Statistics Generalized Linear Models †Free Samples to Students

Question: Discuss about the Statistics Generalized Linear Models. Answer: Introduction: The statistical data analysis plays an important role in the research study regarding any business problem or other organizational problems. The study of the consumption of the different types of beverages is helpful for understanding the habits of the students towards beverages. Also, this study should be helpful for the management of the products and production of the related companies. Here we have to analyze the survey data collected from the 75 students in the university. We have to study the average number of serves of different types of beverages. Also, we are interested in the demand and beverage preferences for the different types of beverages. Also, we want to check the impact of price on the change of preference of the beverages. For the analysis of the given data regarding the student preferences of the beverages, we have to use the descriptive statistics, graphical analysis and inferential statistics for the analysis of the given data. By using the descriptive statistics , we have to study some descriptive characteristics of the data. The use of inferential statistics or testing of hypothesis is mandatory for checking the different claims under study. We would check the claim regarding the difference between the average numbers of serves for the five different types of beverages. Research Question: For this research study, the research question or research hypothesis is established as below: Whether there is any significant difference in the average number of serves of five different types of beverages or not? Data collection is very important initial stage of any research study (Degroot, 2002). As we know the data of 75 students is randomly selected from the given population data, so we would get unbiased estimates for this research study. The selection of the 75 students is based on the simple random sampling method. The data is collected for the different questions in the given questionnaire. Data or responses from the respondents are collected from the students and stored in well prepared table or excel sheet. Then this data is used for the statistical analysis. Statistical Analysis: In this topic, we have to analyze the given data by using the statistical tools and techniques. We have to use descriptive statistics and inferential statistics for understanding the nature of data and checking the claims regarding the data variables. Descriptive statistics explains the idea about the nature and spread of the variable (Bickel, 2000). Frequency distributions are very useful for easy understanding of the distribution of the categories (Babbie, 2009). First of all we have to see some frequency distributions. The frequency distribution for the student origin is given as below: From the above table for frequency distribution for the variable student origin, it is found that there are 7 international students involved in the sample for research study. There are 68 domestic student participated in the research study. Now, we have to see the impact of price on the change of preference. The frequency distributions are summarised as below: From the given data, it is observed that 63 students are not ready for changing the preference of the beverages they use although the costs of the second preference beverages is reduced by 25%. For the same scenario, it is observed that 12 students are ready for changing their preference if the cost of the second preference is less than 25% of their first preference beverage. Now, we have to see the same distribution if the second preference was 40% cheaper than the most preferred beverage. The distribution is given as below: For the scenario of costs for second preference is less than 40%, it is observed that 44 students are not ready to change their first preference beverage while 31 students are ready to change their first preference if the cost of the second preference is less than 40% from the first preference. Now, we have to see the same distribution if the second preference was 60% cheaper than the most preferred beverage. The distribution is given as below: For the scenario of the reduction of the price of second preference by 60%, it is observed that 31 students are not ready for changing their preference. For these 31 students, there is no importance of cost against their preference. Remaining 44 students are ready to change their first preferences if the cost of the second beverage is reduced by 60%. This means, it is observed that the preference of the beverage would be change only if there is more significant difference between the prices of the beverages exists. Inferential statistics plays an important role in the process of decision making (Antony, 2003). Now, we have to check the hypothesis or claim whether the average number of serves of given five types of beverages (such as soft drinks, fruit juice, Tea/Coffee, Energy drinks, and other drinks) are same or not. For comparing the averages for more than two populations, the use of ANOVA is better as compared to multiple uses of t tests (Casella, 2002 Null hypothesis: H0: There is no any statistically significant differences in the average number of serves of given five types of beverages such as soft drinks, fruit juice, Tea/Coffee, Energy drinks, and other drinks. Alternative hypothesis: Ha: There is a statistically significant difference in the average number of serves of given five types of beverages such as soft drinks, fruit juice, Tea/Coffee, Energy drinks, and other drinks. The test statistic value for checking the significant differences between the population average numbers of serves of the five different types of beverages, the test statistic value for this ANOVA test is given as F = 118 approximately with the p-value of 0.00. We reject the null hypothesis that the average numbers of the serves of the beverages are same. This means we conclude that the average numbers of the serves of the beverages are not same. The average number of serves of soft drinks, fruit juice, tea-coffee, energy drinks, and other drinks are different. Conclusions: From the given data, it is observed that 63 students are not ready for changing the preference of the beverages they use although the costs of the second preference beverages is reduced by 25%. For the same scenario, it is observed that 12 students are ready for changing their preference if the cost of the second preference is less than 25% of their first preference beverage. For the scenario of costs for second preference is less than 40%, it is observed that 44 students are not ready to change their first preference beverage while 31 students are ready to change their first preference if the cost of the second preference is less than 40% from the first preference. For the scenario of the reduction of the price of second preference by 60%, it is observed that 31 students are not ready for changing their preference. For these 31 students, there is no importance of cost against their preference. Remaining 44 students are ready to change their first preferences if the cost of the second beverage is reduced by 60%. There is sufficient evidence to conclude that the average numbers of the serves of the beverages are not same. The average number of serves of soft drinks, fruit juice, tea-coffee, energy drinks, and other drinks are different. References: Antony, J, 2003, Design of Experiments for Engineers and Scientists, Butterworth Limited. Babbie, E, R, 2009, The Practice of Social Research, Wadsworth. Beran, R, 2000, React scatterplot smoothers: Superefficiency through basis economy, Journal of the American Statistical Association. Bickel, P, J, and Doksum, K, A, 2000, Mathematical Statistics: Basic Ideas and Selected Topics, Vol I, Prentice Hall. Casella, G, and Berger, R, L, 2002, Statistical Inference, Duxbury Press. Cox, D, R, and Hinkley, D, V, 2000, Theoretical Statistics, Chapman and Hall Ltd. Degroot, M, and Schervish, M, 2002, Probability and Statistics, Addison - Wesley. Dobson, A, J, 2001, An introduction to generalized linear models, Chapman and Hall Ltd.