Statistics for Decision Making

This paper discusses results of a customer segment analysis of the luxury cars BMW, Mercedes and Lexus on behalf of the Automobile Association to aid businesses in their business plans. Factors such as age, annual income and education were taken to be factors of interest in the profiling of customers.

Running head: STATISTICS FOR DECISION MAKING
Statistics for Decision Making
Name of Student
Name of University
Author Note

2STATISTICS FOR DECISION MAKING
Executive Summary
Demand for a particular good may depend on a number of factors. Statistical analysis aids to
study the available purchase data and customer attributes to identify market segments to better
the marketing strategy so that the profits, sales, production and promotion can be customized to
attain target outcomes. This paper discusses results of a customer segment analysis of the luxury
cars BMW, Mercedes and Lexus on behalf of the Automobile Association to aid businesses in
their business plans. Factors such as age, annual income and education were taken to be factors
of interest in the profiling of customers. Descriptive and inferential statistics were used for the
purposes. It was seen that customers had significant differences in terms of car preference with
respect to age, income and education. Older people, people with higher income and with higher
education were seen to prefer Mercedes more than BMW. Furthermore it was seen that as age
increased the odds of the customer to own a Mercedes was greater than the odds of owning a
Lexus or BMW.

3STATISTICS FOR DECISION MAKING
Table of Contents
1. Introduction..................................................................................................................................4
1.1 Business Problem...................................................................................................................4
1.2 Statistical Problem.................................................................................................................4
2. Analysis.......................................................................................................................................5
2.1 Car Ownership on the basis different age groups..................................................................5
2.2 Analysis based on different income groups.........................................................................11
2.3 Output based on various education years............................................................................16
2.4 Hypothesis testing 4.............................................................................................................22
The ANOVA method for comparisons of mean was employed to test the validity of the
hypotheses. The assumed level of significance was 0.05. The p-value of the test was found to
be less than 0.0001 and hence the test was found to be statistically significant, that is the null
was rejected at 5% level of significance. Thus it was concluded that there exists significant
difference among the car owner groups in terms of age............................................................23
2.5 Hypothesis testing 5.............................................................................................................23
2.6 Hypothesis testing 6.............................................................................................................24
2.7 Hypothesis testing 7.............................................................................................................25
3.0 Conclusion and Recommendation...........................................................................................26

4STATISTICS FOR DECISION MAKING
1. Introduction
1.1 Business Problem
This paper is a report on an analysis of the sales of the three car types, namely, BMW,
Lexus and Mercedes. It seeks to identify and segment households into preference or customer
groups for the cars. The analysis was done with respect to the different ages, incomes and
educational qualification of the members of the household. The demand for the cars among the
households are analyzed in terms of these variables. Therefore the aim of this paper is to resolve
what traits to look at in terms of age of the members, economic condition and educational
qualification in a household or a customer to discern their chances of buying either BMW, Lexus
or Mercedes. The problem is thus of market segmentation for the cars. The profiles of customers
who may prefer a BMW or Lexus or Mercedes is required to be defined to help the Automobile
Association and hence the automobile businesses to narrow down business strategies.
1.2 Statistical Problem
The problem here can be approach using a data driven statistical approach, more
specifically using inferential techniques of statistics involving testing of hypothesis. The
techniques of linear models and binary regression also is found to be relevant to the statistical
problem in ways described hence. Data from 420 households including age of members, annual
income and number of years of education as well as the model of car owned were used. The data
is first summarized and explored using descriptive statistical methods. To study the variables
representing the attributes of customers on the basis of which car model preference profiles are
defined, probability distributions of age, income and number of years of education are studied for
each specific car model type owned. The location, spread and shape of these distributions were
then looked at to identify the differences and similarities. The objective behind this is to be able

