Academy of Economic Studies
International
Business and Economics
ECONOMETRICS
ASSIGNMENT
“REGRESSION MODEL”
1. Executive Summary
In this chapter I would
like to justify why of all indicators and from all data bases existing I
specifically chose verifying the intensity of the relationship between a
country’s total advertising expenditures and its GDP.
For once, it will help me with my
Dissertation paper which is on advertising, domain I’ve recently came in touch
with by working at a production company.
Second, the overall increase in the importance given to this
sector, with the gigantic amounts spent in producing a TV commercial are
raising a good question mark regarding how much does a country’s GDP and
welfare influences these spending.
I chose UK
because they put a lot of emphasis on their advertising campaigns, having some
of the biggest and wellknown leading worldwide
commercial production
companies, among which I can mention: Radical Media (with who I got the
opportunity to work), HIS, Factory Films, Tangerine Films, Independent Media,
Mind Works Media UK and also hosting some of the largest global marketers that
have a strong word when it comes to their contribution to the World’s GDP.
All the
calculations made to prove the validity of the model were made in Excel and are
further attached as ANEXES in the end of the Assignment.
2. Introduction
Advertising is a small part of
the daytoday life of business, governments and of the publics with which each
seeks to engage. It is, on the other hand, a business that offers the people
who work in and with it endless excitement, fascination, frustration and,
sometimes, satisfaction – together with the opportunity, from time to time, for
a great deal of fun and even for making a massive contribution to the success
of a brand.
There is an underlying
reason why ad expenditures as a whole has not returned to its 1989 peak share of
GDP in the UK. Advertising is not the whole of the communications mix, and the
most advertising statistics do not include direct marketing, let alone PR,
sales promotion, design and corporate identity, sponsorship and some mirror
media – nor do they yet include the Internet, which is undoubtedly the fastest
growing form of marketing communication, though still from a very small base
everywhere outside the USA. All the available evidence shows that direct mail
has been growing faster than media advertising in recent years, and PR
expenditures have certainly grown very fast in the last three years. Data on
sales promotion expenditure are extremely hard to come by, but US evidence, and
broader estimates by WPP Group, suggest that advertising accounts for only 42%
of total marketing communications expenditures worldwide (including market
research), and less than 35% in the UK. As long as 1986, WPP annual report
highlighted the rapid growth of sales promotion expenditures, and this remains
a worldwide phenomenon.
3. Data Description
As we know, Gross Domestic
Product (GDP) is an integral part of the UK national accounts and provides a
measure of the total economic activity in a region. GDP is often referred to as
one of the main 'summary indicators' of economic activity and references to
'growth in the economy' are quoting the growth in GDP during the latest
quarter.
In the UK three different
theoretical approaches are used in the estimation of one GDP estimate.
GDP from
the output or production approach  GDP(O)
measures the sum of the value added created through the production of goods and
services within the economy (our production or output as an economy). This
approach provides the first estimate of GDP and can be used to show how much different
industries (for example, agriculture) contribute within the economy.
GDP from
the income approach  GDP(I)
measures the total income generated by the production of goods and services
within the economy. The figures provided breakdown this income into, for
example, income earned by companies (corporations), employees and the self
employed.
GDP from
the expenditure approach  GDP(E)
measures the total expenditures on all finished goods and services produced
within the economy.
The estimates are 'Gross'
because the value of the capital assets actually worn away (the 'capital
consumption') during the productive process has not been subtracted.
Thus, by
analyzing the values of GDP by expenditure it will prevail how much its
variation explains the variation in the total advertising figures.
Advertising is an activity with
significance for many countries’ economies: total ad spending runs around +/ 
1% of GDP in most developed countries.
In the UK, while ad agencies as such,
employ only some 15 000 people, it has been estimated that advertising as a
whole is responsible for nearly 100 000 jobs, or 0.4% of total employment. This
includes people working in business supplying the ad industry – studios, TV
production houses, printers, etc. – and advertising staff in client
organizations and the media.
Advertising expenditures, as shown in
the statistics published by the
Advertising Association, consist of two elements: display advertising
and classified advertising, of which display is the dominant sector, though
classified is very important for some media. Advertising is sensitive to the
state of the economy as a whole – it is not merely vulnerable to both downturns
and upswings, but it moves rather rapidly in response to either. Classified
advertising, in fact, is a valuable “lead indicator” of economic progress,
because virtually half of it, at least in the UK, consists of recruitment
advertising, which reflects companies’ experience and expectations of their
markets precisely.
Advertising
thus shows considerable “mood swings” in line with the growth or stagnation of
the economy. Through much of the 1970s, the industry in the UK was in decline:
the 1980s saw a sustained boom after the 198182 recession, followed by hard
times in the early 1990s, and by 1998, display advertising had still not
recovered to its 1989 percentage share of GDP.
4. Analysis
4. a) Collecting the
data
In order to determine at what extent does the wealth of a
country determines the total expenditures in the advertising sector, we will
analyze a model taking as independent variable (x),UK’s GDP for a 20 year
period starting with 1985 and proving how it influences the dependent variable
(y), represented by the advertising expenditures in current prices.
The data was collected from several sources so that the GDP
values initially expressed in million dollars were converted at a parity of
0.509 pound/dollar as shown in the
following table:
Parity: £/ $ =0.509
Figure 1. UK advertising expenditure and GDP 19852004
Nr. crt

