Regression Analysis of Vehicle Market in 22 Countries

This project report carries the study of vehicle market in 22 countries. The data found classified on the basis of various variables like per capita income, vehicles per thousand population, population in millions, density population and percentage of population in urban areas.

B09406
Business Statistics and
Data Analysis

Table of Contents
INTRODUCTION...........................................................................................................................3
a) Scatter graphs of vehicles per thousand against income, population, population density and
% population urban areas.................................................................................................................4
b) Regression line for the vehicles per thousand population and per capita income.......................8
c) Scatter graphs of total vehicle ownership against population, population density per square km
and population in urban areas........................................................................................................10
d) Regression equation for variable more closely correlated to total vehicle ownership..............13
e) Comparison between two regression equations:......................................................................15
f) Estimated total number of vehicles and number of vehicles/1000 Turkey...............................15
CONCLUSION..............................................................................................................................16
REFERENCES..............................................................................................................................17

INTRODUCTION
This project report carries the study of vehicle market in 22 countries. The data found
classified on the basis of various variables like per capita income, vehicles per thousand
population, population in millions, density population and percentage of population in urban
areas. Two regression equations based on per capita income, vehicles per thousand,
population in millions and total vehicles ownership has been found. This equation has been
used to predict estimated total vehicles ownership and number of vehicles per thousand in
Turkey.

a) Scatter graphs of vehicles per thousand against income,
population, population density and % population urban areas
Vehicles per 1000 Vs Income
5 10 15 20 25 30 35 40 45
0
100
200
300
400
500
600
700
800
Scatter Graph
Denmark
Austria
Belgium
Switzerland
Czech Republic
Germany
Spain
Finland
Great Britain
Greece
Hungary
Ireland
Iceland
Italy
Luxembourg
Netherlands
Norway
Poland
Sweden
Per capita income
Vehicles per 1000 pop
Interpretation: In scatter graph; all countries dots sign are moving in same direction and
closely plotted, which shows close relationship or positive relationship. For instance, if
income of population rises than vehicle per 1000 population raise and decrease in income
simultaneously reduce the demand of vehicle per 1000 population.

Vehicles per 1000 Vs Population
0 100 200 300 400 500 600
0
100
200
300
400
500
600
700
800
Scatter Graph
Austria
Belgium
Switzerland
Czech Republic
Germany
Denmark
Spain
Finland
Great Britain
Greece
Hungary
Ireland
Iceland
Italy
Luxembourg
Netherlands
Norway
Poland
Sweden
Population (mill)
Vehicles per 1000 pop
Interpretation: The scatter graph shows plots are situated far from each other, and showing
independent relationship with each other. This indicates that there is no close relationship
between vehicle per thousand and population in millions.

Vehicles per 1000 Vs Population Density
55 60 65 70 75 80 85 90 95 100
0
100
200
300
400
500
600
700
800
Scatter Graph
Austria
Belgium
Switzerland
Czech Republic
Germany
Denmark
Spain
Finland
Great Britain
Greece
Hungary
Ireland
Iceland
Italy
Luxembourg
Netherlands
Norway
Poland
Sweden
Population Density/KM ^2
Vehicles per 1000 pop
Interpretation: The scatter graph shows plots are situated far from each other, and showing
independent relationship with each other. This indicates that there is no close relationship
between vehicle per thousand and population density per KM2 in millions (Julià, Comas and
Vives-Rego, 2000).

Vehicles per 1000 Vs %Population
5 10 15 20 25 30 35 40 45
0
100
200
300
400
500
600
700
800
Scatter Graph
Austria
Belgium
Switzerland
Czech Republic
Germany
Denmark
Spain
Finland
Great Britain
Greece
Hungary
Ireland
Iceland
Italy
Luxembourg
Netherlands
Norway
Poland
Sweden
%Population
Vehicles per 1000 pop
Interpretation: The scatter graph points are very far plotted which shows independent
relationship with each other. But some plotter are showing close to linear line but moving
opposite sides; this indicates that there is opposite relationship between vehicle per thousand
and percentage of population in urban areas. For instance, Increase in percentage of
population in urban areas very rarely impact vehicle per thousand population.
.

