Statistical Analysis of Used Car Data
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# Statistical Analysis of Used Car Data

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### Question

PROJECT – PART A

Your relative wishes to purchase a two or three-year-old used car. They have asked you for information on the price of two and three-year-old cars of the make and model 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 two or three-year-old used car.

PROJECT – PART B

Task 1 Part A Self-Marking – 5 marks

When directed to do so during Week 5 complete the following tasks

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 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 could avoid them in the future,
• consider what you learnt from submitting and marking Part A.

This is to be entered in the space at the bottom of the self-marking sheet for Part A.

6) Save file. This is to be submitted with the rest of Part B – due Friday 22 December 2017.

Task 2 Part B Appendix – Statistical Inference (19 marks)

The following statistical tasks should appear as appendices to your written answer. This should include all necessary steps and appropriate Excel, or equivalent, output.

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.

Statistical Inference

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 B coversheets along with the sample number from Part A.

Question 1 – Topic 5 (8 marks)

Your relative believes that white cars are safer since they are more visible.  Therefore, they would prefer to purchase a white car and wish to know if this will limit their choice.

To provide a justified answer to this question use the White variable (where Yes = car for sale is white and No = car for sale is not white) for ALL 121 cars in your sample and an appropriate statistical inference technique to answer the following question

• What proportion of cars, of the specified make and model, for sale in the specified state are white?

Question 2 – Topic 6 (11 marks)

Your relative would prefer to purchase a car with a low odometer reading, preferably less than 50,000kmThey ask you if two and three-year-old cars of the specified make and model on average have an odometer reading of less than 50,000km.

To provide a justified answer to this question use the Odometer data for 2014 and 2015 cars in your sample and an appropriate statistical inference technique to answer the following question

• On average is the odometer reading of 2014 and 2015 cars, of the specified make and model for sale in the specified state, less than 50,000 km?

Task 3 – Part B Written Answer – Letter or Email (6 marks)

For each question present the results of your calculations, with your interpretation and conclusion, as part of a letter or email to your relative.

Use the instructions given on page five of the Part B coversheets.

This should be one to three pages and 200 to 400 words.

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

Make sure you:

• Introduce each 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.

PROJECT – PART C

Task 1 Part C – Appendix Statistical Inference and Regression and Correlation (31 marks)

The following statistical tasks should appear as appendices to your written answer. This should include all necessary steps and appropriate Excel, or equivalent, output.

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. Enter this value 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 (10 marks)

Your relative asks you 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 and Seller data (where Private indicates a private sale and Dealer a sale through a used car dealer) for all 121 cars in your sample 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 2 and 3 Simple and Multiple Linear Regression (21 marks)

Your relative asks you how the value of the car that they purchase will depreciate.

To answer this question you develop a simple linear regression model to predict price from age and a multiple linear regression model to predict price from age, odometer reading and transmission type. Then, to provide a justified answer to your relative's question, choose and interpret the linear model that best fits your data.

Question 2 Simple Linear Regression Model Topic 8

To explore the relationship between the age of a used car and its price, use Age (independent variable) and Price (dependent variable), for all 121 cars in your sample, to develop and then explore a simple linear relationship between the two variables by:

• Plotting the data with a scatter plot.
• 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 3 Multiple Linear Regression Model Topic 9

To explore what other factors may have an influence on the value of a used car use Age, Odometer and Transmission (three independent variables) and Price (dependent variable), for all 121 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 – Part C – Written Answer – Emails or Letter (9 marks)

For Question 1 and Questions 2 and 3 combined present the results of your calculations, with your interpretation and conclusions as part of a letter of email to your relative.

Use the instructions given on pages four and five of the Part C coversheets.

This should be 300 to 700 words and three to six pages.

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

Make sure you:

• Introduce each question and put it in context.
• Answer the questions in non-statistical language.
• Present the result of your calculations and tests without unnecessary statistical jargon.
• Include conclusions which answer the given questions.

In particular, for Questions 2 and 3:

• Explain the choice of independent and dependent variables.
• From your scatter plot discuss any apparent relationship between age and price. Comment on the strength, shape and sign of the relationship.
• Include and justify the best model.
• Discuss and interpret the values of the regression and correlation coefficients of the best model.
• Provide an answer to your relative's question. That is, how the value of the car that they purchase will depreciate?

### Solution

Letter

ABC

CAB Street,

CAB City

Dear ABC,

I am glad to write this letter to answer your questions regarding the price of used Mazda3 cars in New South Wales as well the different factors that influence the price of used cars in the state.

I appreciate your concern that you want to check that the average prices of used Mazda 3 cars for sales listed with private owners and dealers. Based on your query, I assessed the sample data available with me and found that out of the 121 cars for sale, 40 cars are listed with private owners and 81 cars with dealers in New South Wales and found that average price of these cars are \$16,432.5 and \$16,048.53 respectively. If you notice there is price difference of \$383.97. I have used a boxplot diagram to show that there is negligible difference between the average prices of privately held cars and with dealers.