Demand Analysis Of Luxury Cars Based On Age, Income, And Education In An Essay.

Research Objectives

The Automobile association has been facing problems in targeting the population group to whom which brand of car should be more advertised. The taste and preferences of the people differ with different age group, income and education. Thus, the company wanted to analyse the demand for the luxury cars in the households considering the factors such as age, income and years of education. The main aim of this research will be to identify how each of the considered attributes such as age, income and education of the buyers of luxury cars define their preferences towards any particular brands. The customer profile information will be useful for the association to analyse their demands so that they can come up with some strategies to sell the cars to the potential buyers and attract new customers as well.

The business problem that has been discussed already needs to be evaluated with the help of the application of appropriate statistical techniques and interpretation of the results as well. Measures of shape and location will be used to determine the shape of the distribution of the profiles of the customers. The Association is also interested to know the differences in the age, annual income and years of education of the buyers of the different brands of cars. Appropriate testing strategies will be used in order to test these differences. The preference of the brands of the luxury cars with respect to the influence of age, education and annual income of the customers will be evaluated with the help of logistic regression technique.

It can be seen from table that in the lower age group of 35 – 44 years, preference of people is more towards BMW rather than Lexus and Mercedes, in the age group of 45 – 54 years, people can be seen to be preferring Lexus and between 55 – 64 years, people mostly prefer Mercedes. Thus, it can be said that the older people are more likely to prefer Mercedes than BMW or Lexus and the Younger People are more likely to prefer BMW over Mercedes and Lexus. Lexus is preferred by the middle aged people mostly.

Table 1: Preference of Luxury Cars with respect to Age Groups

Car Type and Age	Car Types
Age Group (In Years)	BMW	Lexus	Mercedes	Grand Total
35-44	58	20	24	102
45-54	66	82	74	222
55-64	6	34	50	90
65-74		4	2	6
Grand Total	130	140	150	420

It can be seen that the average age of the people preferring BMW cars is 45.22 years, preferring Lexus cars is 50.46 years and preferring Mercedes cars is 51.99 years. It can also be seen that the standard deviation of the ages of the people preferring the three types of cars namely BMW, Lexus and Mercedes are 4.4 years, 6.1 years and 6.7 years respectively, which can be said as very low deviations. Thus, it can be said that the ages of the people preferring these types of cars are close to the average ages. Moreover, the mean, median and the mode of the ages are quite close to each other. Thus, the distribution of the ages of the three types of car users can be said to be symmetrically distributed. These has also been illustrated with the help of histograms provided in figures 2, 3 and 4.  

Table 2: Descriptive Summary of Ages
	BMW	Lexus	Mercedes
Mean	45.22	50.46	51.99
Standard Error	0.38	0.52	0.55
Median	45	50	53
Mode	46	55	53
Standard Deviation	4.4	6.1	6.7
Sample Variance	18.96	37.2	45.44
Kurtosis	0.05	0.61	-0.02
Skewness	0.51	0.36	-0.03
Range	21	32	35
Minimum	36	36	35
Maximum	57	68	70
Sum	5878	7064	7798
Count	130	140	150

Methodology

It can be seen from table 3 that the people preferring Mercedes belong to higher income group. The people of the lower income group can be seen to be preferring BMW cars over Lexus and Mercedes. Lexus cars are preferred mostly by people who belong to an average income group.

Table 3: Preference of Luxury Cars with respect to Income Groups

Car Type and Annual Income	Car Types
Annual Income (in $)	BMW	Lexus	Mercedes	Grand Total
45000-74999	2		2	4
75000-104999	16	4	2	22
105000-134999	38	38	16	92
135000-164999	44	48	38	130
165000-194999	26	40	36	102
195000-224999	4	4	28	36
225000-254999		6	20	26
255000-284999			4	4
285000-314999			2	2
315000-344999			2	2
Grand Total	130	140	150	420

It can be seen that the average income of the people preferring BMW cars is $139,271.3, preferring Lexus cars is $154,186.9 and preferring Mercedes cars is $184,423.9. It can also be seen that the standard deviation of the income of the people preferring the three types of cars namely BMW, Lexus and Mercedes are $2,907.85, $2,556.43 and $3,845.33 respectively, which can be said as very low deviations compared to the average income. Thus, it can be said that the income of the people preferring these types of cars are close to the average income. Moreover, the mean, median and the mode of the incomes of the individuals preferring different type of cars are quite close to each other. Thus, the distribution of the income of the three types of car users can be said to be symmetrically distributed. These has also been illustrated with the help of histograms provided in figures 6, 7 and 8.

