Statistics for Decision Making

The report analyzes the business problem related to designing marketing strategy of different luxury cars. The three chosen car models are BMW, Lexus and Mercedes. Along with choice of cars, customers’ profiles are considered in terms of age, income and education years.

Running Head: STATISTICS FOR DECISION MAKING
Statistics for Decision Making
Name of the Student
Name of the University
Course ID

1STATISTICS FOR DECISION MAKING
Executive Summary
In general, there are different factors that influence demand of a particular good. When it comes
to luxury cars, the choice of specific cars depends on specific taste and preferences of customers.
Despite having almost same price with same features choices differ based on preferences. Sellers
often face problems in determining particular targeted group of buyers for a particular model.
The report analyzes the business problem related to designing marketing strategy of different
luxury cars. The three chosen car models are BMW, Lexus and Mercedes. Along with choice of
cars, customers’ profiles are considered in terms of age, income and education years. Total 420
people are surveyed to have an idea regarding choices of three different models. In the sample
surveyed maximum number of people prefer Mercedes followed by Lexus and BMW. In case of
BMW buyers are relatively younger with a relatively lower income and lesser education years.
Buyers of Mercedes are mostly older people with a relatively higher income and higher
education years. The business problem is again analyzed in reference statistical problem like
finding out the location, shape and variability of the distribution of age, income and years of
education. The distribution of three different variables differs for the three different car models.
The average age for buyers of BMW cars is 45 years while that for Lexus and Mercedes are 50
and 52 years respectively. Buyers of BMW, Lexus and Mercedes have a respective income of
139271 dollars, 154186 dollars and 184423 dollars. The average education years for BMW,
Lexus and Mercedes car are almost same and is equal to 16 years. Average age, income and
education years differs significantly among the three chosen group of buyers. The regression
model confirms that older with having a higher income and higher education years prefers
Mercedes to BMW or Lexus.

2STATISTICS FOR DECISION MAKING

3STATISTICS FOR DECISION MAKING
Table of Contents
1. Introduction..................................................................................................................................3
1.1 Business Problem...................................................................................................................3
1.2 Statistical Problem.................................................................................................................3
2. Analysis.......................................................................................................................................4
2.1 Output based on different age groups....................................................................................4
2.2 Analysis based on different income groups...........................................................................9
2.3 Output based on various education years............................................................................14
2.4 Hypothesis testing 4.............................................................................................................19
2.5 Hypothesis testing 5.............................................................................................................20
2.6 Hypothesis testing 6.............................................................................................................21
2.7 Hypothesis testing 7.............................................................................................................22
3. Conclusion and Recommendation.............................................................................................24

4STATISTICS FOR DECISION MAKING
1. Introduction
1.1 Business Problem
The Automobile Association attempts to analyze demand for different luxury cars.
Demand are analyzed among households having different ages, incomes and education years.
The business aims to find out preferences for BMW, Lexus and Mercedes among different
households. The business problem is to understand how age, income and education years’
influence the purchasing decision of different luxury cars. More specifically, the objective is to
analyze preference of buyers for the three different car models based on their age, income and
education. The information regarding customers’ profile of specific car model is helpful for
Automobile businesses to determine specific strategy.
1.2 Statistical Problem
The business problem is to be evaluated in light of statistical knowledge and
interpretation. In order to determine specific form of distribution for age, income and education
years including location and shape of the distribution various measures of central tendency and
dispersions have been used. The association is willing to know whether buyers if BMW, Lexus
and Mercedes have different average ages, average income and average education years.
Hypothesis testing is done to find out whether average age, income and education years differ
significantly among three different group of buyers. Logistic regression is conducted to test the
claim that older people with higher income and higher education mostly prefer Mercedes over
BMW and Lexus.

