You are working for the management of ESK Jewellery as a marketing consultant. The main business of ESK Jewellery is the retailing of diamond jewellery. They opened their first shop on the 1st June 2011. Since then, they have opened ten (10) shops across the city in the locations of the city central district, town centres and housing estates. Most of their shops are located in shopping malls, whereas some of their shops are located in neighbourhood centres. (Neighbourhood centres are the blocks typically located in the centre of the housing estates. Shops can only occupy the ground floors of these blocks.) Although a few members of ESK Jewellery management have good understanding on statistical models and methods, most of the members only have very basic understanding of statistics. It is quite likely that they only know what "mean" means. ESK Jewellery management would like you to study their sales patterns. They are particularly interested in identifying what variables drive "sales value" (i.e. revenue per sale or average price per sale). A market research paper, recently purchased by the management, identified 'caratage' and 'location' as two of the variables (reported as factors) affecting the price. Caratage refers to the size of the diamonds measured in carats. According to the market research paper, the caratage per sale figure was found to be higher in the city shops. Also, the items purchased in the city shops were comparatively more expensive. ESK Jewellery would like to check if this is true in the local market. Your past studies on similar businesses, like watch and cosmetic distribution, indicated that the size of the shop and the wealth of the area influenced purchases. Shop size data were readily available. However, the data for the wealth of the area were not. The average housing rental data were available. Therefore, the rental data of the area have been used in the past studies as a proxy for the wealth. You informed ESK Jewellery that they needed to collect data on price per sale, locations and the sizes of the shops, 'caratage' and the average housing rental of the area that each shop locates. ESK Jewellery randomly selected 1000 transactions from their 10 shops.

Part I

1.  Organise and present the data by using appropriately chosen charts. Explain why you have chosen the charts you used.

2.  Calculate and interpret the measures of location and dispersion for the data. Are all the variables equally suited for being described by the mean and standard deviation? Explain.

3.  Compute the probability that the mean caratage is at most 0.23. Compute the probability of a random transaction with a diamond of at most 0.23 carats. What is the difference between the two probabilities you have computed?  

Part II  

Use a suitable hypothesis-testing approach to analyse the sales patterns. You must do the followings:  

1.  First, state your hypothesis.  Then, explain which test(s) you will use to test your hypothesis. 

2.  Identify and fit a suitable linear regression model to the data. 

3.  Interpret the relevant statistics from the output generated by your software.

4.  Describe the relationship implied by the model you have estimated.

5.  Analyse if the assumptions of the models used are valid for the data. 

Part III  

1.  Apply an Analysis of Variance (ANOVA), and give an appropriate assessment of your model.

2.  Identify any statistical limitations (if any) and give explanations on how they could affect this analysis.

3.  Describe possible improvements which you would recommend in terms of how data may be collected and analysed in any follow-up work.

Part IV  

1.  Write a 500-word executive summary for ESK Jewellery management.  Summarize your analysis with the following:

a. Define the business problem/issue that ESK Jewellery wants to be addressed in your study.

b. Briefly elaborate the analysis/analyses that were found significant in your study.

c. List your findings and explain why these findings were significant.

d. Based on  your findings,  provide ESK Jewellery management  your recommendation(s).

Part V  

1.  Consider the company you are working for, or one you have worked at in the past. Identify a situation in which you believe a linear regression model could be applied. Identify the dependent and explanatory variables of interest for this model.