b) Regression line for the vehicles per thousand population and per
capita income
Regression line is the equation which builds relationship between independent variable
and dependent variable. In this case, from scatter plot diagram it was found that per
capita income and vehicles per thousand populations are closely related, hence it was
decided to form regression equation for these two variables (Goodman, 1959). Where
per capita income is independent variable and vehicles per thousand populations is
dependent on income variable. If per capita income rises than it is estimate that vehicles
per thousand populations will also increase. Below the regression line equation:
Y= a + bx
Where Y: Dependent variable (Vehicles per thousand populations)
And X : Independent variable (Per capita income)
The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the
line and a is the intercept (i.e., the value of Y when X = 0). This calculator will
determine the values of b and a for a set of data comprising two variables, and estimate
the value of Y for any specified value of X (Miller, 1994).
X Y X – Mx Y – My (X – Mx)2 (X – Mx)( Y – My)
26.3 629 2.71 110.55 7.3441 299.5905
24.7 520 1.11 1.55 1.2321 1.7205
27.7 559 4.11 40.55 16.8921 166.6605
13.6 390 -9.99 -128.45 99.8001 1283.216
23.5 586 -0.09 67.55 0.0081 -6.0795
25.9 430 2.31 -88.45 5.3361 -204.32
19.3 564 -4.29 45.55 18.4041 -195.41
24.3 488 0.71 -30.45 0.5041 -21.6195
23.7 576 0.11 57.55 0.0121 6.3305
23.6 515 0.01 -3.45 0.0001 -0.0345
16.1 422 -7.49 -96.45 56.1001 722.4105
12.3 306 -11.29 -212.45 127.4641 2398.561
29.8 472 6.21 -46.45 38.5641 -288.455
26.7 672 3.11 153.55 9.6721 477.5405
23.3 656 -0.29 137.55 0.0841 -39.8895
42.6 716 19.01 197.55 361.3801 3755.426

25.3 477 1.71 -41.45 2.9241 -70.8795
28.1 521 4.51 2.55 20.3401 11.5005
9.6 370 -13.99 -148.45 195.7201 2076.816
25.4 500 1.81 -18.45 3.2761 -33.3945
471.8 10369 965.058 10339.69
Calculation Summary
Sum of X = 471.8
Sum of Y = 10369
Mean X = 23.59
Mean Y = 518.45
Sum of squares (SSX) = 965.058
Sum of products (SP) = 10339.69
Regression Equation = ŷ = bX + a
b = SP/SSX = 10339.69/965.06 = 10.71406
a = MY - bMX = 518.45 - (10.71*23.59) = 265.70531
ŷ = 10.71406X + 265.70531

Interpretation: The result shows that there is positive relationship between both
variables, as per capita income increases; demand for vehicles per thousand populations
also increases. The regression line found is Y = 10.71X + 265.71; through this
regression equation results can be found simply by changing independent variable and
seeing effect on dependent variable Y (Kvanli, Pavur, and Guynes, 1999).
c) Scatter graphs of total vehicle ownership against population,
population density per square km and population in urban areas.
Total vehicle ownership Vs Population:
0 10 20 30 40 50 60 70 80 90
0
10
20
30
40
50
60
Scatter Graph
Denmark
Austria
Belgium
Switzerland
Czech Republic
Germany
Spain
Finland
Great Britain
Greece
Hungary
Ireland
Iceland
Italy
Luxembourg
Netherlands
Norway
Poland
Sweden
Population
Vehicle Ownersip

Interpretation: The scatter graph shows plots are situated far from each other, but
showing linear line. This indicates that there is there can be positive relationship
between vehicle owned and population in millions.
Total vehicle ownership Vs Population density:
55 60 65 70 75 80 85 90 95 100
0
10
20
30
40
50
60
Scatter Graph
Denmark
Austria
Belgium
Switzerland
Czech Republic
Germany
Spain
Finland
Great Britain
Greece
Hungary
Ireland
Iceland
Italy
Luxembourg
Netherlands
Norway
Poland
Sweden
Population density
Vehicle Ownersip
Interpretation: The scatter graph shows plots are situated far from each other, and
showing independent relationship with each other. This indicates that there is no close
relationship between vehicle owned and population density per KM2 in millions.

Total vehicle ownership Vs %Population in Urban areas:
55 60 65 70 75 80 85 90 95 100
0
10
20
30
40
50
60
Scatter Graph
Denmark
Austria
Belgium
Switzerland
Czech Republic
Germany
Spain
Finland
Great Britain
Greece
Hungary
Ireland
Iceland
Italy
Luxembourg
Netherlands
Norway
Poland
Sweden
% population urban
Vehicle Ownersip
Interpretation: The scatter graph points are very far plotted which shows independent
relationship with each other. But some plotter are showing close to linear line but
moving opposite sides; this indicates that there is opposite relationship between vehicle
owned and percentage of population in urban areas. For instance, Increase in percentage
of population in urban areas very rarely impact vehicle owned.

d) Regression equation for variable more closely correlated to total
vehicle ownership
The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the
line and a is the intercept (i.e., the value of Y when X = 0). This calculator will
determine the values of b and a for a set of data comprising two variables, and estimate
the value of Y for any specified value of X (Groebner, and et.Al., 2013).
Here; X = Population in millions and Y= Total vehicles ownership
X Y X – Mx Y – My (X – Mx)2 (X – Mx)( Y – My)
8 5.1 -14.035 -6.75 196.9812 94.7363
10 5.3 -12.035 -6.55 144.8412 78.8293
7 4 -15.035 -7.85 226.0512 118.0248
10 4 -12.035 -7.85 144.8412 94.4748
83 48.3 60.965 36.45 3716.7312 2222.1743
5 2.3 -17.035 -9.55 290.1912 162.6843
41 22.9 18.965 11.05 359.6712 209.5633
5 2.5 -17.035 -9.35 290.1912 159.2773
61 35.3 38.965 23.45 1518.2712 913.7293
59 30.6 36.965 18.75 1366.4112 693.0938
11 4.6 -11.035 -7.25 121.7712 80.0038
10 3 -12.035 -8.85 144.8412 106.5098
4 1.9 -18.035 -9.95 325.2612 179.4483
0.3 0.2 -21.735 -11.65 472.4102 253.2128
57 37.7 34.965 25.85 1222.5512 903.8453
0.4 0.3 -21.635 -11.55 468.0732 249.8843
16 7.7 -6.035 -4.15 36.4212 25.0453
5 2.4 -17.035 -9.45 290.1912 160.9808
39 14.4 16.965 2.55 287.8112 43.2608
9 4.5 -13.035 -7.35 169.9112 95.8073
440.
7 237 11793.425 6844.586
Calculation Summary
Sum of X = 440.7
Sum of Y = 237
Mean X = 22.035
Mean Y = 11.85