5STATISTICS FOR DECISION MAKING
2. Analysis
2.1 Output based on different age groups
Table 1: Ages of buyers of different luxury cars
Count of Age
(Years) Column Labels
Row Labels 1 2 3
Grand
Total
35-39 6 6 4 16
40-44 52 14 20 86
45-49 52 46 26 124
50-54 14 36 48 98
55-59 6 28 34 68
60-64 6 16 22
65-70 4 2 6
Grand Total 130
14
0
15
0 420
35-39 40-44 45-49 50-54 55-59 60-64 65-70
0
10
20
30
40
50
60
1
2
3
Figure 1: Ages of buyers of different luxury cars
The ages are divided into seven groups ranging between 35 and 70. For the age groups 35-39,
there are 6 people preferring BMW, 6 people preferring Lexis and 4 people preferring Mercedes.
In the age group 40-44, maximum number of people prefer BMW followed by Mercedes and

6STATISTICS FOR DECISION MAKING
Lexus. In the age group 45-49, most people prefers BMW followed by Lexus and Mercedes. As
the age increases preference for Mercedes increases. In the age group 50-54, there are 48 people
preferring Mercedes. In the age group 55-59, there are 34 people preferring Mercedes. In the two
higher age group 60-64 and 65-70 there are no people who prefer Mercedes.
Table 2: Descriptive Statistics for ages with preference for BMW
Age (Years) (1)
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
Minimum 36
Maximum 57
Sum 5878
Count 130

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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
There are total 130 people showing their preference for BMW cars. The average age for this age
group is 45. The median age in this group is 45. The mode value is 46 meaning most people in
this age group is aged 46. People in this age group lies in the age between 36 and 57. The
standard deviation for this group is 4.35. The standard deviation being less than mean indicates
the age distribution is less volatile for group of people preferring BMW. The value of Skewness
is 0.51. The positive value of skewness implies that the distribution of age in this group is
positively skewed.
Table 3: Descriptive Statistics for ages with preference for Lexus
Age (Years) (2)
Mean
50.4571
4
Standard Error
0.51547
2
Median 50
Mode 55
Standard 6.09914

8STATISTICS FOR DECISION MAKING
Deviation 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
There are total 140 people showing their preference for Lexus cars. The average age for this age
group is 50. The median age in this group is 50. The mode value is 55 meaning most people in
this age group is aged 55. People in this age group lies in the age between 32 and 36. The
standard deviation for this group is 6.09. The standard deviation being less than mean indicates
the age distribution is less volatile for group of people preferring Lexus. The value of Skewness
is 0.36. The distribution is almost symmetric.

9STATISTICS FOR DECISION MAKING

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Table 4: Descriptive Statistics for ages with preference for Mercedes
Age (Years)(3)
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
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

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Among the people surveyed by the association, most people preferred Mercedes with
total number of people being 150. The average age for this age group is 52. The median and
modal age in this group is 53. The value of Skewness almost equals zero meaning the
distribution is symmetric. People in this group has maximum age of 70 and minimum age of 35.
The standard deviation for this is 6.74. The standard deviation being less than mean indicates the
age distribution is less volatile for group of people showing preference for Mercedes.
2.2 Analysis based on different income groups
Table 5: Income of buyers of different luxury cars
Count of Annual
Income ($) Column Labels
Row Labels 1 2 3
Grand
Total
46068-96067 10 4 14
96068-146067 62 58 30 150
146068-196067 54 72 62 188
196068-246067 4 8 44 56
246068-296067 2 8 10
296068-346067 2 2
Grand Total 130
14
0
15
0 420

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46068-
96067 96068-
146067 146068-
196067 196068-
246067 246068-
296067 296068-
346067
0
10
20
30
40
50
60
70
80
1
2
3
Figure 5: Income of buyers of different luxury cars
420 sample households are divided into six classes depending on their income. In the lowest
income group ranging between 46068 and 96067, no people refer Lexus. Among the 14 people
in this income group, 10 people prefer BMW and only 4 people prefers Mercedes. In the second
income group ranging from 96068 to 146067, most people prefer BMW followed by Lexus and
Mercedes. As income increases, preference for BMW decreases while that for Lexus and
Mercedes uses. In the highest income group (296068-346067), there are only 2 people with both
preferring Mercedes.
Table 6: Descriptive Statistics for income group preferring BMW
Annual Income ($)(1)
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

