ETW1001 Introduction to Statistical Analysis
Group Assignment
Semester: Oct Intake, 2025
Due: Monday, 14 January 2025, 11:55 p.m.
The unit learning objectives of this assignment are:
Assess the relevance and usefulness of predictive modelling to address business and economic challenges.
Communicate statistical results to stakeholders effectively to propose business and economic solutions as a team.
This assignment is worth 30% of your final mark for this unit. The total number of marks for this assignment is 80.
INSTRUCTIONS
1. Make sure that you regularly make back-up copies of your work. Computer, disk, or cloud problems will not be accepted as valid reasons for late submissions or requests for extensions.
2. Students should pay particular emphasis on the narration, and how the results are presented and interpreted. Students should endeavour to ensure that the report is complete and well-composed. Poor presentation, poor command of English writing and/or failure to comply with instructions may result in a mark penalty.
3. Your answer to the questions should be no more than 15 pages (inclusive of graphs and tables). Any part of the report beyond the 15-page limit will be struck out and not marked.
(a) Use default format, paragraph, and margin settings.
(b) Font size: 12
(c) At least 1.15 line spacing between lines.
(d) Reference list is not counted in the 15-page limit.
(e) Penalties may apply if the assignment does not conform to the formatting guide- lines.
(g) All workings and relevant Excel output must be clearly shown where appropriate as marks will be awarded for workings. Make sure all your workings are included in an Excel file with proper labels. All tables and visualisations must be included in the written report. The presentation of output must be in reasonable size and readable.
4. Students must uphold academic integrity at all times. Any students caught for cheating, plagiarizing or permitting others to plagiarize their work will be reported to the Responsible Officer for academic misconduct in accordance to the Student Academic Misconduct Procedure. Severe penalties may apply resulting from the investigation.
5. Generative AI tools are restricted for certain functions in this assessment task. In this assessment, you can use generative artificial intelligence (AI) in order to conduct research pertaining to the assessment task only. Any use of generative AI must be appropriately acknowledged (see Learn HQ).
6. All submissions will be via Moodle by 14th January,2025 [before 11.55pm]
(a) Please type your report in Microsoft Word, save it as a PDF file, and submit the PDF document. Additionally, you must submit the accompanying Excel document. In total, you are required to submit two files:
1. The PDF file (containing all relevant answers). Written report (Format: .pdf) [Should have the name and student ID for each member]
2. The Excel file. Excel workbook (Format: .xlsx). Important:
All answers must be included in the PDF file. Only the PDF file will be graded. Any answers found exclusively in the Excel file will not be marked.
(b) You will also be required to put your assignment through a Turnitin report. The similarity index should not be more than 20%. Note that this is only a rough guideline we understand that some common usage of phrases and sentences may contribute to the similarity index. Students should not be worried for this particular instance.
Problem Scenario
Presume that you are a real estate agent working for an international property firm. Your task is to investigate the variables that are relevant in determining house selling prices. The firm has access to a large dataset, and you have selected a sample of 1,250 properties for your analysis.
As a property agent, your primary role is to identify and analyze the significant factors that influence house selling prices. By understanding these variables, you can provide valuable insights to clients, assist in strategic pricing decisions, and support the firmin staying competitive in the real estate.
Data
Download the data file “HousePrice” from Moodle
The key dependent variables are as follows:
The file contains the following variable:
Selling Price: Selling house price in $. [Dependent Variable]
Land Value : Land area value in $.
Building Value : Total building value in $.
Basement: basement room in square feet.
Baths: Number of bathrooms.
[Note: Most bathrooms contain a toilet and sink as well as a bathtub and shower]
Toilets: Number of toilets.
[Note: In most houses, the toilet is located within the bathroom. However, in newer homes, it is increasingly common to find toilets situated in separate spaces, such as a powder room or a dedicated hall area, which contain only a toilet and a sink, without a bathtub or shower.]
Fireplaces: Number of fireplaces in a house.
Beds: Number of bedrooms in a house.
Rooms: Rooms without bed such as power room, TV room etc.