Sum of squares (SSX) = 11793.4255
Sum of products (SP) = 6844.585
Regression Equation = ŷ = bX + a
b = SP/SSX = 6844.59/11793.43 = 0.58037
a = MY - bMX = 11.85 - (0.58*22.04) = -0.93852
ŷ = 0.58037X - 0.93852
Interpretation: The result shows that there is negative relationship between both
variables, as population increases total vehicles ownership decreases and any decrease
in population increases the vehicle ownership. The regression line found is Y = 0.58X –
0.94; through this regression equation results can be found simply by changing
independent variable and seeing effect on dependent variable Y (Ott, 1994).

e) Comparison between two regression equations:
Among two regression equation; the equation which shows positive relationship was
found more useful for company because regression equation between total vehicle
ownership and population has no direct impact (Ruppert, 2011). For instance, it will be
not logical to say that due to increase in population people sold their vehicle. But the
negative effect shown on total vehicle ownership is due to the fact that any increase in
population will automatically reduce the proportion of vehicle ownership with
population. On the other hand; it will logical to say that with decrease in per capita
income vehicles per thousand population increases (Lind, Marchal and Wathen, 2006).
f) Estimated total number of vehicles and number of vehicles/1000
Turkey
Total Number of vehicles:
Taking equation 2; the total number of vehicles in Turkey is:
Y = 0.58X – 0.94
Y = 0.58(67) – 0.94
Y = 37.92 or 38 million
Vehicles per thousand:
Taking equation 1; vehicles per thousand in Turkey is:
Y = 10.71X + 265.71
Y = 10.71(6.1) + 265.71
Y = 331 approximate
Actual figures:
Total number of vehicles ownership = 6.4 million
Number of vehicles per 1000 = 96 per thousand populations

Reason for difference in prediction:
The main reason behind difference in prediction is limitation of regression equation; as
this method is very useful tool of prediction but it has certain limitations like accuracy
of data, avoiding other factors and based on past data (Webster, 1992).
Regression equation calculated above covers prediction of 22 countries together; hence
it cannot be applied for single country because there is no perfect correlation between
variables (Meyer and Meyer, 1975). Therefore the chance of variance in the result of
single country prediction through 22 countries regression model is more. This is the
main reason behind difference in the actual outcome and prediction result of Turkey
(Evans, Olson and Olson, 2007).
CONCLUSION
After doing whole analyses, it can be concluded that no regression equation shows perfect
result; various other factors also impact the outcome of this model with actual result.
Therefore it is suggested that company should do deep market research, past trend analysis,
gather information related with economic and government policies, risk factors, etc. On the
basis of evaluation of external factors and regression equation best fitted decision should be
implemented.

REFERENCES
Books and Journals
Evans, J.R., Olson, D.L. and Olson, D.L., 2007. Statistics, data analysis, and decision
modeling. Pearson/Prentice Hall.
Goodman, L.A., 1959. Some alternatives to ecological correlation. American Journal of
Sociology, 64(6), pp.610-625.
Groebner, D.F., Shannon, P.W., Fry, P.C. and Smith, K.D., 2013. Business statistics.
Pearson Education UK.
Julià, O., Comas, J. and Vives-Rego, J., 2000. Second-order functions are the simplest
correlations between flow cytometric light scatter and bacterial diameter. Journal of
microbiological methods, 40(1), pp.57-61.
Kvanli, A.H., Pavur, R.J. and Guynes, C.S., 1999. Introduction to business statistics: a
computer integrated, data analysis approach. Dryden Press.
Lind, D.A., Marchal, W.G. and Wathen, S.A., 2006. Basic statistics for business &
economics. Boston: McGraw-Hill/Irwin,.
Meyer, S.L. and Meyer, S.L., 1975. Data analysis for scientists and engineers (p. 513). New
York: Wiley.
Miller, R.B., 1994. Statistics for business: Data analysis and modeling. Duxbury Press.
Ott, W.R., 1994. Environmental statistics and data analysis. CRC Press.
Ruppert, D., 2011. Statistics and data analysis for financial engineering (Vol. 13). New
York: Springer.
Webster, A., 1992. Applied statistics for business and economics. Homewood, IL: Irwin.