Statistics for Decision Making

This report discusses recent car survey data with the aid of statistical tools and software like Excel. It considers different hypotheses and depicts the data with graphical presentation. The report analyses the impact of the findings and provides recommendations to enhance the present situation. The business problem lies within the relation between age, education years of the buyer, and income with the car purchasing preference. The statistical problem is analysed with the help of statistical tools and theories. The report considers different age groups, income groups, and education years to determine the consumer profile for different car models.

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

1STATISTICS FOR DECISION MAKING
Executive Summary:
Luxury cars are one of the main source of showcasing the persona of the human being,
however, as per the latest survey by the Nelson Perera during 2012 there is much amount of
ambiguity regarding the same. As per the survey, there are factors like age, income, education
that alters the preference of the buyers and among all the car producers MBW, Mercedes and
Lexus is the most popular luxury car makers among people. This report is aimed to discuss the
recent car survey data with the aid of the statistical tools and software like Excel. For better
understanding of the preference for buying cars, the report will consider different hypothesis and
depict the data with the graphical presentation. From the analysis, it can be seen that the
Mercedes is one of the most favoured car among all the three alternative of luxury cars.
Purchasing of the same is influenced by the age, income and education level. Whereas, the above
analysis has also showcased that there is considerable amount if importance of education, age
and income on the selection of luxury car.

2STATISTICS FOR DECISION MAKING
Table of Contents
Introduction:....................................................................................................................................3
Business Problem:.......................................................................................................................3
Statistical Problem:......................................................................................................................3
Analysis:..........................................................................................................................................5
Different age group statistical output analysis:...........................................................................5
Analysis of statistical data of different income groups:............................................................11
Analysis of different education years:.......................................................................................17
Significant difference of the average ages of the buyers:..........................................................23
Significant difference in mean household income:...................................................................23
Significant difference in average years of education:................................................................24
Preference of car of older people:..............................................................................................26
Recommendation and conclusion:.................................................................................................27
Reference:......................................................................................................................................29

3STATISTICS FOR DECISION MAKING
Introduction:
This report is aimed to discuss the recent car survey data with the aid of the statistical
tools and software like Excel. For better understanding of the preference for buying cars, the
report will consider different hypothesis and depict the data with the graphical presentation.
Moving forward, the report will portray the impact of the finding and recommendations will be
given to gauge to enhance the present situation.
Business Problem:
As per the given context, it can be seen that the Automobile Association attempted to
predict the demand of luxury cars utilising the survey performed by Nelson Perera during the
year 2012. In order to direct the survey, various factors that can alter the preference of the buyer
and change the demand of the cars has been chosen. The business problem in this case lies within
the relation between age, education years of the buyer, and income with the car purchasing
preference (Zhang and Kim 2013). To be more specific, objective of the business is to determine
three different models of consumer preference for purchasing cars depending upon the age of
consumer, education years of the buyer and income of the purchaser. It will help the Automobile
Association to establish consumer profile for different cars model and help the industry to mark
their prospect buyers.
Statistical Problem:
The business problem as per the direction need to be analysed with the help of statistical
tool and theories. In order to perform statistical interpretation of the given data, distribution of
income, education years of the consumer and age will be utilised. In addition to this, shape of the
distribution, location, will be judged with the help of dispersions and central tendency (Dotsch et
al. 2017). In order to determine whether there is any association between the willingness to buy

4STATISTICS FOR DECISION MAKING
Lexus, Mercedes or BMW with the age of the consumer, income of the purchaser and
educational year of the buyer. Considering the case study, it can be seen that there is much
amount of ambiguity regarding the consumer preference of buying Mercedes and for this
purpose Logistics regression has been performed and it has tested, whether older people who
have high income and higher level of education prefer Mercedes over other luxury car brands or
not (Chatterjee and Hadi 2015). Apart from this, in order to mitigate the question of relation
regarding income, average education years with the car purchasing, the report has considered
hypothesis testing that will allow the researcher to provide concrete evidence and consumer
profiling.