AC: Indicator variable for house being air-conditioned (1 = air-condition, 0 = otherwise).
Age: age of the house.
Your group is required to use a subset of the survey data to answer the following questions. Specifically, your sample should consist of 250 consecutive observations, starting from the observation whose ID matches the last three digits of any group member’s student number. For example, if a group member’s student ID is 20275749, group should start with observation 749 and include observations up to 998.
Question 1 [Total 40 marks]
a) Construct an appropriate chart to illustrate the relationship between the dependent variable on the land value, building value, age of the house, toilets and air condition. Describe the relationship suggested by the charts in part (a). [10 marks]
b) Run a Simple Linear Regression (SLR) with the dependent variable on the land value, building value, age of the house, toilets and air condition. The summary output of the SLR should be shown. [5 marks]
c) Report the estimated equation from part (b). Label each of the models as Model 1, Model 2, Model 3, Model 4, and Model 5. [5 marks]
d) Interpret the estimated values of the regression coefficients for Model 1 and Model 2 only. [Hint: required to interpret intercepts and slopes] [4 marks]
e) Obtain a 95% confidence interval for the slope coefficient in Model 1 [You required to show the calculation for the confidence interval. Answer direct from the excel output will not be awarded any marks. You are required to show the working] Interpret your results. [4 marks]
f) What is the value of the coefficient of determination for Model 1? Interpret this value. [2 marks]
g) Test the null hypothesis that land value is not a significant predictor of the selling house prices at a 5% level of significance against the alternative that are significant. Use the critical value approach. Carefully show all steps. [4 marks]
h) Using a p-value approach at a 5% level of significance, test the null hypothesis that building value not a significant predictor of the selling house prices at a 5% level of significance against the alternative that it has a significant positive effect. Carefully show all the steps. [2 marks]
i) Predict the selling price of a house if the building value is $70,000. [1 mark]
j) Predict the selling price of a house if the building value is $156,000. [1 mark]
k) Explain whether the predictions in (i) and (j) are reliable. [2 marks]
Question 2 [Total 28 marks]
a) Run a Multiple Linear Regression (MLR) with a house selling price as the dependent variable with ALL the independent variables. Name this model as Model 6. Summary output of the MLR should be shown. [3 marks]
b) Formulate an appropriate Multiple Linear Regression estimated model [Model 6] that predicts the selling house price. [4 marks]
c) Write down the estimated Multiple Linear Regression equation based on Model 6. [3 marks]
d) Interpret the estimated coefficient of the land value and air-condition using Model 6. [4 marks]
e) What is the expected sign for age of the house? Explain your reasoning. [2 marks]
f) Using a p-value approach at a 5% level of significance, test the null hypothesis that age of the house is not a significant predictor of the selling house prices at a 5% level of significance against the alternative that it has a significant negative effect. Carefully show all the steps. [4 marks]
g) Without doing any calculation which variables contribute significantly to the prediction of house selling price? Why? [2 marks]
h) By removing all the insignificant variables from Model 6 and then form a Multiple Linear Regression with significant variables. [Name it as Model 7]. Summary output should be shown. [2 marks]
i) Using an appropriate method compare Model 6 and 7. Which model is better? Explain. [2 marks]
j) Using Model 7, predict the house selling price by substituting the fifth observation from your sample. [2 marks]
Question 3 [10 marks]
Based on your analysis above, write a concise report summarizing the key findings for your firm.
Your report should highlight the significant variables influencing house selling prices and explain how these factors can guide strategic pricing decisions. Emphasize the practical implications of the results, such as how the insights can help the firm optimize pricing strategies for the house sellers and remain competitive in the real estate market. Additionally, discuss how these findings can be used to identify trends, improve client recommendations, practical implications of the results, enhance the firm's overall market positioning and recommendations. [Your report should be less than 250 words]
Your report should have following scopes:
o An introduction to the topic
o Key findings or analysis
o A conclusion or summary
o References if any [10 marks]
Formatting [2 marks] The overall report should provide a concise and consistent format with a clear label for each figure. Remember, you are representing your organization to present this study so prepare your report that will be detailed and suitable for readers.