demand estimation and regression analysis

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SUBJECT: Managerial Economics
TOPIC: Demand estimation using regression
REGRESSION
ANALYSIS
Presented by-
Patel Shubhamkumar.
Patel Vaishnavi.
Patidar Manjari.
Paul Rishi raj.
Prajapati Milan.
Rankawat Abhishek.

2. Roll No Name of Student
1 Asodariya Ankur P
2 Baladaniya Shailesh K
5 Bhalu Jatin P
14 Chitte Ankita R
43 Kukadiya Chirag D
52 Mohnot Aastha S
ByWhat is Demand estimation
• Demand estimation is a process that involves coming up
with an estimate of the amount of demand for a product or
service. The estimate of demand is typically confined to a
particular period of time, such as a month, quarter or year.
•To understand the functional relationship between demands
and its various determinants.
•Demand function –> Q = f( Px, Y, Pr, Ad,etc)

3. Roll No Name of Student
1 Asodariya Ankur P
2 Baladaniya Shailesh K
5 Bhalu Jatin P
14 Chitte Ankita R
43 Kukadiya Chirag D
52 Mohnot Aastha S
ByTools or Techniques of demand estimation
• Questioning the consumer to determining
his behavior
Consumer
surveys
• Experimental group to understand the
relation between the variables.
Consumer clinic
or focus group
• Direct market experiments to understand the
changes in demand due to changes in it s
depended variables
Market
experiments
• The regression analysis
Statistical
techniques

4. The Simple Linear
Regression Analysis
• Regression analysis is used to:
– Predict the value of a dependent variable based on the value of
at least one independent variable
– Explain the impact of changes in an independent variable on the
dependent variable
Dependent variable: the variable we wish to predict or explain
Independent variable: the variable used to explain the dependent
variable
 Suppose the advertising cost 𝑥 and sales (𝑦) are correlated, then
we can predict the future sales (𝑦) in terms of advertising cost (𝑥).

5. Correlation
 A correlation describes a relationship between two
variables
 Correlation tries to answer the following questions:
 What is the relationship between variable X and variable
Y?
 How are the scores on one measure associated with scores
on another measure?
 To what extent do the high scores on one variable go with
the high scores on the second variable?

6. Types of Relationships
Y
X
Y
X
Y
Y
X
X
Linear relationships Curvilinear relationships

7. Types of Relationships
Y
X
Y
X
Y
Y
X
X
Strong relationships Weak relationships

8. Types of Relationships
Y
X
Y
X
No relationship

9. Example
The following table
lists the monthly
sales and advertising
expenditures for all
of last year by a
digital electronics
company.
Month Sales(in
1000s)
Advertising
Rupees(in
1000s)
January 100 2.5
February 110 3
March 112 1.2
April 115 3.5
May 116 4.1
June 118 2.2
July 120 5.1
August 117 6
September 121 6.2
October 119 4.3
November 115 5.5
December 114 2.4

10. Scatter Diagram
Sales(in
1000s)
Adverti
sing
Rupees(
in
1000s)
100 2.5
110 3
112 1.2
115 3.5
116 4.1
118 2.2
120 5.1
117 6
121 6.2
119 4.3
115 5.5
114 2.4
0
20
40
60
80
100
120
140
0 2 4 6 8
Sales(in 1000s)
Sales(in 1000s)
Linear (Sales(in
1000s))

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Problem : Is there a significant relationship between the Sales
and Advertising expenditure?
Hypotheses :
Level of significance :
𝜶 = 𝟎. 𝟎𝟓
𝒓. 𝟎𝟓 = 𝟎. 𝟓𝟕𝟔
There is no significant relationship between the Sales and
Advertising expenditureHo:
There is a significant relationship between the Sales and
Advertising expenditure
H1:
df = n – 2
= 12 – 2
= 10

12. S
T
A
T
I
S
T
I
C
S
∑𝒚 = 𝟏𝟑𝟕𝟕
∑𝒙 𝟐 = 𝟐𝟎𝟓. 𝟓𝟒
∑𝒚 𝟐 = 𝟏𝟓𝟖𝟑𝟔𝟏
∑𝒙𝒚 = 5334.1
𝒏 = 𝟏𝟐
𝒙 = 𝟑. 𝟖𝟑
𝒚 = 𝟏𝟏𝟒. 𝟕𝟓
Pearson Product Moment
Coefficient of Correlation 𝒓
𝒙 𝒚 𝒙 𝟐 𝒚 𝟐 𝒙𝒚
2.5 100 6.25 10000 250
3 110 9 12100 330
1.2 112 1.44 12544 134.4
3.5 115 12.25 13225 402.2
4.1 116 16.81 13456 475.6
2.2 118 4.84 13924 259.6
5.1 120 26.01 14400 612
6 117 36 13689 702
6.2 121 38.44 14641 750.2
4.3 119 18.49 14161 511.7
5.5 115 30.25 13225 632.5
2.4 114 5.76 12996 273.6
∑𝒙 = 𝟒𝟔