Table 4: Descriptive Summary of Annual Income
	BMW	Lexus	Mercedes
Mean	139271.3	154186.9	184423.9
Standard Error	2907.846	2556.425	3845.333
Median	138512	154492	186070
Mode	109568	179617	161590
Standard Deviation	33154.54	30248.02	47095.52
Sample Variance	1.1E+09	9.15E+08	2.22E+09
Kurtosis	-0.22439	0.963641	0.987178
Skewness	-0.03855	0.693685	0.273966
Range	170652	152065	284882
Minimum	46068	96069	49941
Maximum	216720	248134	334823
Sum	18105274	21586160	27663592
Count	130	140	150

It can be seen from table 5 that in the lower education group of 11 – 13 years, preference of people is more towards Lexus rather than BMW and Mercedes, in the education group of 14 – 16 years, people can be seen to be preferring BMW and between 17 – 22 years, people mostly prefer Mercedes. Thus, it can be said that the people with higher education are more likely to prefer Mercedes than BMW or Lexus and the people with lower income groups are more likely to prefer Lexus over Mercedes and BMW. BMW is preferred by the mostly by the people with 14 – 16 years of education.

Table 5: Preference of Luxury Cars with respect to Years of Education

Car Type and Education	Car Types
Education (in Years)	BMW	Lexus	Mercedes	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

It can be seen that the average years of education the people preferring BMW cars is 15.8 years, preferring Lexus cars is 15.8 years and preferring Mercedes cars is 17.3 years. It can also be seen that the standard deviation of the years of education of the people preferring the three types of cars namely BMW, Lexus and Mercedes are 1.8 years, 2.4 years and 1.7 years respectively, which can be said as very low deviations. Thus, it can be said that the years of education of the people preferring these types of cars are close to the average years of education. Moreover, the mean, median and the mode of the years of education are quite close to each other for each of the car types. Thus, the distribution of the years of education of the three types of car users can be said to be symmetrically distributed. These has also been illustrated with the help of histograms provided in figures 10, 11 and 12.

Table 6: Descriptive Summary of Years of Education
	BMW	Lexus	Mercedes
Mean	15.83077	15.8	17.29333
Standard Error	0.160923	0.20407	0.142067
Median	16	16	17
Mode	16	16	17
Standard Deviation	1.834799	2.414584	1.739963
Sample Variance	3.366488	5.830216	3.027472
Kurtosis	-0.17288	-0.97728	0.039633
Skewness	-0.4345	0.16972	0.081676
Range	8	9	9
Minimum	11	12	13
Maximum	19	21	22
Sum	2058	2212	2594
Count	130	140	150

Analysis of Age Group Preferences

In order to check independency of average ages of buyers of belonging to groups of three different luxury cars, hypothesis testing needs to be done. The most significant statistical tool for analyzing mean ages of three different group the test of Analysis of Variance or ANOVA.

The null and alternative hypothesis for the specific ANOVA test is given as follows.

Null hypothesis: Average ages of buyers of three different groups are equal.

Alternative Hypothesis: Average ages of buyers are significantly different.

Result of the ANOVA test is produced below.

Table 7: ANOVA test result for independency of average ages

Groups	Count	Sum	Average	Variance
BMW	130	5878	45.21538	18.961
Lexus	140	7064	50.45714	37.19959
Mercedes	150	7798	51.98667	45.43606

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	3436.362	2	1718.181	49.802	0.000	3.017
Within Groups	14386.69	417	34.500
Total	17823.05	419

Decision rule of the ANOVA test indicates that the null hypothesis is rejected at 5% level of significance if the estimated value F exceeds the tabulated value. The estimated F value of the given test is obtained as 49.8. The critical F value or tabulated F value is given as 3.017. As the estimated F value exceeds the critical F value, null hypothesis is rejected.  It can thus be said that average ages of buyers of three groups are not equal. The mean ages differ significantly among the three groups.

In order to check independency of average income of buyers of belonging to groups of three different luxury cars, hypothesis testing needs to be done. The most significant statistical tool for analyzing mean incomes of three different group the test of Analysis of Variance or ANOVA.

The null and alternative hypothesis for the specific ANOVA test is given as follows.

Null hypothesis: Average income of buyers of three different groups are equal.

Alternative Hypothesis: Average income of buyers are significantly different.

Result of the ANOVA test is produced below.