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Range 170652
Minimum 46068
Maximum 216720
Sum
1810527
4
Count 130
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
People demanding BMW cars have an average income of 139271 dollar. The median income is
138512 implying exactly 50% people in this group has an income of 138512 dollar. Maximum
number of people preferring BMW cars having an income of 109568. Standard deviation of
income distribution of this group is 33154.54. As standard deviation is less than mean, the
coefficient of variation is less than 100 implying a smaller variation in the income distribution.
People belong to this group have a maximum income of 216720 dollar while that of a minimum
income of 46068 dollar. The skewness measure has a value of -0.0385 indicating the distribution
is slightly negatively skewed.
Table 7: Descriptive Statistics for income group preferring Lexus

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Annual Income ($) (2)
Mean 154186.9
Standard Error 2556.425
Median 154492
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
People who prefers Lexus cars have an average income of 154186 dollar. The median income is
154492 implying exactly 50% people in this group has an income of 154492 dollar. Mode of the
income distribution is 17961 that is most people preferring Lexus cars having an income of

15STATISTICS FOR DECISION MAKING
17961. Standard deviation of income distribution of this group is 30248. As standard deviation
is less than mean, the coefficient of variation is less than 100 implying a smaller variation in the
income distribution. Range of this income distribution is 152065 with a maximum income of
248134 dollar and minimum income of 96069 dollar. The skewness measure has a value of -
0.6937 indicating income has a positively skewed distribution for this group.
Table 8: Descriptive Statistics for income group preferring Mercedes
Annual Income ($) (3)
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

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49941-109940 109941-169940 169941-229940 229941-289940 289941-349940
0
20
40
60
80
100
120
140
Mercedes
Figure 8: Income Distribution of Mercedes
People demanding Mercedes cars have a higher average income as compared to two other groups
with mean income being 184423. The median income is 186070 that is 50% people in this group
have an income of 186070 dollar. Maximum number of people preferring Mercedes cars having
an income of 161590 dollar as indicated from its mode. Standard deviation of income
distribution of this group is 47095.52. As standard deviation is less than mean, the coefficient of
variation is less than 100 implying the income distribution has less variation. People belong to
this group have a maximum income of 334823 dollar while that of a minimum income of 49941
dollar. The skewness measure has a value of 0.2740 indicating the distribution is slightly skewed
positive.
2.3 Output based on various education years
Table 9: Income of buyers of different luxury cars
Count of Education
(Years) Column Labels
Row Labels 1 2 3 Grand

17STATISTICS FOR DECISION MAKING
Total
11-13 12 34 2 48
14-16 66 52 38 156
17-19 52 44 94 190
20-22 10 16 26
Grand Total 130
14
0
15
0 420
11-13 14-16 17-19 20-22
0
10
20
30
40
50
60
70
80
90
100
1
2
3
Figure 9: Education years of buyers of different luxury cars
The years of education are divided into four groups. People having an education years of 11 to
13 mostly prefer Lexus. In the education group of 14 to 16 years most people having preference
for BMW. People with higher education prefers Mercedes. People having maximum education
years (20-22) have high preference for Mercedes.
Table 10: Descriptive Statistics for education years showing preference for BMW
Education (Years) (1)
Mean
15.8307
7
Standard Error 0.16092

18STATISTICS FOR DECISION MAKING
3
Median 16
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
The descriptive statistics suggest that households preferring BMW has an average
education years of 16. The media and modal education years of 16 years. The maximum and
minimum education years are 19 and 11 respectively with range being 8. Low volatility of the
distribution is indicated from a relatively small value of standard deviation. Standard deviation is

19STATISTICS FOR DECISION MAKING
obtained as 1.83. As the mean and median are almost equal, which is also equal to mode,
indicate an almost symmetric distribution.
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

