Econ940 Statistics For Decision Making Assessment Answers

Answer:

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 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.

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.

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.

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).

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. 

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.

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.  

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).

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.

Table 5: Income distribution of buyers of different luxury cars

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.

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.

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).

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.

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).

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.

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.

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.

Table 9: Income 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.

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 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 16^th level.

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 16^th level.

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 16^th level.

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 17^th level.

Table 12: Descriptive Statistics for education years showing preference for Mercedes

Figure 12 additionally showcase that people who have education level at 17^th, prefer Mercedes most and with rise in the education level preference of Mercedes falls gradually. 

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.

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).

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:

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.

Table 14.1: Summary of different income of different buyers’ group

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.

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.

Table 15.1: Summary of average income of different buyers’ group

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.

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.

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.

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).

Table 16.3: Goodness of fit statistics

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))))

Conclusion: 

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.

Reference:

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