5STATISTICS FOR DECISION MAKING
Analysis:
Different age group statistical output analysis:
As it can be seen from the table 1 and figure 1, ages of the buyers have been divided into
seven groups ranging from 35 to 70. As the table 1 highlights, most of the people who prefers the
given luxury cars are aged between 45 and 49 because people within this age range has highest
number of population. When it comes to BMW, then people aging from 40 to 49 prefers the
brand most and when it comes to Lexus, then people within the age range from 45 to 49 prefers
the brand most. Contrary to this, from the table 1, it can be seen that people who are 50 to 54
years old, prefer the Mercedes brand.
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 130 140 150 420
Table 1: Buyer’s age of different luxury cars
Figure 1, depicts the same thing graphically and utilising the figure, it can be seen that
most of the people of different ages prefer Mercedes over other given brands. On the other hand,
figure 1, also depicts that people who are older than 59 years do not prefer BMW at all thus, the
figure does not shows any upward bar diagram.

6STATISTICS FOR DECISION MAKING
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: Buyer’s age of different luxury cars
Descriptive statistics of different age groups showcase that out of 130 people who prefer
BWM has mean age of 45. On the other hand median age is 45 and the mode value being 46
depicting that most people within the population of BMW courtesan is aged between 45 and 46.
Minimum age of the people who prefer BMW over other brand is 36 years and the maximum
aged people who prefer BWM over other brand is 57 years. With lower standard deviation of
4.35, it can be entailed from the descriptive statistics that age distribution among the people who
prefer BWM is low. Skewness with 0.51 positive value shows that the distribution of the age is
positively skewed that define few smaller values of age cannot shift the mean value of ages
leftward leading it to fall (Desmond and Weeks 2014).

7STATISTICS FOR DECISION MAKING
Age (Years) (1)
Mean 45.21538
Standard Error 0.381908
Median 45
Mode 46
Standard
Deviation
4.354423
Sample Variance 18.961
Kurtosis 0.04742
Skewness 0.508655
Range 21
Minimum 36
Maximum 57
Sum 5878
Count 130
Table 2: Descriptive Statistics for ages with preference for BMW
From the figure 2, it can also be seen that people who are aged between 40 and 47 prefer
BMW most, whereas, with rise in the age number of people preferring BMW over other brand
has been falling.
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 buyers

8STATISTICS FOR DECISION MAKING
Age (Years) (2)
Mean 50.45714
Standard Error 0.515472
Median 50
Mode 55
Standard
Deviation
6.099147
Sample Variance 37.19959
Kurtosis 0.611214
Skewness 0.360262
Range 32
Minimum 36
Maximum 68
Sum 7064
Count 140
Table 3: Descriptive Statistics for ages with preference for Lexus
Moving forward, if the age distribution of people who prefer Lexus is observed, then it
can be seen that people who are 46 to 55 years old prefer the Lexus most. As the table 3
showcase, mean value of the population who prefer Lexus is 50 years and the median is also
same depicting symmetric distribution of ages. If mean and median are same, then it also implies
that Skewness will also be lower and considering the descriptive statistics table (table 3), it can
be seen that Skewness is 0.36 depicting the symmetric distribution of ages. People who are 36
years old and aged less than 69 years, prefer Lexus over other brands. Out of the given data, it
can be seen that total 140 people prefer Lexus over any other brand and it showcase that range
within the age distribution is 32.

9STATISTICS FOR DECISION MAKING
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 buyers
figure 3, depicts that people who are aged between 46 and 55, prefer Lexus most and the
range of people who prefer the same car brand lies within 36 years to 70 years with central spike
at 46 to 55. This depicts that standard deviation will be lower and as the table 2 depicts it is only
6.09.

10STATISTICS FOR DECISION MAKING
Age (Years)(3)
Mean 51.98667
Standard Error 0.55037
Median 53
Mode 53
Standard
Deviation
6.740628
Sample Variance 45.43606
Kurtosis -0.0195
Skewness -0.02894
Range 35
Minimum 35
Maximum 70
Sum 7798
Count 150
Table 4: Descriptive Statistics for ages with preference for Mercedes
Considering the table 4 it can be seen that out of total sample population, 150 people
prefer Mercedes over any other brand. People who are aged between 50 and 54, prefer the
Mercedes most, whereas minimum aged people who prefer Mercedes over other brand is 35 and
the maximum aged population who prefer the same car brand is 70 years old. Table 4 depicts
that, average age of the people who prefer Mercedes is 52 and the modal as well as median age
group is 53. This showcase than age distribution is almost symmetric, however, negative
Skewness of -0.02894 depict that there is leftward central tendency. Standard deviation is 6.74
and it showcase low amount of volatility among the different age groups who prefer Mercedes
over other brands (Hannagan and Morduch 2015).

