# STATISTICAL ANALYSIS PROJECT This project leads you through a statistical analysis of used car data.

STATISTICAL ANALYSIS PROJECT

This project leads you through a statistical analysis of used car data. The data for this project was obtained from the car sales website 2 to 10 January 2019 (inclusive).

Project Data

The data set provided contains 10 randomly chosen samples of size 115.

To obtain your data

(1) Click on the Project Data file. This will download an Excel file.

(2) Select the 7 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 7 columns (Year to Price)

Your sample number matches the last digit of your SCU student ID number. For example, if your student ID number ends in 2 your sample is Sample 2 and you will be analysing used car data for Toyota Corolla cars for sale in Western Australiain columns Q2:W120.

Project Situation

An online consumer group Oz-Price-Watch regularly analyses used car prices in various Australian states. As a research assistant for Oz-Price-Watch, you are analysing the data for the Car and state specified by your sample. For example, if your student ID number ends in 0 your sample is Sample 0 and you will be analysing prices of used Toyota RAV4 (4 cylinder) in New South Wales.

You are required to analyse your sample data in response to the given questions and provide a written answer. You can assume that your written answers are components of a longer report on used car prices.

Project Preparation

You are expected to use Excel when completing the project.

Your written answers presenting your findings and conclusions should be considered as a part of a larger report on used car prices. Each written answer should be a word document into which your Excel output has been copied

In addition, your statistical workings for Part B should appear as appendices to your written answer. This should include all necessary steps and appropriate Excel output.

Each part of the project should be submitted as a SINGLE Word document, with appropriate Excel output added.

Notes

– You should not need to read beyond the study guide and textbook to complete the project.

Referencing

You are not required to reference.

However, as the format of your written answers are components of a longer report it may be appropriate to reference. In this case, use any consistent referencing style.

Furthermore, you are not required to use real references. That is, any reference can be fictitious/fake.

You are not required to reference any output or text from Part A that you reuse in Part B.

PROJECT – PART A

Part A Preliminary Analysis of Sample Data

Oz-Price-Watch has asked you for a preliminary analysis of your sample data. Your calculations and conclusions from this analysis may be incorporated in your answer for Part B

Tasks – Part A Submission

Complete the following

1) Download and save your data.

2) Download the Project Part A cover sheets, name and save this file as

“FamilyName_FirstName_Part_A_Campus”

3) Enter your Sample Number on page 2 of the Part A coversheets.

4) Statistical Answers: For used cars of the make and model for sale in the state specified by your sample perform the following

a) Price of two and three year old cars

UsingPrice (7th column of data) explore prices of 2016 and 2017 used cars, by using Excel to:

– Construct a frequency histogram or polygon for the price of two and three year old cars.

– Calculatedescriptive statistics for the price of two and three year old cars.

Note:The required data for 2016 and 2017 used cars is in the first rows of your sample.

b) Difference in price between cars for sale privately and those for sale by a used car dealer.

Use Price (7th column of data)andSeller(5th column of data), where Private indicates a private sale and Dealer a sale through a used car dealer, for all 115cars in your sample to explore if there is a difference in price between the samples by using Excel to:

– Construct separate boxplots, on the same plot or separately, for private sale prices and for used car dealer prices.

– Calculate descriptive statisticsfor private sale prices and for used car dealer prices.

Hint:Sort data on Seller to obtain two samples. That is, price of used cars sold privately and price of used cars sold through a used car dealer.

c) Relationship between price and age and between price and odometer reading

Explore the relationship between the price of a used car and its age and also the price of a used car and its odometer reading, by using Age (2nd column of data)and Odometer(3rd column of data)as independent variables with Price(7th column of data)as the dependent variable for all 115 cars in your sample, by using Excel to:

– Construct scatter plots for Age and Price and for Odometer and Price

– Calculate the correlation coefficient for Age and Price and for Odometer and Price.

5) Written Answer – Preliminary Analysis

Using the instructions given on pages4 and 5 of the Part A coversheets, introduce your data and the results of your preliminary investigation of theprice ofused cars, of the make and model in the state specified by your sample.

This should bethree to fivepages and 400 to 800words.

Use an appropriate style, without statistical jargon and equations, to clearly communicate your results.

PROJECT – PART B

Task 1 Part B – Appendices Statistical Inference and Regression and Correlation Tasks

The following statistical tasks should appear as appendices to your written answers. These should include all necessary steps and appropriate Excel output.

These appendices should come after your written answer within your single Word document for Part B.

Statistical Inference

Choose a level of significance for any hypothesis tests and a level of confidence for any confidence intervals. Enter these values on page 2 of the Part B coversheets along with the sample number from Part A.

For used cars of the make and model for sale in the state specified by your sample answer the following questions using appropriate statistical inference and regression techniques.

Question 1 – Topic 5

Since many buyers wish to purchase a two or three year old used car Oz-Price-Watch has asked you to provide information onthe average price of 2016 and 2017 cars of the make and model for sale in the state specified by your sample.

