BSTA011 - BUSINESS STATISTICS

GROUP ASSIGNMENT

This assignment is designed to assist you to achieve the following learning outcomes:

a.   Apply appropriate quantitative analytical techniques to qualify, support, select and evaluate data as information for use in business decision-making.

b.   Interpret and communicate results of quantitative analyses for business decision-making.

c.    Use a computer-based data analysis package (i.e. Excel) to critically analyse data.

Assignment value: 20%

Group of 3-5 students. The group members must be from the same tutorial. Your tutor will put you in groups in tutorials. In the event that you cannot find any group, let your Lecturer/tutor know asap. You are NOT allowed to complete this assignment by yourself or in groups of less than 3 members.

Submission:

Your team have been accepted as interns at Landcom. Landcom manages strategic and complex residential projects. Your first job is to conduct an analysis based on the recent sales price of the three suburbs of New

South Wales for the years 2021, 2022 and 2023 from All Homes or real estate. Your team needs to perform a comprehensive statistical analysis of the suburbs, which your tutors will suggest.

Q1. Collect and Compute the appropriate descriptive statistics of the “sold house price”, “Sold house land size”, and “sold house number of rooms” for the years 2021,2022 and 2023 of the suburban selected by your tutor. The descriptive statistics measures include central tendency (mean), variability (standard deviation), Mode, Quartiles, Range, and Interquartile range and show the infographics (e.g., pie chart, bar chart, etc.) of 2021, 2022 and 2023 data for the following variables:

(a) Sold house price

(b) Sold house land size

(c) Sold house number of rooms

The sample size should be at least 30 for each year (2021, 2022 and 2023) for each suburb. So, for one suburb, the total at least the number of houses recorded should be 90 for a three-years period.

Q2. Based on the descriptive statistics from Q1, briefly comment on the central tendency and variability of three suburbs for 2021, 2022 and 2023

Combine data from all group members in an Excel spreadsheet and use this collated sample to answer the following questions.

Q3. Choose one suburb and perform. the following task from 2021 and 2022 data: The historical data indicates that the high house prices (more than the average price; You should have the average house price of each suburb from question 1) are more likely to be associated with land size as compare to low house price (Below average house price). What is the probability of a high house price given that the house land size is extended (more than the average land size for the suburb)? What is the probability of low house prices given that the land size is non-extended (Land size below average)? Analyse your collated sample and examine whether it is indeed the case. Show the steps in your analysis (including justification for choice of techniques used and all calculations) and report your findings clearly and use a probability matrix.

Table: Probability matrix for 2021

Table: Probability matrix for 2022

Q4. (a) Choose one suburb and perform the following task from 2021,2022 and 2023 data. It is a common perception that the land size and the number of rooms available influence the house price. Investigate  the  following  relationships  using  multiple  linear  regression  analysis.  (i) Explore the relationship between land size and the house price, (ii) Explore the relationship between the available number of rooms and the house price. Use the multiple linear regression model and interpret the  result  of  p-values  of  independent  variables,  multiple  R,  Adjusted  R-squared, physical meaning of co-efficient and significance of “f“statistics.

(b) Using the suburb selected for part (a), conduct a regression analysis with the house prices and external economic factors (cash rate target, inflation rate, and unemployment rate) for the years 2021, 2022, and  2023,  utilizing  data  from  the Reserve  Bank  of  Australia  (RBA). Apply  multiple  linear regression models to examine the relationships between these variables.

Interpret the statistical measures derived from the regression models, including the multiple R, adjusted R-squared, and the significance of the F-statistic. Evaluate the importance of the independent variables by interpreting their p-values.

Develop two distinct regression models for task (a) and (b).

Q5. Choose one suburb and perform. the following task from 2022 data: Analyze the frequencies of two variables (House price level and land size) with multiple categories to determine whether the two variables are independent. Conduct Chi-Square Hypothesis test at 0.05 level to ensure that, whether house price level and land size are independent. Use the following table for Chi - square test:

Q6. What is the average house price of each selected suburb for 2023 (Use the house price average from question 1 and construct a 95% confidence interval for the average house price for each selected  suburb  of  New  South  Wales  for  the  year  2023)?  Note:  The  population  standard deviation of house prices in New South Wales is $20,000.

Q7. A recent study has claimed that the average house price in New South Wales is $1,187,200. Use your collected data to test this claim for each selected suburb for the year 2023 (Note: Use the sample statistics from question 1). Note: The population standard deviation of house prices in New South Wales is $20,000. Is there any evidence to suggest that the average house price has changed at a 5% significance level? Report your findings with clear conclusions and all supporting calculations.

Q8. Develop a rating for the three suburbs assigned to you, based on the provided crime statistics from Sydney Suburban Review . Complete the following tasks:

(i) Define a rating scale for the suburbs based on crime rates. For example:

• A: Suburbs with the lowest crime rates.

• B: Suburbs with moderate crime rates.

• C: Suburbs with the highest crime rates.

To establish the ratings, calculate the average crime incidents for NSW based on 408 suburbans crime average incident provided on Sydney Suburban Review . Suburbs with crime rates above the average should be categorized as C, those around the average as B, and those below the average as A.

(ii)Create visual representations, such as bar charts or maps, to display the crime ratings for each suburb.

(iii) Investigate the influence of crime rates on house prices. Provide a well-supported argument based on relevant evidence and research findings.