5STATISTICS FOR DECISION MAKING
to discern whether buyers of a specific car type differ by income, age or educational qualification
or not. Following this, techniques of hypothesis testing are carried out to determine whether the
car buyer groups have statistically significant differences among each other on the basis of age,
income and education or not. Another research question addressed is whether there exists a bias
among older people to prefer Mercedes over BMW or Lexus or not.
2. Analysis
2.1 Car Ownership on the basis different age groups
Table 1: Ages of buyers of luxury car models
Count of Age (Years)
Column
Labels
Row Labels 1 2 3 Grand Total
35-44 56.86% 19.61% 23.53% 100.00%
45-54 29.73% 36.94% 33.33% 100.00%
55-64 6.67% 37.78% 55.56% 100.00%
65-74 0.00% 66.67% 33.33% 100.00%
Grand Total
30.95% 33.33% 35.71% 100.00%
35-44 45-54 55-64 65-74
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
56.86%
29.73%
6.67% 0.00%
19.61%
36.94%
37.78%
66.67%
23.53% 33.33%
55.56%
33.33%
Car Type ownership by age
3
2
1

6STATISTICS FOR DECISION MAKING
Figure 1: Ages of buyers of different luxury cars
The ages divided into four age groups, ranging from 35 as minimum age to 70 as
maximum age are considered with each group interval having length of 10 years each. 56.83% of
the owners in age group 33 to 44 years were found to be BMW owners. 29.73% of the owners in
the age group 45 to 54 years were found to be BMW owners, 6.67% were in the age group 55 to
64 years were found to have BMW and no BMW owners were found to be in the age group
above 65 years. 19.61 % of the owners in the age group 35 to 44 years, 36.94 % in the age group
45 to 54 years, 37.78% in the age group 55 to 64 years and 66.67% in the age group above 65
years were found to own Lexus model cars. 23.53% of owners aged between 35 to 44 years
owned Mercedes, 33.33% aged between 45 to 54 years were found to own Mercedes and 55.56%
were in age group 55 to 64 years. 33.33% of owner in age group above 65 years owned
Mercedes. Therefore owners in age group 65 to 74 primarily owned Lexus followed by
Mercedes. Those in age group 55 to 64 years mostly owned Mercedes followed by Lexus. The
owners aged 35 to 44 years owned mostly BMW followed by Mercedes and then Lexus.
Table 2: Descriptive Statistics for ages with preference for BMW
Age ( in Years) (BMW)
Mean 45.2153
8
Standard Error 0.38190
8
Median 45
Mode 46
Standard
Deviation
4.35442
3
Sample Variance 18.961
Kurtosis 0.04742
Skewness 0.50865
5
Range 21

7STATISTICS FOR DECISION MAKING
Minimum 36
Maximum 57
Sum 5878
Count 130
36-39 40-43 44-47 48-51 52-55 56-59
0
5
10
15
20
25
30
35
40
45
50
BMW
Figure 2: Age distribution of BMW
A total of 130 people were seen to be owners of BMW model. The mean age of a
household for this model ownership group is 45. The median age of this customer segment group
is 45. The mode value of the age in years of BMW owners was found to be 46 implying that
most of the people in owning BMW is in aged 46. The range of ages of BMW owners lie
between 36 and 57. The variance measured by the standard deviation is 4.35. Since the standard
deviation is found to be lesser than the mean age, this indicates that the age distribution is not as
consistent for the group of people who own BMW. The measure of shape or Skewness being
0.51 was thus indicated to be close to normal shape. The distribution has slight positive value
which implies some degree of positive skewness.
Table 3: Descriptive Statistics for ages with preference for Lexus
Age (in Years) (Lexus)

8STATISTICS FOR DECISION MAKING
Mean 50.4571
4
Standard Error 0.51547
2
Median 50
Mode 55
Standard
Deviation
6.09914
7
Sample Variance 37.1995
9
Kurtosis 0.61121
4
Skewness 0.36026
2
Range 32
Minimum 36
Maximum 68
Sum 7064
Count 140
36-40 41-45 46-50 51-55 56-60 61-65 66-70
0
5
10
15
20
25
30
35
40
45
50
Lexus
Figure 3: Age distribution of Lexus
A total of 140 people were seen to be owners of Lexus model. The mean age of a household for
this model ownership group 50.45. The median age of this customer segment group is 50. The
mode value of the age in years of Lexus owners was found to be 50 implying that most of the