Table 8: ANOVA test result for independency of average income

Groups	Count	Sum	Average	Variance
BMW	130	18105274	139271.3	1.1E+09
Lexus	140	21586160	154186.9	9.15E+08
Mercedes	150	27663592	184423.9	2.22E+09

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1.5E+11	2	7.5E+10	52.176	0.000	3.017
Within Groups	5.99E+11	417	1.44E+09
Total	7.49E+11	419

Decision rule of the ANOVA test indicates that the null hypothesis is rejected at 5% level of significance if the estimated value F exceeds the tabulated value. The estimated F value of the given test is obtained as 52.18. The critical F value or tabulated F value is given as 3.017. As the estimated F value exceeds the critical F value, null hypothesis is rejected.  It can thus be said that average income of buyers of three groups are not equal. The mean incomes differ significantly among the three groups.

In order to check independency of average years of education of buyers of belonging to groups of three different luxury cars, hypothesis testing needs to be done. The most significant statistical tool for analyzing mean education years of three different group the test of Analysis of Variance or ANOVA.

The null and alternative hypothesis for the specific ANOVA test is given as follows.

Null hypothesis: Average education years of buyers of three different groups are equal.

Alternative Hypothesis: Average education years of buyers are significantly different.

Result of the ANOVA test is produced below.

Table 9: ANOVA test result for independency of average education years

Groups	Count	Sum	Average	Variance
BMW	130	2058	15.83077	3.366488
Lexus	140	2212	15.8	5.830216
Mercedes	150	2594	17.29333	3.027472

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	210.858	2	105.429	25.926	0.000	3.017
Within Groups	1695.770	417	4.067
Total	1906.629	419

Decision rule of the ANOVA test indicates that the null hypothesis is rejected at 5% level of significance if the estimated value F exceeds the tabulated value. The estimated F value of the given test is obtained as 25.93. The critical F value or tabulated F value is given as 3.017. As the estimated F value exceeds the critical F value, null hypothesis is rejected.  It can thus be said that average education years of buyers of three groups are not equal. The mean education years differ significantly among the three groups.

Some dealers claim that there is a higher chance of buying Mercedes cars in case of buyers with higher age, higher income and higher years of education. To verify this claim regression analysis needs to be done. The simple linear regression however cannot be done here because of categorical nature of the dependent variable. For this, logistic regression has been done. The dependent variable takes two values 0 and 1. 1 represents probability of buying Mercedes and 0 represents probability of buying Lexus or Mercedes.

The table below represents proportion of samples choosing Mercedes and other two types of cars.

Table 10: Proportion of choosing Mercedes and two other types of cars

	Suc-Obs	Fail-Obs	Total
Suc-Pred	88	26	114
Fail-Pred	62	244	306
Total	150	270	420

In the selected sample group, among the 420 household 150 are buying Mercedes and 270 are buying BMW or Mercedes. That is in chosen sample, 35.7% are preferring Mercedes over BMW or Lexus.

The result of logistic regression is given in the following table:

Table 11: Logistic Regression Coefficients

	coeff b	s.e.	Wald	p-value	exp(b)	lower	upper
Intercept	-14.857	1.677	78.523	0.000	0.000
Age (Years)	0.098	0.020	24.641	0.000	1.103	1.061	1.146
Annual Income ($)	0.000	0.000	47.145	0.000	1.000	1.000	1.000
Education (Years)	0.326	0.064	26.170	0.000	1.386	1.223	1.570

From the regression result the estimated regression equation is obtained as:

From regression table coefficient of all the independent variables are found to be positive. This implies that with increase in each of the independent variable the probability of buying Mercedes cars increases. P values corresponding to all the independent variables are 0.000. The p value lower than the significance level indicates rejection of null hypothesis stating no significant relation between the dependent and independent variables. The regression result thus supports the claim that older people who has higher income and more years of education tend to buy Mercedes cars.

Conclusion

The analysis conducted so far in this research paper indicates that the people with lower age groups prefer BMW and higher age groups prefer Mercedes cars. People having higher income prefer Mercedes whereas with lower income prefer BMW. The people with lower years of education prefer Lexus cars whereas with higher years of education prefer BMW vars. Thus, it can be concluded that older people with higher income group and higher years of education prefer Mercedes over other car types. Significant differences have also been observed in the average ages, average income and average years of education for the three different car types. Further, it has also been observed that the preference of Mercedes cars is positively influenced by the attributes such as age, income and years of education.

The information obtained so far can be used to determine the marketing strategy for the Automobile association. The advertisement for the different types of cars can be targeted to different people belonging to different customer profile. Mercedes cars can be shown to older people with higher income and higher education years. They will be more likely to buy the car. The middle aged people must be given preference for selling of Lexus and BMW cars.