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ECON 1030 - BUSINESS STATISTICS 1 PROJECT (WEDNESDAY) Due: 16**More:**

**ECON 1030 ? BUSINESS STATISTICS 1 PROJECT (WEDNESDAY)**

**Due: 16 October at 23:59**

** **

**Instructions:**

**This is a project where you can work alone or with two other students (a maximum group size of three). All group members will receive the same marks for the assignment. All group members must be enrolled in the same tutorial. The assignment must be provided in the form of a (brief) business report approximately 8-14 pages. You must submit an electronic copy of your assignment in Blackboard. Hard copies will not be accepted. SHOW YOUR WORK for calculation based questions.**

** **

**This assignment requires the use of Microsoft Excel. If you have Windows, you will also need to use the Data Analysis ToolPak. If you have a Mac with Excel 2011, you will need to use StatPlus:MAC LE.**

** **

**Problem Description:**

**A resale market for automobiles would like to know what features of automobiles are typically driving the prices of new vehicles. This is especially important in helping to design their website in order to highlight the critical features that consumers are concerned with. A sample of 35 recent models of automobiles was taken. Several characteristics of the automobiles including the power of the engine, weight, fuel efficiency, type of transmission as well as the body style were included in the table.**

** **

**You will use descriptive statistics, inferential statistics and your knowledge of multiple linear regression to complete this task.**

** **

**Price (Dependent Variable) and several characteristics (Independent Variables) are given in the Excel file: Wednesday.xlsx.**

** **

**Here is a table describing the variables in the data set:**

Variable | Definition |

Price | Drive-away price of vehicle including taxes and fees |

Power | Power of engine in kW |

Kerb Weight | Mass of vehicle in kg with standard equipment and unoccupied |

Fuel | Typical fuel usage in Litres per 100 km |

Automatic | Dummy variable to indicate that the vehicle has an automatic transmission |

Hatchback | Dummy variable to indicate that the body type is a hatchback |

Sedan | Dummy variable to indicate that the body type is a sedan |

SUV | Dummy variable to indicate that the body type is a SUV |

Convertible | Dummy variable to indicate that the body type is a convertible |

** **

** **

**Required:**

** **

**Calculate the descriptive statistics from the data and display in a table. Be sure to comment on the central tendency, variability and shape for Price, Power, Kerb Weight and Fuel. How would you interpret the mean of dummy variables such as Automatic or Hatchback? (1 Mark)**

**Draw a graph that displays the distribution of fuel consumption. Be sure to comment on the distribution. (1 Mark)**

**Create a box-and-whisker plot for the distribution of the prices and describe the shape. Is there evidence of outliers in the data? (1 Mark)**

**There is a common belief that hatchbacks are underpowered. What is the likelihood that a hatchback will has an engine that has more than 100 kW power? Is the engine power statistically independent of the type of vehicle body? Use a Contingency Table. (2 Marks)**

**Estimate the 95% confidence interval for the population mean kerb weight. (1 Mark)**

**The Department of Infrastructure and Regional Development has recently stated that they would like to see SUVs become more fuel efficient, specifically under 9 L per 100 km. Test the claim at the 10% level of significance that the fuel efficiency is below 9 L per 100 km. (1 Mark)**

**Run a multiple linear regression using the data and show the output from Excel. Exclude the dummy variable ?Convertible? from the regression results. (1 Mark)**

**Is the coefficient estimate for the Power statistically different than zero at the 5% level of significance? Set-up the correct hypothesis test using the results found in the table in Part (G) using both the critical value and p-value approach. Interpret the coefficient estimate of the slope. (2 Marks)**

**Interpret the remaining slope coefficient estimates. Discuss whether the signs are what you are expecting and explain your reasoning. (2 Marks)**

**Interpret the value of the Adjusted R ^{2}. Is there a large difference between the R^{2} and the Adjusted R^{2}? If so, what may explain the reasoning for this? (1/2 Mark)**