9STATISTICS FOR DECISION MAKING
people in owning Lexus is in aged 50. The range of ages of Lexus owners lie between 36 and 68.
The variance measured by the standard deviation is 6.099. Since the standard deviation is found
to be lesser than the mean age, this indicates that the age distribution is not as volatile for the
group of people who own Lexus. The measure of shape or Skewness being 0.360. The
distribution has slight positive value which implies some degree of positive skewness.
Table 4: Descriptive Statistics for ages with preference for Mercedes
Age (Years)(Merceded)
Mean 51.9866
7
Standard Error 0.55037
Median 53
Mode 53
Standard
Deviation
6.74062
8
Sample Variance 45.4360
6
Kurtosis -0.0195
Skewness -0.02894
Range 35
Minimum 35
Maximum 70
Sum 7798
Count 150

10STATISTICS FOR DECISION MAKING
35-39 40-44 45-49 50-54 55-59 60-64 65-70
0
10
20
30
40
50
60
Mercedes
Figure 4: Age distribution of Mercedes
A total of 150 people were seen to be owners of Mercedes model. The mean age of a
household for this model ownership group is 51.98. The median age of this customer segment
group is 53. The mode value of the age in years of Mercedes owners was found to be 53
implying that most of the people in owning Mercedes is in aged 53. The range of ages of BMW
owners lie between 35 and 70. The variance measured by the standard deviation is 6.74. Since
the standard deviation is found to be lesser than the mean age, this indicates that the age
distribution is not volatile for the group of people who own BMW. The measure of shape or
Skewness being -0.02 was thus indicated to be close to normal shape. The distribution has slight
negatibve value which implies some degree of negative skewness.
2.2 Analysis based on different income groups
Table 5: Income of buyers of different luxury cars
Count of Type of
Car Column Labels
Annual Income BMW Lexus
Mercede
s
Grand
Total
46068-121067 62.16% 27.03 10.81% 100.00%

11STATISTICS FOR DECISION MAKING
%
121068-196067 28.78%
39.57
% 31.65% 100.00%
196068-271067 6.45%
16.13
% 77.42% 100.00%
271068-346067 0.00% 0.00% 100.00% 100.00%
Grand Total 30.95%
33.33
% 35.71% 100.00%
46068-121067 121068-196067 196068-271067 271068-346067
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
62.16%
28.78%
6.45% 0.00%
27.03%
39.57%
16.13%
0.00%
10.81%
31.65%
77.42%
100.00%
Income and Car Type
3
2
1
Figure 5: Income of buyers of different luxury cars
The 420 sampled households were then divided on the basis of their annual income in to 4
groups, namely, the first interval, that is, group 1 had income between $46068 and $121067.The
next interval, say group 2 had income between $121068 and $196067, the following group 2 had
income between $196068 and $271067. The group 4 had income between $27168 and $346067
in a year. 62.16% of the people in income group 1 owned a BMW, 27.03% of those in income
group 1 owned a Lexus, and 10.81 % in the income group 1 had a Mercedes. 28.78% of the
people in group 2 had a BMW, 39.57% of those I income group 2 had a Lexus and 31.65% of

12STATISTICS FOR DECISION MAKING
those in group 2 had a Mercedes. 6.45% of the people in group 3 had a BMW whereas 16.13%
owned a Lexus and 77.42% had a Mercedes. 0% of the people in income group 4 had any BMW
or Lexus. It was seen that all 100% of the people with income between $271068 and
$346067owned a Mercedes. Therefor it is seen that higher income groups are most likely to own
a Mercedes whereas BMW is more common among the relatively lower income groups.
Table 6: Descriptive Statistics for income group preferring BMW
Annual Income ($)(BMW)
Mean 139271.3
Standard Error 2907.846
Median 138512
Mode 109568
Standard
Deviation
33154.54
Sample Variance 1.1E+09
Kurtosis -0.22439
Skewness -0.03855
Range 170652
Minimum 46068
Maximum 216720
Sum 1810527
4
Count 130

