STATISTICAL ANALYSIS PROJECT

This project leads you through a statistical analysis of residential property data from a given non-capital city or town in Australia. This property data is also compared with property data from another non-capital city or town.

Project Situation - To analyse the real estate market in non-capital cities and towns Safe-As-Houses Real Estate, a large national real estate company, has collected data from random samples of residential properties for sale for a selection of non-capital cities and towns in States A, B and C.

As a research assistant for Safe-As-Houses Real Estate, you are analysing this data for the town or city specified by your sample. In addition, you compare the price data for this location with price data from another town or city. For example, if your student ID number ends in 8 your sample is Sample 8. That is, you will be analysing the real-estate market in Regional City 1, State B. You will also compare the residential property price data in Regional City 1, State B with the price data for Regional City 2, State A.

In each part of the project, you are required to analyse your sample data in response to given questions and provide a written answer. You can assume that the written answers are components of a longer report on the real estate market in your given city or town.

Data Analysis Project Part A -

Purpose: To

• introduce you to the project data, situation and Excel
• use Excel to graph data and calculate summary statistics
• interpret and communicate Excel results.

Part A Question -

From past research, Safe-As-Houses Real Estate is aware that the majority of first homebuyers purchase properties with three bedrooms.

You are asked to provide information on the price of three bedroom residential properties for sale in the location and state specified by your sample. In particular, information on the minimum and maximum price and the average price is required. As is an estimated price range for a three-bedroom property.

Data Analysis Project Part B -

Purpose: To

• obtain feedback on your submission in Part A and to gain experience in self-evaluation of submitted work
• apply your knowledge of statistical inference to answer questions about property prices by analysing the data and communicating the results.

Question 1 - Topic 5

Older buyers are often looking to downsize, moving from a four or more bedroom house to a smaller two or three bedroom unit.

Explore if older buyers wishing to downsize have a reasonable choice of units to choose from by using the Type data (6th column of your data) for ALL 125 residential properties for sale and an appropriate statistical inference technique to answer the following question

• What proportion of residential properties for sale, in the location and state specified by your sample, are units?

Question 2 - Topic 6

From past research, Safe-As-Houses Real Estate is aware that many potential buyers consider a non-capital city or town too expensive if the average house price is more than half a million dollars.

Explore if potential buyers would consider house prices in the location and state specified by your sample too expensive by using the Price $000 data (first column of your data) for ALL houses for sale and an appropriate statistical inference technique to answer the following question

• In the location and state specified by your sample, is the mean house price more than $500,000?

Data Analysis Project Part C -

Purpose: To answer questions about property prices by applying your knowledge of statistical inference, and regression and correlation. To communicate the results.

Question 1 Statistical Inference Topic 7

Safe-As-Houses Real Estate is comparing residential property prices in different locations. In particular, they are interested if there is a difference in average price between two given locations.

You are required to decide if there is a difference in average price between the residential properties for sale in the location and state specified by your sample and those in the location and state specified in the last column of your data.

For example, if your student ID number ends in 2 you will be comparing residential property prices in Coastal City 1 State A with those in Coastal City 1 State B.

To provide a justified decision use Price $000 (first column of your data) and Location X State Y Price $000 (last column of your data) for ALL 125 residential properties for sale in each sample, with an appropriate statistical inference technique to answer the following question.

• Is there a difference in the mean price of residential properties for sale in the two locations?

Questions 2 and 3 Simple and Multiple Linear Regression

Safe-As-Houses Real Estate is interested in developing a model to predict the price of a residential property for sale.

To develop such a model, first develop a simple linear regression model to predict price from internal area and then a multiple linear regression model to predict price from internal area, number of bedrooms and if the property is a unit or house. Finally choose, or construct, and then interpret the linear model that best fits your data.

Question 2 Simple Linear Regression Model Topic 8

To explore the relationship between the internal area of a residential property and its price use Internal Area m^2 (independent variable - second column of your data) and Price $000s (dependent variable - first column of your data) for all 125 residential properties for sale in your sample. Using this data 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 equation, 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 price of a residential property for sale use Internal Area m^2, Bedrooms and Type, (three independent variables - second, third and sixth columns of your data) and Price $000 (dependent variable - first column of your data), for all 125 residential properties for sale in your sample. Using this data 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 residential property for sale by:

• Using appropriate tests to determine which independent variables make a significant contribution to the regression model.
• Using the results of the above tests to give or calculate the simple or multiple regression equation which best fits the data.

Attachment:- Assignment File.rar