Reference no: EM132310071

Assignment

Part A

Purpose:   

To

• introduce you to the project data, situation and Excel

• use Excel to graph data and calculate statistics

• interpret and communicate Excel results

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.

• Calculate descriptive 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.

Part B
 
Purpose: To apply your knowledge of statistical inference and regression to answer questions about used cars for sale by analysing the data and communicating the results.

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?

Hint: Sort data on White to enable you to easily count the number of white cars in your sample.

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 (12 marks)

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.