**Is the overall model statistically significant at the 5% level of significance? Use the p-value approach. (1/2 Mark)**

**Based on the results of the regressions, what other factors would have influenced the price of vehicles? Provide a couple possible examples and indicate their predicted relationship with the review score if they were included. (1 Mark)**

**Predict the average price of an automatic hatchback which weighs 1100 kg with 97 kW of power that uses 6.7 L per 100 km of fuel if it is appropriate to do so. Show the predicted regression equation. (1 Mark)**

**Do the results suggest that the data satisfy the assumptions of a linear regression: Linearity, Normality of the Errors, and Homoscedasticity of Errors? Show using scatter diagrams, normal probability plots and/or histograms and Explain. (2 Marks)**

**Would these results tell us anything about the population distribution of vehicles on the road? If not, describe a scenario in how you would construct a sample to sample vehicles on the road. (1 Mark)**

** **

** **

**Allocation of Marks:**

**Professional Business Report 2 Marks Part A 1 Mark Part B 1 Mark Part C 1 Mark Part D 2 Marks Part E 1 Mark Part F 1 Mark Part G 1 Mark Part H 2 Marks Part I 2 Marks Part J 1/2 Mark Part K 1/2 Mark Part L 1 Mark Part M 1 Mark Part N 2 Marks Part O 1 MarkTotal: 20 Marks**

Cover sheet for submission of work for

Cover sheet for submission of work for

assessment School: Economics, Finance and Marketing

Program Name

Course/unit name

Business Statistics 1

Due Date 16 October 2016 Program Code

Course/unit code ECON1030 Name of

Lecturer

Tutor?s Name Tutorial Day/Time

STUDENT/S

Family name Given name Student number (1)

(2)

(3) DECLARATION AND STATEMENT OF AUTHORSHIP

1.

2.

3.

4.

5.

6. I/we hold a copy of this work which can be produced if the original is lost/damaged.

This work is my/our original work and no part of it has been copied from any other student?s work or from any other source except where

due acknowledgement is made.

No part of this work has been written for me/us by any other person except where such collaboration has been authorized by the

lecturer/teacher concerned.

I/we have not previously submitted this work for this or any other course/unit.

I/we give permission for this work to be reproduced, communicated, compared and archived for the purpose of detecting plagiarism.

I/we give permission for a copy of my/our marked work to be retained by the school for review and comparison, including review by

external examiners. I/we understand that:

7. 8. Plagiarism is the presentation of the work, idea or creation of another person as though it is my/our own. It is a form of cheating and is a

very serious academic offence that may lead to exclusion from the University. Plagiarised material can be drawn from, and presented in,

written, graphic and visual form, including electronic data and oral presentations. Plagiarism occurs when the origin of the material used

is not appropriately cited.

Plagiarism includes the act of assisting or allowing another person to plagiarise or to copy my/our work. Student signature/s

I/we declare that I/we have read and understood the declaration and statement of authorship.

(1)

(2)

(3) Further information relating to the penalties for plagiarism, which range from a notation on your student file to expulsion from the University, is

contained in Regulation 6.1.1 Student Discipline and the Plagiarism Policy which are available on the Policies and Procedures website at

www.rmit.edu.au/policies. ECON 1030 ? BUSINESS STATISTICS 1 PROJECT (WEDNESDAY)

Due: 16 October at 23:59 Instructions:

This is a project where you can work alone or with two other students (a maximum group size of three). All

group members will receive the same marks for the assignment. All group members must be enrolled in the

same tutorial. The assignment must be provided in the form of a (brief) business report approximately 8-14

pages. You must submit an electronic copy of your assignment in Blackboard. Hard copies will not be

accepted. SHOW YOUR WORK for calculation based questions.

This assignment requires the use of Microsoft Excel. If you have Windows, you will also need to use the Data

Analysis ToolPak. If you have a Mac with Excel 2011, you will need to use StatPlus:MAC LE.

Problem Description:

A resale market for automobiles would like to know what features of automobiles are typically driving the

prices of new vehicles. This is especially important in helping to design their website in order to highlight the

critical features that consumers are concerned with. A sample of 35 recent models of automobiles was taken.