13. 𝒓 =
𝟔𝟒𝟎𝟎𝟗. 𝟐 − 𝟔𝟑𝟑𝟒𝟐
𝟐𝟒𝟔𝟔. 𝟒𝟖 − 𝟐𝟏𝟏𝟔 𝟏𝟗𝟎𝟎𝟑𝟑𝟐 − 𝟏𝟖𝟗𝟔𝟏𝟐𝟗
𝒓 =
𝟏𝟐 𝟓𝟑𝟑𝟒. 𝟏 − 𝟏𝟑𝟕𝟕 𝟒𝟔
𝟏𝟐 𝟐𝟎𝟓. 𝟓𝟒 − 𝟒𝟔 𝟐 𝟏𝟐 𝟏𝟓𝟖𝟑𝟔𝟏 − 𝟏𝟑𝟕𝟕 𝟐
𝒓 =
𝟔𝟔𝟕. 𝟐
𝟑𝟓𝟎. 𝟒𝟖 𝟒𝟐𝟎𝟑
𝒓 =
𝟔𝟔𝟕. 𝟐
𝟏𝟐𝟏𝟑. 𝟕𝟎
𝒓 = 𝟎. 𝟓𝟓

14. The computed r value of 0.55 is less than critical value of
0.576 at 0.05 level of significance with 10degrees of freedom, so
the null hypothesis is accepted.
This means that there is no significant relationship between the
Sales and Advertising expenditure?
Decision Rule :
If the r computed value is greater than or beyond the
critical value, reject Ho.
Conclusion :

15. Suppose we want to predict the sales (𝒚) of the company when
company do expenditure of 8 (𝒙). To get the value of x, the simple
linear regression analysis will be used.
𝒚 = 𝒂 + 𝒃𝒙𝒂 = 𝒚 − 𝒃 𝒙
= 114.75 − 1.90 3.83
= 114.75 – (7.277)
𝒂 = 𝟏𝟎𝟕. 𝟒𝟕
𝒃 =
𝒏 ∑ 𝒙𝒚 − ∑ 𝒙 ∑ 𝒚
𝒏 ∑ 𝒙2 − ∑ 𝒙 2
=
12 5334.1 − 46 1377
12 205.54 − 46 2
=
64009.2 − 63342
2466.48 − 2116
=
667.2
350.48
𝒃 = 𝟏. 𝟗𝟎
= 107.47 + 1.90 𝑥
= 107.47 + 1.90 8
= 𝟏𝟐𝟐. 𝟔𝟕 or 123
123000(y) is sales
when advertisement
expense is 8000(x)

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Remarks:
 It is important to remember that the values of a
and b are only estimates of the corresponding
parameters of a and b.
 If there are two or more independent variables,
the regression equation becomes 𝑦 = 𝑏0 +
𝑏1 𝑥1+𝑏2 𝑥2 + ⋯ + 𝑏 𝑛 𝑥 𝑛

17. 0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6
y-axis
x-axis
𝒚 = 𝒂 + 𝒃𝒙
If 𝒃 = 𝟎
𝑦 = 1 + 0(1)
y = 1 + 0(2)
𝑦 = 1 + 0 3
𝑦 = 1 + 0 4
𝑦 = 1 + 0(5)
A horizontal line means there is no
association between two variables.
Slope of
Linear Regression

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Multiple Regression
 Multiple regression is an extension of simple
linear regression.
 It is used when we want to predict the value of a
variable based on the value of two or more other
variables.
 The variable we want to predict is called the
dependent variable (or sometimes, the outcome,
target or criterion variable).

19. Advantages of Simple Regression
Analysis & Forecasting
1. Predicting the Future
2. Supporting Decisions
3. Correcting Errors
4. New Insights

20. Conclusion
 Regression analysis is a family of statistical tools that can
help business analysts build models to predict trends,
make trade off decisions, and model the real world for
decision making support.
 These models can be used to predict the value of one or
more variables from a knowledge of the value of other
variables.

21. THANK YOU