Year

Advertising expenditure
(yi)

GDP $mil by expenditure

GDP £ bn
by expenditure
(xi)

1

1985

5.05

455506.9902

894.9056783

2

1986

5.8

558954.1052

1098.14166

3

1987

6.57

685753.9263

1347.257223

4

1988

7.61

833174.7712

1636.885602

5

1989

8.64

841280.9635

1652.811323

6

1990

8.93

989564.2668

1944.134119

7

1991

8.53

1033481.752

2030.416015

8

1992

8.86

1071585.965

2105.276944

9

1993

9.14

962406.7387

1890.779447

10

1994

10.14

1041342.663

2045.859849

11

1995

11.03

1133689.667

2227.288147

12

1996

12.08

1191280.39

2340.432986

13

1997

13.34

1327035.159

2607.141767

14

1998

14.42

1464975.281

2878.14397

15

1999

15.41

1442777.295

2834.532996

16

2000

16.99

1434896.459

2819.050018

17

2001

16.54

1571371.904

3087.174665

18

2002

16.73

1805663.111

3547.471732

19

2003

17.23

2132156.066

4188.911721

20

2004

18.47

2198795.754

4319.834487

Source: www.unctad.org and A.A., Advertising
Statistics Yearbook 1998, NTC Publications), http://www.ipa.co.uk/resource_centre/totaladspend.cfm
4.b) Graphical
representation – Scatter diagram
Specifying
the econometrical model implies choosing a function f(x) which can describe the
relationship between the 2 variables.
The
graphical representation of the data presented in Table 1 is made
through a scatter diagram which shows that there is a positive relationship
between UK’s GDP by expenditure and the advertising expenditures from 1985 till
2004, since the two variables tend to move in the same direction forming a
linear pattern as follows:
Figure 2. The relation between
UK’s GDP and Total advertising expenditures in 19852004
Source: Figure 1. UK
advertising expenditure and GDP 19852004
Both the equation and the
value of R^{2 } displayed on the diagram, we shall see, that
are the same as the ones obtained after making all the computations and their
values will be described when analyzing the regression model.
4.c) The Regression
After
collecting the data and drawing the graph, the next step is to create the
regression model using the Regression function in Excel, which automatically
generated the Summary output:
Figure 3. Summary output
SUMMARY OUTPUT



Regression Statistics

Multiple R

0.9487517

R Square

0.90012979

Adjusted R Square

0.89458144

Standard Error

1.38047841

Observations

20

Where:
 Multiple
R (r) = Coefficient of correlation. Is used to characterize the intensity
of the relation between variables, independent of the type of the
connection or the number of variables taken into consideration.
It
is calculated as a ratio between covariance and the product of the
standard
deviation of the two variables, as in the formula:
r = _{}
The value
of 0.94 obtained in the table shows that there is a strong positive association
between UK’s GDP by expenditure and the advertising expenditures, since it
falls in the interval (0.95 , 0.75] and every point falls on a increasing regression
line.
 R
square = Coefficient of determination. Shows that the linear regression
function catches 90% from the total variation of the advertising
expenditures (yi) and it is calculated according to the formula:
R^{2 }=_{}
 Standard
Error (S) = S_{nYn }= _{}_{}= 1.38047841
The
value obtained in the summary output reveals that there is only a slight
difference of ~ 1,39 between the real values and the theoretical ones.
 Adjusted RSquare = 1 – [ MS error / (SS total
/ df total)]
Accounts for the number of predictors in your model and is
useful for comparing models with different numbers of predictors.
Next,
it’s easy to determine the equation of regression Y=a+bx+_{}
based on the coefficients obtained
in the ANOVA table.
Figure 4. ANOVA
ANOVA