11STATISTICS 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 buyers
As the figure 4 depicts, people are aged more than 50 and less than 54 prefer Mercedes
more, whereas, with rise in the age there has been subsequent fall in the preference.
Analysis of statistical data of different income groups:
Considering the table 5, it can be seen that total 420 people were chosen for the survey
and when it comes to analysis of statistical data of different income groups, then it can be seen
that lowest income group earns 46068 to 96067 dollars as their annual income. People with
lowest income prefer BMW most and no one from the lowest income prefer Lexus. As per the
table 5, highest income groups earns 296068 to 346067 dollar annually.
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 130 140 150 420
Table 5: Income distribution of buyers of different luxury cars

12STATISTICS FOR DECISION MAKING
People who earn highest neither prefer BMW nor prefer Lexus, they only want to obtain
Mercedes. Considering the second and third lowest income group, it can be seen that 150 and
188 people respectively earns second and third tier annual income. As per table 5, second tier
earners prefer BMW most and the third tier income earner prefer Lexus most. If the fourth tier
income earner is considered, then it can be seen that most people prefer Mercedes over any other
brand.
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 distribution of buyers of different luxury cars
As per the figure 5, it can be seen that most of the population lies within the second and
third tier income group who prefer type 1 and type 2 cars and with rise in income preference of
Mercedes eventually expands.

13STATISTICS FOR DECISION MAKING
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
Range 170652
Minimum 46068
Maximum 216720
Sum 18105274
Count 130
Table 6: Descriptive Statistics for income group preferring BMW
As per the table 6, it can be seen that people who prefer BMW possess a mean income of
139271 dollars and the median being 138512 depicts half of the population of the group earns the
mean income. Mode being 109568 dollars depicts people who prefer BMW over other have this
much or higher income and that standard deviation being 33154.54 means there is a smaller
variation in the income distribution. Negative Skewness of -0.03855 depicts that central tendency
provides a left ward inclines (Ho and Yu 2015).
46068-76067 76068-106067 106068-
136067 136068-
166067 166068-
196067 196068-
226067
0
5
10
15
20
25
30
35
40
45
50
BMW

14STATISTICS FOR DECISION MAKING
Figure 6: Income distribution of buyers of BMW cars
As per the figure 6, it can be seen that people who have income higher than 46068 dollar
annually prefer BMW and people who have income less than 216720 dollars prefers the same car
brand.
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 21586160
Count 140
Table 7: Descriptive Statistics for income group preferring Lexus
As per the table 7, it can be seen that people who prefer Lexus possess a mean income of
154186 dollars and the median being 154492 depicts half of the population of the group earns the
mean income. Mode being 179617 dollars depicts people who prefer Lexus over other have this
much or higher income and that standard deviation being 30248 means there is a smaller
variation in the income distribution. Negative Skewness of -0.06937 depicts that central tendency
provides a left ward inclines (Cain et al. 2017).

15STATISTICS FOR DECISION MAKING
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
As per the figure 7, it can be seen that people who have income higher than 49941 dollar
annually prefer Lexus and people who have income less than 27663592 dollars prefers the same
car brand.

16STATISTICS FOR DECISION MAKING
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 27663592
Count 150
Table 8: Descriptive Statistics for income group preferring Mercedes
As per the table 8, it can be seen that people who prefer Mercedes possess a mean income
of 184423 dollars and the median being 186070 depicts half of the population of the group earns
the mean income. Mode being 161590 dollars depicts people who prefer Mercedes over other
have this much or higher income and that standard deviation being 47095.52 means there is a
smaller variation in the income distribution. Skewness of 0.2739 depicts that central tendency
provides a rightward inclines.
49941-109940 109941-169940 169941-229940 229941-289940 289941-349940
0
20
40
60
80
100
120
140
Mercedes

17STATISTICS FOR DECISION MAKING
Figure 8: Income Distribution of Mercedes
As per the figure 7, it can be seen that people who have income higher than 49941 dollar
annually prefer Mercedes and people who have income less than 27663592 dollars prefers the
same car brand.
Analysis of different education years:
As far as education of the owners is concerned, it can be seen that out of total sample
population, most educated people prefer Lexus and Mercedes by a large number. Lowest
educated people prefer Lexus over other brands and in the second and third tier of education
level most people prefers all the three brands with slight difference. Second tier education level
people prefer BMW most and as it can be seen from table 9, third tier education level people
prefer Merced most.
Count of Education (Years) Column Labels
Row Labels 1 2 3 Grand
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 130 140 150 420
Table 9: Income of buyers of different luxury cars