13STATISTICS FOR DECISION MAKING
46068-76067 76068-106067 106068-
136067 136068-
166067 166068-
196067 196068-
226067
0
5
10
15
20
25
30
35
40
45
50
BMW
Figure 6: Income distribution for BMW
The mean annual income of people owning BMW cars was found to be 139271 dollars. The
median income was found to be 138512 dollars implying that exactly 50% of the people in this
group had an annual income equal to 138512 dollar. The range of the annual income of the
people owning a BMW was found to be 170652 dollars with minimum being 46068 dollars and
maximum being 216720 dollars. The variation in the data measured by the standard deviation of
income distribution of this group is 33154.54. As standard deviation is less than mean, therefore
the coefficient of variation would be less than 100 and this implies that the income distribution
has smaller variation than that of the distribution of the other attribute variable of age. The shape
of the distribution as measured using the skewness measure was found to have the value -0.0385
which indicates a slight negative skewness in the distribution.
Table 7: Descriptive Statistics for income group preferring Lexus
Annual Income ($) (2)
Mean 154186.9
Standard Error 2556.425
Median 154492

14STATISTICS FOR DECISION MAKING
Mode 179617
Standard
Deviation
30248.02
Sample Variance 9.15E+08
Kurtosis 0.963641
Skewness 0.693685
Range 152065
Minimum 96069
Maximum 248134
Sum 2158616
0
Count 140
96069-126068 126069-156068 156069-186068 186069-216068 216069-246068 246069-276068
0
10
20
30
40
50
60
Lexus
Figure 7: Income Distribution of Lexus
The mean annual income of people owning Lexus cars was found to be 154186 dollars. The
median income was found to be 154492 dollars implying that exactly 50% of the people in this
group had at least an annual income equal to 154492 dollar. The range of the annual income of
the people owning a Lexus was found to be 152065 dollars with minimum being 96069 dollars
and maximum being 248134 dollars. The variation in the data measured by the standard
deviation of income distribution of this group is 30248.02. As standard deviation is less than
mean, therefore the coefficient of variation would be less than 100 and this implies that the

15STATISTICS FOR DECISION MAKING
income distribution has smaller variation than that of the distribution of the other attribute
variable of age. The shape of the distribution as measured using the skewness measure was found
to have the value 0.693 which indicates strong positive skewness in the distribution.
Table 8: Descriptive Statistics for income group preferring Mercedes
Annual Income ($)
(Mercedes)
Mean 184423.9
Standard Error 3845.333
Median 186070
Mode 161590
Standard
Deviation
47095.52
Sample Variance 2.22E+09
Kurtosis 0.987178
Skewness 0.273966
Range 284882
Minimum 49941
Maximum 334823
Sum 2766359
2
Count 150
49941-109940 109941-169940 169941-229940 229941-289940 289941-349940
0
20
40
60
80
100
120
140
Mercedes

16STATISTICS FOR DECISION MAKING
Figure 8: Income Distribution of Mercedes
The mean annual income of people owning Mercedes cars was found to be 184423.9 dollars. The
median income was found to be 186070 dollars implying that exactly 50% of the people in this
group had at least an annual income equal to 186070 dollar. The range of the annual income of
the people owning a Lexus was found to be 284882 dollars with minimum being 49941 dollars
and maximum being 334823 dollars. The variation in the data measured by the standard
deviation of income distribution of this group is 47095.52. As standard deviation is less than
mean, therefore the coefficient of variation would be less than 100 and this implies that the
income distribution has smaller variation than that of the distribution of the other attribute
variable of age. The shape of the distribution as measured using the skewness measure was found
to have the value 0.273 which indicates moderate positive skewness in the distribution.
2.3 Output based on various education years
Table 9: Income of buyers of different luxury cars
Count of Type of
Car Column Labels
Row Labels 1 2 3
Grand
Total
11-13 25.00%
70.83
% 4.17% 100.00%
14-16 42.31%
33.33
%
24.36
% 100.00%
17-19 27.37%
23.16
%
49.47
% 100.00%
20-22 0.00%
38.46
%
61.54
% 100.00%
Grand Total 30.95%
33.33
%
35.71
% 100.00%