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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
From the descriptive statistics, average education years for household preferring Lexus cars is
almost same as that for BMW. For both, the mean education year is almost 16. The median and
modal education years is 16. The maximum and minimum education years are 21 and 12
respectively with range being 9. Standard deviation of the distribution is 2.14. Since standard
deviation is less than average education years, the distribution is less volatile. The distribution is
almost symmetrical as reflected from almost equal value of mean, median and mode.
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
Sample Variance 3.027472
Kurtosis 0.039633
Skewness 0.081676

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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
From the descriptive statistics, average education years for household preferring
Mercedes cars is higher than that of two other groups. The average education year for this group
is 17. The median and modal education years of 17 years. The maximum and minimum
education years are 22 and 13 respectively with range being 9. Low volatility of the distribution
is indicated from a relatively small value of standard deviation. Standard deviation is obtained as
1.74. As the mean and median are almost equal, which is also equal to mode, indicate an almost
symmetric distribution.
2.4 Hypothesis testing 4

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In order to test whether there exists any significant difference of average ages of buyers
of three different luxury car buyers, ANOVA test is conducted.
Null Hypothesis: There exists no significant difference among the average ages of three different
group of luxury cars.
Alternative Hypothesis: A statistically significant difference exists among the average ages of
household of three different luxury cars.
Table 13: Hypothesis testing for average ages of three different group of buyers
SUMMARY
Groups Count Sum Average Variance
1 130 5878 45.21538 18.961
2 140 7064 50.45714 37.19959
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
If computed value of F is greater than the critical value, then the null hypothesis is rejected and
conclusion is drawn in favor of alternative hypothesis. From the table the critical F value is
obtained as 3.0174. The computed F value is 49.8017. As F > F critical, the null hypothesis is
rejected. This indicates average ages of buyers of three different luxury cars are not equal. At
least mean age of one group is significantly different from the two others.
2.5 Hypothesis testing 5

23STATISTICS FOR DECISION MAKING
Null Hypothesis: There exists no significant difference among the average income of household
of three different luxury cars.
Alternative Hypothesis: A statistically significant difference exists among average income of
household of three different luxury cars.
In order to test the proposed hypothesis ANOVA test is done. Result of the ANOVA test
is given in the following table.
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 null hypothesis is rejected if the critical F value is less than the computed F value. From the
table the critical F value is obtained as 3.0174. The computed F value is 52.1761. As computed
F value is greater than critical F, the null hypothesis is rejected. This indicates average income of
buyers of three different luxury cars are not equal. At least mean income of one group is
significantly different from the two others.
2.6 Hypothesis testing 6

24STATISTICS FOR DECISION MAKING
Null Hypothesis: There exists no significant difference among the average education years of
household of three different luxury cars.
Alternative Hypothesis: A statistically significant difference exists among average education
years of household of three different luxury cars.
Table 15: Hypothesis testing for average income 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 null hypothesis is rejected if the critical F value < computed F value. From the table,
the critical F value is obtained as 3.0174. The computed F value is 25.9257. As computed F
value is greater than critical F, the null hypothesis is rejected. This indicates that there exists
significant difference among the mean education years of buyers of three different luxury cars.
The average education years thus differ for different luxury car buyers.

25STATISTICS FOR DECISION MAKING
2.7 Hypothesis testing 7
To test the claim whether older people having higher income and more years of education
prefer Mercedes to BMW or Lexus regression analysis needs to be conducted. As the dependent
variable is categorical logistic regression should be done. Result of the logistic regression is
given below.
Variable
Categorie
s Frequencies %
Car 0 270 64.286
1 150 35.714
In the above table, 1 represents events of choosing Mercedes while 0 represents events of
choosing BMW or Lexus.
The table below presents details about the model. The table helps to understand the effect of age,
income and years of education on their choice of luxury cars.
Model parameters (Variable Car)
Source Value
Standar
d error
Wald Chi-
Square Pr > Chi²
Wald Lower
bound (95%)
Wald Upper
bound (95%)
Intercept -14.857 1.677 78.523 < 0.0001 -18.143 -11.571
Age (Years) 0.098 0.020 24.641 < 0.0001 0.059 0.136
Annual
Income ($) 0.000 0.000 47.145 < 0.0001 0.000 0.000
Education
(Years) 0.326 0.064 26.170 < 0.0001 0.201 0.451
The coefficient of all the variables are positive implying ages, income and education
positively influence the choice of car models. Significance of the coefficients is indicated from
the probability of Chi-squares value. For all the independent variables, the probability of chi-
square is less than the significance level of 0.05. This indicates rejection of null hypothesis