18STATISTICS FOR DECISION MAKING
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
As figure 9 depicts, people with lowest education level prefer Lexus most, people with
second tier of education level prefer BMW and people with third and higher level of education
level prefer Mercedes most.
Education (Years) (1)
Mean 15.83077
Standard Error 0.160923
Median 16
Mode 16
Standard
Deviation
1.834799
Sample Variance 3.366488
Kurtosis -0.17288
Skewness -0.4345
Range 8
Minimum 11
Maximum 19
Sum 2058
Count 130
Table 10: Descriptive Statistics for education years showing preference for BMW
As it can be seen from the table 10, out of 130 people who prefer BMW within the
sample population most of them have mean education level of 15. Median and mode being same

19STATISTICS FOR DECISION MAKING
at 16 depicts there education distribution among the people who love BMW is symmetric that
leads to the negative Skewness within the data that highlight central tendency being leftward
skewed. Figure 10 depicts that, people who prefer BWM have lowest education level of 11 and
highest education level of 19 and the median education level of 16 highlights that half of the
people have more education than 16th level.
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
As it can be seen from the table 11, out of 130 people who prefer BMW within the
sample population most of them have mean education level of 15. Median and mode being same
at 16 depicts there education distribution among the people who love BMW is symmetric that
leads to the negative Skewness within the data that highlight central tendency being leftward
skewed. Figure 10 depicts that, people who prefer BWM have lowest education level of 11 and
highest education level of 19 and the median education level of 16 highlights that half of the
people have more education than 16th level.
Education (Years) (2)
Mean 15.8

20STATISTICS FOR DECISION MAKING
Standard Error 0.204069593
Median 16
Mode 16
Standard
Deviation
2.414583986
Sample Variance 5.830215827
Kurtosis -
0.977282698
Skewness 0.169719918
Range 9
Minimum 12
Maximum 21
Sum 2212
Count 140
Table 11: Descriptive Statistics for education years showing preference for Lexus
As it can be seen from the table 11, out of 140 people who prefer Lexus within the
sample population most of them have mean education level of 16. Median and mode being same
at 16 depicts there education distribution among the people who love Lexus is symmetric that
leads to the Skewness of 0.1697 within the data that highlight central tendency being rightward
slightly skewed. Figure 11 depicts that, people who prefer Lexus have lowest education level of
12 and highest education level of 21 and the median education level of 16 highlights that half of
the people have more education than 16th level.

21STATISTICS 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
As it can be seen from the table 12, out of 150 people who prefer Mercedes within the
sample population most of them have mean education level of 17. Median and mode being same
at 17 depicts there education distribution among the people who love Mercedes is symmetric that
leads to the negative Skewness within the data that highlight central tendency being leftward
skewed. Figure 12 depicts that, people who prefer Mercedes have lowest education level of 13
and highest education level of 22 and the median education level of 17 highlights that half of the
people have more education than 17th level.

22STATISTICS FOR DECISION MAKING
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
Range 9
Minimum 13
Maximum 22
Sum 2594
Count 150
Table 12: Descriptive Statistics for education years showing preference for Mercedes
Figure 12 additionally showcase that people who have education level at 17th, prefer
Mercedes most and with rise in the education level preference of Mercedes falls gradually.
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

23STATISTICS FOR DECISION MAKING
Significant difference of the average ages of the buyers:
To test whether there exists any significant difference of average ages of buyers of three
different luxury car buyers here ANOVA is performed.
Null hypothesis: No significant difference within the average ages of people who prefer different
luxury car.
Alternative hypothesis: There is a statistically significant difference within the average ages of
people who prefer different luxury car.
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
Table 13.1: Summary of different ages of different buyers’ group
As per the statistical theories, if the computed F value is larger than the critical value,
then null hypothesis need to be rejected and the alternative will be accepted (Bretz et al. 2016).
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
Table 13.2: Hypothesis testing for of different ages of different buyers’ group
Considering the ANOVA, it can be seen than obtained Ft value is 3.017357 and the
computed Fc value is 49.8017. Thus, Fc>Ft that determine null hypothesis need to be rejected.
Under this situation, it can be entailed that average age of the buyers who prefer different luxury
cars are not equal. To be specific, there is at least one group who’s mean age differ from two
other age groups (Greenland et al. 2016).
Significant difference in mean household income:

