SECTION A
GenXY Motors Pte Ltd sells second hand cars. The company has four shops in different locations either within or outside of the city area. Mr. Branson Lim, the general manager of GenXY, would like to expand their business by adding four more locations. The main objective is to maximise revenue by increasing the number of cars sold and the prices of transactions. Mr. Lim would like know the followings:
Where should the new locations be?
What make (brand) of cars should they hold in these locations?
What models of cars should they hold in these locations?
What features should be built in as standard in these cars?
What features should be added optionally?
Mr. Lim came across a study done by the Car Dealers Association (CDA) on sales of cars in year 2012. The sample had 1000 transactions randomly selected from car dealers in the country. The sample proportions for make, model and locations are similar to those of the population. Mr. Lim speculates that this study could help him to address the above questions but he is not sure how to interpret this study. Mr. Lim has engaged you as a consultant to help and has provided you an excel file “cars_dataset.xlsx” with this random sample of 1000 transactions. The variables in the data are:
CarID: Autogenerated ID of transactions in the sample
Price$: Price of car sold in Singapore Dollars
Mileage: Number of kilometres completed
MakeID: Numeric ID of the make (or brand) of the car
Make: Make (or brand) of the car
ModelID: NumericID of the model of the car
Model: Model of the car which briefly describes the main features of the car
Engine Capacity: Size of the engine capacity
Doors: Number of doors in the car
Sound: Sound upgrading; 1 indicates an upgrade and 0 indicates no upgrade
LocationID: Numeric ID of the location
Store Location: Location; 1 indicates within the city and 2 indicates outside of the city

Part I
1. Select three (3) factors (variables) from the data. There should be at least one (1) quantitative and one (1) qualitative variable. Describe 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 these variables. Explain when these measures are suitable for analysing the variables.
3. Identify the probability that a random transaction has a price that is more than $95,000. From past data, the population distribution for Price$ is normal with a mean of $82,333 and a standard deviation of $20,100. Discuss whether the probability can be computed if the population distribution is not normal.
Part II
Execute a statistical test to analyse which variables affect the price of cars significantly. You must do the following:
1. First, state your hypothesis and select an appropriate test to test your hypothesis. You must explain why you choose the test.
2. Identify and fit a suitable linear regression model to the data and interpret relevant statistics.
3. Determine two (2) Makes and two (2) Models that GenXY Motors should stock. Explain your choices.
4. Describe the relationship between the price and variables implied by the regression model you have estimated in question 2.
5. Discuss whether the assumptions used in estimating the regression model are valid for the data.
Part III
1. Apply a Correlation Analysis between Price$ and each independent variable. Compare this analysis with the method used in Part II. Discuss which method you would prefer to explain the variations in prices.
2. Discuss any statistical limitations (if any) in this analysis and give explanations on how they could affect this analysis.
3. State possible improvements which you would recommend in terms of how data may be collected and analysed in any follow-up work.
Part IV
1. Describe your findings in a 300-word executive summary for GenXY Motors Pte Ltd. The purpose of an executive summary is to provide an overview of your analysis. Summarise your analysis by including the following:
a. Your findings, conclusions, limitations and recommendations.
b. Essential analysis that support your findings, conclusions, limitations and recommendations.
c. A concise description of how your analysis was done.
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.