26STATISTICS FOR DECISION MAKING
stating no significant relation exists between choice of Mercedes cars and age, income and
education years of household.
Next table shows goodness of fit of the model. This gives equivalent result of R square of
a linear regression model. The most important component of this table is the probability of Chi-
square based upon the log ratio. This provides significance of overall model. From the table
probability corresponding to Chi-square of the log ratio is less than 0.0001. From the result, it
can be concluded that the model has an overall significance that is the independent variables
bring important information about choice of luxury cars.
Goodness of fit statistics (Variable Car)
Statistic Independent Full
Observations 420 420
Sum of weights 420.000 420.000
DF 419 416
-2 Log(Likelihood) 547.476 405.453
R²(McFadden) 0.000 0.259
R²(Cox and Snell) 0.000 0.287
R²(Nagelkerke) 0.000 0.394
AIC 549.476 413.453
SBC 553.516 429.614
Iterations 0 6
Test of the null hypothesis H0: Y=0.357 (Variable Car)
Statistic DF Chi-square Pr > Chi²
-2 Log(Likelihood) 3 142.023 < 0.0001
Score 3 121.512 < 0.0001
Wald 3 86.750 < 0.0001
Equation of the model (Variable Car):
Pred(Car) = 1/(1 + exp(-(-14.8572933879954+0.097839878084683*Age (Years)+2.41610940803203E-
05*Annual Income ($)+0.326147090262717*Education (Years))))

27STATISTICS FOR DECISION MAKING
Standardized coefficients (Variable Car)
Source Value
Standard
error
Wald Chi-
Square Pr > Chi²
Wald Lower
bound (95%)
Wald Upper
bound (95%)
Age (Years) 0.351 0.071 24.641 < 0.0001 0.213 0.490
Annual
Income ($) 0.563 0.082 47.145 < 0.0001 0.402 0.723
Education
(Years) 0.383 0.075 26.170 < 0.0001 0.236 0.530
3. Conclusion and Recommendation
The report briefly analyzes customers’ profiles of three different luxury cars. The three
different car models considered here are BMW, Lexus and Mercedes. The customers’ profile are
segregated into three different attributes age, income and education. Among the 420 samples
taken into consideration, total 130 people buy BMW. Number of people buying Lexus and
Mercedes are 140 and 150 respectively. Maximum number of people buying BMW belong to the
age group ranging from 40 to 49, having an income lying in the range of 96068- 196067 dollar
and have education years of 14 to 19 years. In case of Lexus, buyers mostly belong to the age
group between 45 and 59. Most buyers of Lexus have an income ranging from 96068 to 196067
and education years of 11 to 19 years. Most buyers of Mercedes belong to the age group of 50 to
59 years; have an income of 146068 to 246067 dollar with education years of 17 to 19 years. For
BMW, the distribution of age is positively skewed, income distribution is negatively skewed and
years of education has symmetric distribution. Buyers of BMW cars have an average age of
45years, average income of 139271 dollar with average education years of 16. In case of Lexus
cars, buyers have an average age of 50, average income of 154186 dollar and average education
years of 16 years. For Mercedes, average age is 52, average income is 184423 dollar and average
education years of 16. Average income, ages and education years differ significantly among

28STATISTICS FOR DECISION MAKING
buyers of three different luxury cars. Finally, demand for Mercedes cars found to be significantly
influenced by age, income and education years. Older people with higher income and higher
education years tend to buy Mercedes over BMW or Lexus.
The sellers of different luxury cars should use this information in determining their
marketing strategy. The sellers of Mercedes cars should target older people having higher
income and more education years. For BMW and Lexus, sellers should focus on middle-aged
people having income ranging between 96068 and 196067 dollar.