24STATISTICS FOR DECISION MAKING
To test whether there exists any significant difference of average income of buyers of
three different luxury car buyers here ANOVA is performed.
Null hypothesis: No significant difference within the average income of people who prefer
different luxury car.
Alternative hypothesis: There is a statistically significant difference within the average income
of people who prefer different luxury car.
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
Table 14.1: Summary of different income of different buyers’ group
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+1
1
417 1.44E+09
Total 7.49E+1
1
419
Table 14.2: Hypothesis testing of different income of different buyers’ group
Considering the ANOVA, it can be seen than obtained Ft value is 3.017357 and the
computed Fc value is 52.1761. Thus, Fc>Ft that determine null hypothesis need to be rejected
(Montgomery 2017). Under this situation, it can be entailed that average income of the buyers
who prefer different luxury cars are not equal. To be specific, there is at least one group who’s
mean income differ from two other age groups.
Significant difference in average years of education:
To test whether there exists any significant difference of average education years of
buyers of three different luxury car buyers here ANOVA is performed.

25STATISTICS FOR DECISION MAKING
Null hypothesis: No significant difference within the average education years of people who
prefer different luxury car.
Alternative hypothesis: There is a statistically significant difference within the average education
years of people who prefer different luxury car.
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
Table 15.1: Summary of average income of different buyers’ group
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
Table 15.2: Hypothesis testing for average income of different buyers’ group
Considering the ANOVA, it can be seen than obtained Ft value is 3.017357 and the
computed Fc value is 25.92566. Thus, Fc>Ft that determine null hypothesis need to be rejected.
Under this situation, it can be entailed that average income of the buyers who prefer different
luxury cars are not equal. To be specific, there is at least one group who’s mean income differ
from two other age groups.

26STATISTICS FOR DECISION MAKING
Preference of car of older people:
In order to test that claim that older people prefer Mercedes over other two brands
regression analysis will be done where categorical logistic regression has been utilised.
Variable
Categorie
s Frequencies %
Car 0 270 64.286
1 150 35.714
Table 16.1: Frequency distribution
Table 16.1 depicts 1 as Mercedes and the other as 0. Table 16.2 showcase that there is
positive impact on car model selection by the age, education and income. If Chi-squares value is
less than significance level of 0.05, then null hypothesis will be rejected.
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
Table 16.2: Model parameters
Considering the table 16.2, it can be seen that chi-square probability is less than the
significance and thus null hypothesis will be rejected while accepting the alternative.
Considering the goodness of fit statistics, it can be seen that chi-square of the log ratio is
lower than 0.0001 and it can be depicted that overall significance of the independent variables
bring in important information regarding the selection of luxury cars (D’Agostino 2017).

27STATISTICS FOR DECISION MAKING
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
Table 16.3: Goodness of fit statistics
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
Table 16.4: Test of null hypothesis
Equation of the model with car as variable:
Pred (Car) = 1/ (1 + exp (-(-14.8572933879954+0.097839878084683*Age (Years)
+2.41610940803203E-05*Annual Income ($) +0.326147090262717*Education (Years))))
Standardized coefficients (Variable Car)
Source Value Standard
error
Wald Chi-
Square
Pr >
Chi²
Wald Lower
bound (95%)
Wald Upper
bound (95%)
Age (Years) 0.351 0.071 24.641 < 0.0001 0.213 0.490
Annual
Income ($)
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
Recommendation and conclusion:

28STATISTICS FOR DECISION MAKING
From the analysis, it can be seen that the Mercedes is one of the most favoured car among
all the three alternative of luxury cars. Purchasing of the same is influenced by the age, income
and education level. Whereas, the above analysis has also showcased that there is considerable
amount if importance of education, age and income on the selection of luxury car. For instance,
the report has showcased that, it with rise in age people prefer Mercedes rather than going for
BMW, whereas, people who have lower education, goes for Lexus. On the other hand, BMW is
preferred by the people who have low income.
When it comes to the recommendations, then it would be ideal for the Mercedes to bring
in competitive price so that it can be purchased large amount of population and on the other
hand, BMW need to bring in more amount of models that are old age friendly and smooth to
drive so that older people also can purchase the same. When it comes to Lexus, then it can be
seen that they are doing well, however, price need to be revised so that lower income group
people can also afford the same.

29STATISTICS FOR DECISION MAKING
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