df

SS

MS

F

Significance F

Regression

1

309.1725235

309.172524

162.233917

1.9216E10

Residual

18

34.30297146

1.90572064



Total

19

343.475495











Coefficients

Standard Error

t Stat

Pvalue

Lower 95%

Intercept

1.2506

0.867400354

1.44178415

0.16653638

0.5717364

GDP

4E06

0.00000034

12.7371079

1.9216E10

3.6305E06

So the
equation will be :
Y= 1.2506 +
0.000004*x
Where: a = 1.2506 ( intercept) ; it
indicates the value of Y when the x=0;
b = 0.0000004 (the slope of the line)
The
interpretation of the equation is that an increase of 1 pound in UK’s GDP by
expenditures in one year (xi), will determine an increase of 0.000004 pounds in
the total advertising expenditures of UK in that year.
The
formulas for the other coefficients that appeared whilst creating the
regression model are encountered below along with the afferent explanations.
 Sum
of squares (SS)  The sum of squared distances. SS Total is the total
variation in the data. SS Regression is the portion of the variation
explained by the model, while SS Error is the portion not explained by the
model and is attributed to error.
 Degrees
of freedom (d.f.). Indicates the number of independent pieces of
information involving the response data needed to calculate the sum of
squares. The degrees of freedom for each component of the model are:
DF Regression = p
DF Error = n  p  1
Total = n  1
where n
= number of observations and p = number of predictors.
 MS
Regression (Mean square regression) = the ratio of SS Regression and
DF Regression.
 MS
Error (Mean square error) = is the variance around the fitted regression
line. MS Error = s. The formula is:
MS Error = SS Error / DF Error
 F = If the calculated Fvalue is greater
than the Fvalue from the Fdistribution, then at least one of the
coefficients is not equal to zero. The Fvalue is used to determine the
pvalue.
Fvalue = MS Regression / MS Error
 Residuals = The difference between the observed values
and predicted values.
SRegression = _{}
SSResidual = _{}
MSRegression =_{}, where 1 = degrees of freedom
MSResidual =_{}, where 23 = degrees of freedom
Standard error_{(b)} = _{}
t Stat = _{}
Figure 5. Table with all computation needed to
make the regression model
Year

Advertising
expenditure*
(yi)

GDP**
(xi)

Yi

(Yiyavg)^2

(yiYi)

(yiYi)^2

(xixavg)^2

1985

5.05

894.9056783

5.14

41.40

0.09

0.0083

2171703966

1986

5.8

1098.14166

6.02

30.81

0.22

0.0506

2152803049

1987

6.57

1347.257223

7.11

19.96

0.54

0.2895

2129748026

1988

7.61

1636.885602

8.37

10.29

0.76

0.5734

2103099679

1989

8.64

1652.811323

8.44

9.85

0.20

0.0414

2101639239

1990

8.93

1944.134119

9.70

3.51

0.77

0.5976

2075013514

1991

8.53

2030.416015

10.08

2.24

1.55

2.3967

2067160278

1992

8.86

2105.276944

10.40

1.37

1.54

2.3827

2060358623

1993

9.14

1890.779447

9.47

4.43

0.33

0.1096

2079877219

1994

10.14

2045.859849

10.15

2.05

0.01

0.0000

2065756177

1995

11.03

2227.288147

10.93

0.41

0.10

0.0092

2049297047

1996

12.08

2340.432986

11.43

0.02

0.65

0.4277

2039065904

1997

13.34

2607.141767

12.59

1.02

0.75

0.5692

2015050025

1998

14.42

2878.14397

13.76

4.79

0.66

0.4306

1990793264

1999

15.41

2834.532996

13.57

3.99

1.84

3.3703

1994686862

2000

16.99

2819.050018

13.51

3.73

3.48

12.1324

1996070100

2001

16.54

3087.174665

14.67

9.59

1.87

3.4873

1972183767

2002

16.73

3547.471732

16.67

25.99

0.06

0.0032

1931512722

2003

17.23

4188.911721

19.46

62.21

2.23

4.9842

1875542902

2004

18.47

4319.834487

20.03

71.51

1.56

2.4390

1864220157


231.51

47496.45035

231.51

309.17

0.00

34.3030

40735582521

*
Advertising expenditures (bn pounds in current prices)
**GDP
in total expenditures (bn pounds)
4.d) Testing the Regression model
There are
several methods used to test the accuracy of the model, among which the
simplest one is to look at the P value in the ANOVA table (Figure 4) which is
1.9216*10^{10 } , obviously
smaller than 0.05 degrees of freedom meaning that the model is correct.
As well, by comparing F value with F
table (from the statistical tables), it can be proven the correctness of the
model since F value > F table, with the values of 162.233917 > 4.4138734.
4.e) Testing the linear relationship between the two variables
In order to
verify if between UK’s GDP by expenditure and the total advertising
expenditures really is a linear relation, comparing t Stat value and the t
table (from the statistical tables) and, as we see, 12.7371079 > 2.10092204, therefore between the 2 variables
is a linear relationship.
Conclusion
The regression model analyzed
is a good proof that a country’s GDP is a top ranked indicator that influences
all parts of the economy, true, in different extent but still plays a huge role
in the development of some certain areas, like in the given example.
It’s been
demonstrated that by choosing UK’s GDP as independent variable and the
country’s advertising expenditures as dependent one, a positive linear
relationship is established, and we have the formula to sustain that evidence:
Y= 1.2506 + 0.000004*x
This will be useful for future
predictions of UK’s advertising expenditures, in a faster way now just by
looking at the country’s GDP in the year needed.
ANEXES