17STATISTICS FOR DECISION MAKING
11-13 14-16 17-19 20-22
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
25.00%
42.31%
27.37%
0.00%
70.83% 33.33%
23.16%
38.46%
4.17%
24.36%
49.47%
61.54%
Car Type and Education in Years
3
2
1
Figure 9: Education years of buyers of different luxury cars
The households were then divided into four education years intervals, viz. , group 1 with
years of education between 11 and 13, group 2 with education between 14 to 16 years, group 3
with years between 17 and 19 years and group 4 with years of education between 20 and 22
years. 25% of the households in group 1 were seen to have a BMW, 70.83% had a Lexus and
4.17% had a Mercedes. 42.31% of those in group 2 are owners of BMW car model, 33.33%
owned a Lexus and 24.36% owned a Mercedes. 27.37% of those in group 3 owned a BMW,
23.16% owned a Lexus and 49.47% owned Mercedes. 61.54% of the household in group 4
owned a Mercedes, 38.46% owned a Lexus but none owned a BMW.
Table 10: Descriptive Statistics for education years showing preference for BMW
Education (Years) (1)
Mean 15.8307
7
Standard Error 0.16092
3
Median 16

18STATISTICS FOR DECISION MAKING
Mode 16
Standard
Deviation
1.83479
9
Sample Variance 3.36648
8
Kurtosis -0.17288
Skewness -0.4345
Range 8
Minimum 11
Maximum 19
Sum 2058
Count 130
11 13 14 15 16 17 18 19
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
BMW
Figure 10: Distribution of education years for BMW
It is seen that the mean of the number of education years of those households that have a
BMW is 15.83 or approximately 16 or at least 15. The median of the distribution for BMW
owners was found to be 16, that is, 50% of the households have at least 16 years of education.
The mode of the distribution for BMW was also 16 that is majority of the households that own a
BMW have 16 years of education. The maximum number of years of education was found to be
19 years and the minimum number of years of education among those owning a BMW was 11.
The range was thus found to be 8. The variability in the data as measured using the standard

19STATISTICS FOR DECISION MAKING
deviation was found to be 1.834. Since the standard deviation is lower than the mean, the
coefficient of variation is indicated to be less than 0 and hence the estimate is considered to have
low volatility. Again, the skewness is -0.43 indicating a low skewness or in other words a
distribution which is close to symmetric normal shape.
Table 11: Descriptive Statistics for education years showing preference for Lexus
Education (Years) (2)
Mean 15.8
Standard Error
0.20406959
3
Median 16
Mode 16
Standard
Deviation
2.41458398
6
Sample Variance
5.83021582
7
Kurtosis
-
0.97728269
8
Skewness
0.16971991
8
Range 9
Minimum 12
Maximum 21
Sum 2212
Count 140

20STATISTICS FOR DECISION MAKING
12 13 14 15 16 17 18 19 20 21
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
Lexus
Figure 11: Distribution of education years for Lexus
A total of 140 people were seen to be owners of Lexus model. The mean age of a household for
this model ownership group is 15.8. The median age of this customer segment group is 16. The
mode value of the age in years of Lexus owners was found to be 16 implying that most of the
people in owning Lexus is in aged 16. The range of ages of Lexus owners is 9 where the values
lie between 12 and 21. The variance measured by the standard deviation is 5.830. Since the
standard deviation is found to be lesser than the mean age, this indicates that the age distribution
is not as consistent for the group of people who own Lexus. The measure of shape or Skewness
being 0.169 was thus indicated to be close to normal shape. The distribution has slight positive
value which implies some degree of positive skewness.
Table 12: Descriptive Statistics for education years showing preference for Mercedes
Education (Years) (3)
Mean 17.29333
Standard Error 0.142067
Median 17
Mode 17
Standard Deviation 1.739963

