This project leads you through a statistical analysis of used car price data. The data for this project was obtained from the car sales website www.carsales.com.au between 4 and 11 January 2016 (inclusive).
Part A covers parts of Topic 1, Part B parts of Topics 5 and 6 and Part Cparts of Topics 7 to 9.
It is suggested that you work on this project throughout Session 1.
Project Data
The data for this project can be accessed from the MySCU site for MAT10251 in Project under Assessment.
The data set provided contains 10 randomly chosen samples of size 125.
To obtain your data
(1) Click on the 'Project Data' file. This will download an Excel file.
(2) Select the 5 columns (Year to Price) of data for the sample specified by the last digit of your student ID number.
(3) Copy this into a new Excel file.
There are 10 sample data sets each of 5 columns (Year to Price)
Project Situation
Your statistical analysis ofused car price data is to enable you to answer questions from a relative or friend who is seeking to buy a used car of the make and model specified by your sample and has asked you for information and advice. Your relative or friend is restricting their search to the state they are living in also specified by the sample. For example, if your student ID number ends in 0 your sample is Sample 0 so your friend or relative is seeking to buy a Mazda 3 in New South Wales.
In each part of the project you are required to analyse your sample data in response to given questions and provide a written answer. You can assume that each written answer is a part of a letter or email to your friend or relative.
Project Preparation
You are expected to use Excel, or another spreadsheet or statistical package, when completing the project.
Your written answers presenting findings and conclusions should be considered as a part of a letter or email to a friend or relative.Each written answer should be a word document into which your Excel, or similar, output has been copied.
In addition, your statistical workings for Parts B and C should appear as appendices to your written answers. These should include all necessary steps and appropriate Excel output.
The written answers, with appendices for Parts B and C, should each be submitted as a single word document.
In preparing your appendices you may use one of the following formats:
- Word with Excel output added.
- Handwritten with Excel output added. This will then need to be scanned and added to your word document.
Notes
- You should not need to read beyond the study guide and textbook to complete the project.
- You probably will not need to reference, but if you do, use any consistent referencing style.
Part A Question
Your friend or relative has asked you for information on theprice of three and four year old cars of the make and model and in the state specified by your sample.
In particular, he/she is interested in the minimum and maximum price, the average price and an estimated price range for a three or four year old used car.
Tasks - Part A Submission
Complete the following tasks
1) Download and save your data.
2) Download the Project Part A cover sheets, name and save this file as
"Family Name_First Name_Part_A_Campus".
3) Enter your Sample Number on page 2 of the Part A coversheets.
4) Statistical Tasks
Using Pricedata explore prices of 2012 and 2013 used cars, by using Excel to:
- Construct a frequency histogram or polygon.
- Calculatedescriptive statistics.
Hint:The required data for 2012 and 2013 used carsis in the first rows of your sample.
5) Written Answer - Email or Letter
Using the instructions given on page four of the Part A coversheets, introduce your data and the results of your preliminary investigation ofprices ofthree and four year old used cars, of the make and model and in the state specified by your sample.
This should beone to two pages and 300 to 500 words.
Use an appropriate style, without statistical jargon and equations, to clearly communicate your results.
6) Complete Coversheets 1 and 2, save and submit Part A of the project online using Project Part A link in Submit Projectby the due date Tuesday15th March 2016.
Written Answer - Letter/Email
- 300 to500 words and one to two pages - marks will be deducted if this is greatly exceeded.
- To obtain full marks must:
- Be well structured.
- Clearly communicate the results of the Excel output in language appropriate for your audience.
- Include appropriate graph and summary statistics.
- Provide information on average price ofthree and four year old used cars, how prices vary and any pattern to prices.
- Provide an estimated price range for a three or four year old used car.
- Marks will be deducted if:
- There is little or no comment on, or interpretation of, the Excel output.
- Unnecessary statistical jargon and equations appear.
- It is confusing or not readable.
- It is handwritten.
- For each major spelling and/or grammatical error half a mark will be deducted, up to a maximum of two marks.
- Also up to two marks may be deducted for poor structure and/or presentation.
Data Analysis Project - Part B
Tasks
Task 1 Part A Self-Marking
When directed to do so during Week 5 complete the following tasks
1) Open yoursaved copy of your submission for Part A.
2) Replace the Part A coversheets (three pages) with the Part B coversheets (first four pages).
3) Rename and save this file as
"Family Name_First Name_Part_B_Campus".
4) Use the solution template and marking guide provided to mark your submission for Part A. Enter recommended marks on the self-marking sheet for Part A, page 3 of the file in 3) above.
5) Write a short (approximately 200 words) reflection/feedback on your submission and marking of Part A. In particular;
- consider the good aspects of your submission, what did you do well,
- identify where you made mistakes, and how you would avoid them in the future,
- considerwhat you learnt from submitting and marking Part A.