Several characteristics of the automobiles including the power of the engine, weight, fuel efficiency, type of

transmission as well as the body style were included in the table.

You will use descriptive statistics, inferential statistics and your knowledge of multiple linear regression to

complete this task.

Price (Dependent Variable) and several characteristics (Independent Variables) are given in the Excel file:

Wednesday.xlsx.

Here is a table describing the variables in the data set:

Variable

Price

Power

Kerb Weight

Fuel

Automatic

Hatchback

Sedan

SUV

Convertible Definition

Drive-away price of vehicle including taxes and fees

Power of engine in kW

Mass of vehicle in kg with standard equipment and unoccupied

Typical fuel usage in Litres per 100 km

Dummy variable to indicate that the vehicle has an automatic

transmission

Dummy variable to indicate that the body type is a hatchback

Dummy variable to indicate that the body type is a sedan

Dummy variable to indicate that the body type is a SUV

Dummy variable to indicate that the body type is a convertible Required:

A. Calculate the descriptive statistics from the data and display in a table. Be sure to comment on the

central tendency, variability and shape for Price, Power, Kerb Weight and Fuel. How would you

interpret the mean of dummy variables such as Automatic or Hatchback? (1 Mark)

B. Draw a graph that displays the distribution of fuel consumption. Be sure to comment on the distribution.

(1 Mark)

C. Create a box-and-whisker plot for the distribution of the prices and describe the shape. Is there evidence

of outliers in the data? (1 Mark)

D. There is a common belief that hatchbacks are underpowered. What is the likelihood that a hatchback will

has an engine that has more than 100 kW power? Is the engine power statistically independent of the

type of vehicle body? Use a Contingency Table. (2 Marks)

E. Estimate the 95% confidence interval for the population mean kerb weight. (1 Mark)

F. The Department of Infrastructure and Regional Development has recently stated that they would like to

see SUVs become more fuel efficient, specifically under 9 L per 100 km. Test the claim at the 10% level

of significance that the fuel efficiency is below 9 L per 100 km. (1 Mark)

G. Run a multiple linear regression using the data and show the output from Excel. Exclude the dummy

variable ?Convertible? from the regression results. (1 Mark)

H. Is the coefficient estimate for the Power statistically different than zero at the 5% level of significance?

Set-up the correct hypothesis test using the results found in the table in Part (G) using both the critical

value and p-value approach. Interpret the coefficient estimate of the slope. (2 Marks)

I. Interpret the remaining slope coefficient estimates. Discuss whether the signs are what you are expecting

and explain your reasoning. (2 Marks)

J. Interpret the value of the Adjusted R 2. Is there a large difference between the R 2 and the Adjusted R2? If

so, what may explain the reasoning for this? (1/2 Mark)

K. Is the overall model statistically significant at the 5% level of significance? Use the p-value approach.

(1/2 Mark)

L. Based on the results of the regressions, what other factors would have influenced the price of vehicles?

Provide a couple possible examples and indicate their predicted relationship with the review score if

they were included. (1 Mark)

M. Predict the average price of a hatchback which weighs 1100 kg with 97 kW of power that uses 6.7 L per

100 km of fuel if it is appropriate to do so. Show the predicted regression equation. (1 Mark)

N. Do the results suggest that the data satisfy the assumptions of a linear regression: Linearity, Normality of

the Errors, and Homoscedasticity of Errors? Show using scatter diagrams, normal probability plots

and/or histograms and Explain. (2 Marks)

O. Would these results tell us anything about the population distribution of vehicles on the road? If not,

describe a scenario in how you would construct a sample to sample vehicles on the road. (1 Mark) Allocation of Marks:

Professional Business Report

Part A

Part B

Part C

Part D

Part E

Part F

Part G

Part H

Part I

Part J

Part K

Part L

Part M

Part N

Part O

Total: 2 Marks

1 Mark

1 Mark

1 Mark

2 Marks

1 Mark

1 Mark

1 Mark

2 Marks

2 Marks

1/2 Mark

1/2 Mark

1 Mark

1 Mark

2 Marks

1 Mark

20 Marks

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