21STATISTICS FOR DECISION MAKING
Sample Variance 3.027472
Kurtosis 0.039633
Skewness 0.081676
Range 9
Minimum 13
Maximum 22
Sum 2594
Count 150
13 14 15 16 17 18 19 20 21 22
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
Mercedes
Figure 12: Distribution of education years for BMW users
A total of 150 people were seen to be owners of Mercedes model. The mean age of a household
for this model ownership group is 17.293. The median age of this customer segment group is 17.
The mode value of the age in years of Mercedes owners was found to be 17 implying that most
of the people in owning Mercedes is in aged 17. The range of ages of Mercedes owners is 9
where the values lie between 13 and 22. The variance measured by the standard deviation is
1.739. Since the standard deviation is found to be lesser than the mean age, this indicates that the
coefficient of variation is less than 0 and that means that the estimate of mean is consistent for
the age distribution for people who own Mercedes. The measure of shape or Skewness being

22STATISTICS FOR DECISION MAKING
0.0816 was thus indicated to be close to normal shape. The distribution has slight positive value
which implies some degree of positive skewness.
2.4 Hypothesis testing 4
It is of then interest to check whether there is any statistically significant difference
between the ages of the owners of the three car model types, namely BMW, Lexus and
Mercedes..
Null Hypothesis: mean age of BMW owners= mean age of Lexus owners = mean age of
Mercedes owners.
Alternative Hypothesis: At least one inequality exists in the equation specified in the null.
Table 13: Hypothesis testing for average ages of three different group of buyers
SUMMARY
Groups Count Sum Average Variance
BMW 1 130 5878 45.21538 18.961
LEXUS 2 140 7064 50.45714 37.19959
MERCEDE
S 3
150 7798 51.98667 45.43606
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 3436.362 2 1718.181 49.80171 4.02787E-20 3.017357
Within Groups 14386.69 417 34.50044
Total 17823.05 419

23STATISTICS FOR DECISION MAKING
The ANOVA method for comparisons of mean was employed to test the validity of the
hypotheses. The assumed level of significance was 0.05. The p-value of the test was found to be
less than 0.0001 and hence the test was found to be statistically significant, that is the null was
rejected at 5% level of significance. Thus it was concluded that there exists significant difference
among the car owner groups in terms of age.
2.5 Hypothesis testing 5
It is of then interest to check whether there is any statistically significant difference in the
annual income levels of the owners of the three car model types, namely BMW, Lexus and
Mercedes.
Null Hypothesis: mean annual income of BMW owners= mean annual income of Lexus owners
= mean annual income of Mercedes owners.
Alternative Hypothesis: At least one inequality exists in the equation specified in the null.
Table 14: Hypothesis testing for average income of three different group of buyers
SUMMARY
Groups Count Sum Average Variance
1 130 18105274 139271.3 1.1E+09
2 140 21586160 154186.9 9.15E+08
3 150 27663592 184423.9 2.22E+09
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 1.5E+11 2 7.5E+10 52.1761 5.98E-21 3.017357
Within Groups 5.99E+11
41
7 1.44E+09
Total 7.49E+11
41
9
The ANOVA method for comparisons of mean was employed to test the validity of the
hypotheses. The assumed level of significance was 0.05. The p-value of the test was found to be