This is to be entered in the space at the bottom ofthe self-marking sheet for Part A.
6) Save file. This is to be submitted with Part B - due Tuesday 26th April 2016.
Task 2 Part B Appendix - Statistical Inference
The following statistical tasks should appear as appendices to your written answer. This should include all necessary steps and appropriate Excel, or equivalent, output.
These appendices should come after your written answerwithin your single word document for Part B.
In preparing your appendices you may use one of the following formats:
- Word with Excel output added.
- Handwritten with Excel output added. This will then need to be scanned and added to your word document.
Question 1 - Topic 5
Your relative or friend asks you for an estimate of the averageprice of a three or four year old car of the specified make and model in the state specified by your sample.
To provide this estimate use Pricedata for 2012 and 2013 used cars and an appropriate statistical inference technique to answer the following question.
What is the mean price of athree or four year old car of the specified make and model in the specified state?
Note: the required data for 2012 and 2013 cars is in the first rows of your sample.
Question 2 - Topic 6
Your relative or friendwould prefer to purchase a car with a manual transmission and wishes to know if this will limit their choice.
To provide a justified answer to this question use the Transmission data (where A = Automatic transmission, M = Manual transmission) for all cars in your sample and an appropriate statistical inference technique to answer the following question
Do more than 30% of cars, of the specified make and model, for sale in the specified state have manual transmission?
Task 3 - Part B Written Answer- Letter or Emails
For each question present the results of your calculations, with your interpretation and conclusion, as part of a letter or email to your friend or relative.
Use the instructions given on page five of the Part B coversheets.
This should be one to three pagesand200 to 400 words.
It should be submitted as a Word file with Excel output included.
Make sure you:
- Introduce the question and put it in context.
- Answer the question in non-statistical language.
- Present the results of your intervals or tests without unnecessary statistical jargon.
- Include conclusions which answer the given questions.
Part A Self-Marking
Full marks will be given for an "acceptable self-marking and reflection". This is defined as the majority of errors (in particular major or obvious errors) are recognised and considered in marking and reflection.
Zero marks will be given if no or minimal reflection and/or self-marking or major errors are not recognised.
Statistical Calculation
- For the intervals and tests marks will be given for:
- Choice of appropriate statistical technique/s.
- Random variable defined.
- Correct hypotheses for a test.
- Correct statistical calculations, including Excel.
- Correct interpretation of results.
Written Task - Letter/Emails
- 200 to 400 words and one to three pages - marks will be deducted if this is greatly exceeded.
- To obtain full marks must:
- Be well structured and analysed.
- Answer the questions and clearly communicate the results of the Excel output in language appropriate for your audience.
- Include an introduction to and conclusion for each question.
- Include appropriate Excel output.
Data Analysis Project - Part C
Task 1 Part C - Appendix Statistical Inference and Regression and Correlation
The following statistical tasks should appear as appendices to your written answer. This should include all necessary steps and appropriate Excel, or equivalent, output.
These appendices should come after your written answer within your single word document for Part C.
In preparing your appendices you may use one of the following formats:
- Word with Excel output added.
- Handwritten with Excel output added. This will then need to be scanned and added to your word document.
Choose a level of significance for any hypothesis test and a level of confidence for any confidence interval. Enter these values on page 2 of the Part C cover sheets along with the sample number from Part A.
Use your sample and appropriate statistical inference and regression and correlation techniques to answer the following questions.
Question 1 Statistical Inference Topic 7
Your relative or friend asks you if used car prices are generally higher for cars with automatic transmission than those with manual.
Use Price and Transmission data (where A = Automatic transmission, M = Manual transmission) for all cars in your sample and an appropriate statistical inference technique to answer the following question
On average is the price of cars, of the specified make and modelfor sale in the specified state, with automatic transmission higher than those with manual transmission?
Question 2 Simple Linear Regression model Topic 8
Your friend or relative asks you how the value of the car that they decide to purchase will depreciate in value.
Use Age(independent variable) andPrice (dependent variable) to model the relationship between age of a used car and its price.
Then to provide an answer on how how the value of the car that your friend or relative decides to purchase will depreciate in valueexplore this relationship by
1. Plotting the data with a scatter plot.
2. Calculating the least squares regression line, correlation coefficient and coefficient of determination.
Question 3 Multiple Linear Regression model Topic 9
Your relative or friend now wants to know what other factors may have an influence on price.
To explore this addKilometres and Transmission as additional independent variables to the regression model developed in Question 2. Then explore the relationship between these variables by
1. Calculating the multiple regression equation, multiple correlation coefficient, and coefficient of multiple determination
2. Using appropriate tests to determine which independent variables make a significant contribution to the regression model.
Hence, determine which independent variables to include in your model.
Attachment:- Project Data.xlsx