

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simple linear regressionInterpretation of parameters

Y 13 2,6 X i

i

The "a" parameter determines the point of

intersection of the regression line with the Y axis

"a" has no economic sense in the demand equation

Option "b" determines the slope of the regression line

"b" represents the individual contribution of each independent variable

to the value of the dependent variable

The positive sign of the parameter "b" indicates that the variables

change in the same direction

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simple linear regressionEvaluation of the regression equation

The goal of linear regression evaluation: to get a linear equation, which can be used to

determine the values of the independent variable Y on any existing values of the

independent variable X

˄

How informative or accurate the determined Y is?

When analyzing simple regression use two statistical

indicators:

The root - mean - square error of the estimation, Se;

The coefficient of determination, r^2, and its square

root, r, which is called the correlation coefficient.

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1) The root – mean - square error of the estimation, Se;Represents the deviation of experimental points from the

estimated regression line (determines the variance of random

Y values)

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1) The root - mean - square error of the estimation, Se;Observed Y for Xi

Evaluated Y for Xi

˄ 2

(Y

Y

i

i)

S

e

n k 1

Root-mean-square error

Number of observations

Number of independent

variables

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1) Root-mean-square error, Se;(Y

Y

i

i)

S

e

n k 1

2

If Se = 0, than the estimated equation fits perfectly the observed

data (all points lie on the regression line)

The more root-mean-square error is, the greater the range of

deviations are

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2) coefficient of determination, r^2Shows how well the regression model describes the variation

of the dependent variable

ЕХ: if r^2 = 0,975, than approximately 97.5% of the

changes in the dependent variable explained by the

variation of the independent variable X

Values can range from 0 to 1 or from 0 to 100%

0 - there is no relationship between the variables,

1 - the regression line is perfect (all changes are explained

by changes in X)

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## 26.

3) the correlation coefficient, r,Determines the degree of connection between variables

-1 < r > 1

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