24STATISTICS FOR DECISION MAKING
less than 0.0001 and hence the test was found to be statistically significant, that is the null was
rejected at 5% level of significance. Thus it was concluded that there exists significant difference
among the car owner groups in terms of annual income.
2.6 Hypothesis testing 6
Null Hypothesis: mean years of education of BMW owners= mean years of education of Lexus
owners = mean years of education of Mercedes owners.
Alternative Hypothesis: At least one inequality exists in the equation specified in the null.
Table 15: Hypothesis testing for years of education of three different group of buyers
SUMMARY
Groups Count Sum Average Variance
1 130 2058 15.83077 3.366488
2 140 2212 15.8 5.830216
3 150 2594 17.29333 3.027472
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 210.8583 2 105.4292 25.92566 2.44085E-11 3.017357
Within Groups 1695.77 417 4.066595
Total 1906.629 419
The ANOVA method for comparisons of mean was employed to test the validity of the
hypotheses. The assumed level of significance was 0.05. The p-value of the test was found to be
less than 0.0001 and hence the test was found to be statistically significant, that is the null was
rejected at 5% level of significance. Thus it was concluded that there exists significant difference
among the car owner groups in terms of years of education.

25STATISTICS FOR DECISION MAKING
2.7 Hypothesis testing 7
Finally, it is of interest to check whether people who are in older age groups tend to buy
Mercedes more than BMW or Lexus. To address this problem the car type is re-coded as 0 when
the car type is either Lexus or BMW and 1 when it is Mercedes. Then the relationship between
the age and car type is analysed using logistic regression. The results of the logistic regression is
given in the following table:
Variable Categorie
s
Frequencies %
Car 0 270 64.286
1 150 35.714
The above table depicts the frequency of the incidence of Mercedes and a car being not
Mercedes as per the re-coded data.
The fitted model parameters of the logistic regression is specified in the following table. The
table shows the results of the regression analysis:
Model parameters (Variable Cars)
Source Value Standard error Wald Chi-Square Pr > Chi² Odds ratio
Intercept -5.647 0.881 41.037 < 0.0001
Age
(Years)
0.101 0.017 33.942 < 0.0001 1.107
The level of significance was assumed to be 0.05. It is seen that the covariates age (in
years), annual income and education (in years) are all significant at 0.05 since they have p-values
less than 0.0001. The effect are all positive with odd ratio of age being 1.107. This means that
with 0.101 unit increase in age in years the chance of car being Mercedes is 1.107 times as likely
that of others.

26STATISTICS FOR DECISION MAKING
The goodness of fit of the fitted model was checked for using the Hosmer
Lemeshow test for goodness of fit. The p-value was found to be 0.058 which is greater than 0.05
and hence the model had moderately good fit.
Statistic Chi-square DF Pr > Chi²
Hosmer-Lemeshow Statistic 13.657 7 0.058
The age in years variable has effect size of 0.357 and testing for the validity of the
results, it was seen that p-value for Wald’s test is less than 0.05b and hence significant indicating
that the model constructed using the variable being considered as indeed significant is a good
model.
Test of the null hypothesis H0: Y=0.357 (Variable Car)
Statistic DF Chi-square Pr > Chi²
-2 Log(Likelihood) 1 38.208 < 0.0001
Score 1 37.333 < 0.0001
Wald 1 33.942 < 0.0001
Equation of the model (Variable Car):
Pred(Car) = 1 / (1 + exp(-(-5.64688902487644+0.101415874522654*Age (Years))))
3. Conclusion and Recommendation
The analysis showed that people who had higher age were more likely to have a Mercedes rather
than a Lexus or a BMW. Customers with higher annual incomes were seen to have and prefer
mostly Mercedes cars rather than BMW cars.Again, higher education years were seen to
correspond to owning Mercedes cars rather than BMW or Lexus.

27STATISTICS FOR DECISION MAKING
Therefore, it is recommended that the businesses focus toward s aiming their promotional
efforts for Mercedes towards older and higher paid customers or higher paid and highly educated
customer whereas target the comparatively younger customers or those with annual income less
than about 22,000 USD with BMW or less than 50,000 USD with Lexus.