To enable you to answer this use Price (7th column of your data) for 2016 and 2017cars only, your output from Part A and an appropriate statistical inference technique to:

Estimate the population mean price of two and three year old used cars of the make and model for sale in the state specified by your sample.

Note: The required data for 2016 and 2017 cars is in the first rows of your sample.

Question 2 – Topic 6

Many buyers believe that white cars are safer since they are more visible. Therefore, they wish to purchase a white car.Oz-Price-Watch has asked you to explore if restricting a purchase to white cars will limit abuyer's choice. Past research by Oz-Price-Watch has shown that if a search is restricted to a feature, for example colour or transmission, which at most 30% of cars for sale have then buyer choice is limited.

To provide a justified answer to the question use White (6th column of data,where Yes = car for sale is white and No = car for sale is not white) for ALL 115 cars in your sample and an appropriate statistical inference technique to answer the following question

Are more than 30% of used cars of the make and model for sale in the state specified by your sample white?

Question 3 Topic 7

Oz-Price-Watch wishes to know if there is a difference in price between cars for sale privately and those for sale by a used car dealer.

To provide a justified answer to this question use Price(7th column of data)and Seller (5th column of data) for all 115cars in your sample, your output from Part A and an appropriate statistical inference technique to answer the following question

Is there a difference in the average price of cars, of the specified make and model for sale in the specified state, for sale privately and by a used car dealer?

Hint: Sort data on Seller to easily obtain two samples – Prices for private sellers and for used car dealers.

Questions 4 and 5 Simple and Multiple Linear Regression

Oz-Price-Watch asks you how the value of a used car, of the specified make and model, depreciates.

To answer this you develop a simple linear regression model to predict price from age or odometer reading and a multiple linear regression model to predict price from age, odometer reading and transmission type. Then, to provide a justified answer to Oz-Price-Watch, choose and interpret the linear model that best fits your data.

Question 4 Simple Linear Regression Model Topic 8

From your results in Part A choose either Age or Odometer as an independent variable, to predict Price.

To explore the relationship between the age or odometer reading of a used car and its price, use your output from Part A and Ageor Odometer(2ndor 3rdcolumn of data)as an independent variable with Price(7th column of data)as the dependent variable, for all 115 cars in your sample, to develop and then explore a simple linear relationship between the two variables by:

– Calculating the least squares regression line, correlation coefficient and coefficient of determination.

– Interpreting the gradient and vertical intercept of the simple linear regression equation.

– Interpreting the correlation coefficient and coefficient of determination. Are these values consistent with your scatter plot?

Note: You can choose either Age or Odometer as the independent variable in this model.

Question 5 Multiple Linear Regression Model Topic 9

To explore what other factors may have an influence on the value of a used car use your output from Part A andAge, Odometer and Transmission (2nd, 3rd and 4th columns of data) as three independent variableswith Price (7th column of data) as the dependent variable for all115 cars in your sample, to develop and then explore the relationship between these four variables by:

– Calculating the multiple regression equation, multiple correlation coefficient, and coefficient of multiple determination.

– Interpreting the values of the multiple regression coefficients.

– Interpreting the values of the multiple correlation coefficient and coefficient of multiple determination. Compare these values with the corresponding values for the simple linear regression model.

Then determine the best model to predict the price of a used car by:

– Using appropriate tests to determine which independent variables make a significant contribution to the regression model.

– Give or calculate the simple or multiple regression equation which best fits the data.

Notes:

– You may need to transform or manipulate the given data, before using Excel for the corresponding statistical calculations.

– Use Excel for all statistical calculations. You do not need to repeat any Excel calculations by hand. However, make sure that you define your random variables and include any steps not given by Excel. For example, in a hypothesis test include the null and alternative hypotheses, along with the decision to reject or not reject the null hypothesis.

– Mention any assumptions you need to make, where appropriate justify these from Part A output.

– In Question 4 fit a linear model even if from your scatter plot you decide that a non-linear relationship better fits the data or that no apparent relationship exists. However, mention this in your written answer and/or corresponding appendix.

– Comment on why a test or confidence interval has been chosen. Where appropriate include and refer to Part A output.

– Make sure you interpret confidence intervals and write conclusions to hypothesis tests.

Task 2 – Written Answer – Components of a report

For Questions 1, 2, 3 and Questions 4 and 5 combined present the results of your calculations, with your interpretation and conclusions as components of a longer report on used car prices.

Use the instructions given on pages 4 and 5 of the Part B coversheets.

This should be 500 to 1100 words and three to seven pages.

It should be submitted as a Word file with Excel output included.

Make sure you:

– Introduce each question and put it in context

– Answer each question in non-statistical language.

– Present the result of your calculations and tests without unnecessary statistical jargon

– Include a conclusion which answers the given question.

In particular, for Questions 4 and 5

– Mention or explain your choice of independent and dependent variables

– Include and justify the best model.

– Discuss and interpret the values of the regression and correlation coefficients of the best model.