MAT1025 - Statistical Analysis - Project Data Assessment Answer

Internal Code: 1AGICG Code: MAT1025

Statistical Analysis Project Data Assessment Answer

Assignment Task: MAT1025  This project leads you through a statistical analysis of used car data. The data for this project was obtained from the car sales website www.carsales.com.au2 to 10 January 2019 (inclusive). Part A - MAT1025 

1. 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.

The difference in price between cars for sale privately and those for sale by a used car dealer. MAT1025  Use Price (7^th column of data)and the seller(5^th column of data), where Private indicates a private sale and Dealer a sale through a used car dealer, for all 115 cars 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.

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 (2^nd column of data)and Odometer(3^rd column of data)as independent variables with Price(7^th 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.

Written Answer – Preliminary Analysis - MAT1025  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 be three to five pages and 400 to 800words. Use an appropriate style, without statistical jargon and equations, to clearly communicate your results. Complete Coversheets 1 and 2, save and submit Part A of the project online using Project Part A link in Submit Project by the due date Tuesday 26 March 2019. PART B - Task 1 Part B - AppendicesStatistical Inference and Regression and Correlation Tasks  The following statistical tasks should appear as appendices to your written answers. These should include all the necessary steps and appropriate Excel output. These appendices should come after your written answer within your single Word document for Part B. Statistical Inference - MAT1025  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  - MAT1025  Since many buyers wish to purchase a two or three-year-old used car Oz-Price-Watch has asked you to provide information on the average price of 2016 and 2017 cars of the make and model for sale in the state specified by your sample. MAT1025 To enable you to answer this use Price (7^th column of your data) for 2016 and 2017cars only, your output from Part A and an appropriate statistical inference technique to: Estimate the population means price of two and three-year-old used cars of the make and model for sale in the state specified by your sample. Question 2 – Topic 6 - MAT1025  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 purchase to white cars will limit buyer's choice.  Past research by Oz-Price-Watch has shown that if a search is restricted to a feature, for example, color 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 - MAT1025  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(7^th column of data)and Seller (5^th 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? Questions 4 and 5 Simple and Multiple Linear Regression - MAT1025  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 - MAT1025  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(2^ndor 3^rdcolumn of data)as an independent variable with Price(7^th 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?

Question 5 Multiple Linear Regression Model Topic 9 To explore what other factors may have an influence on the value of a used car using your output from Part A and, Odometer and Transmission (2^nd, 3^rd and 4^th columns of data) as three independent variables with Price (7^th 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.

Task 2 - Written Answer – Components of a report - MAT1025  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: MAT1025

• 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 - MAT1025

• 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.

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