Calculating the least squares regression equation

Assignment Help Applied Statistics

Reference no: EM131994288 , Length: word count:2000

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

Reference no: EM131994288

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Reviews

len1994288

5/24/2018 1:44:09 AM

Word Count: 2000 words. Project Preparation - You are expected to use Excel when completing the project. Your written answers presenting your findings and conclusions should be considered as a part of a larger report on the real estate market in your given city or town. Each written answer should be a word document into which your Excel output has been copied. In addition, your statistical workings for Parts B and C should appear as appendices to your written answers. These should include all necessary steps and appropriate Excel output.

len1994288

5/24/2018 1:44:00 AM

Each part of the project should be submitted as a single Word document. 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. Notes - You should not need to read beyond the study guide and textbook to complete the project. Referencing - You are not required to reference. However, as the format of your written answer is a component of a longer report it may be appropriate to reference. In this case, use any consistent referencing style.

len1994288

5/24/2018 1:43:53 AM

Project Submission - Each part of the project should be a SINGLE Word file with Excel output included. The given cover sheets should be the first pages of your submitted project and are not part of the page limit. DO NOT submit your appendices, which are not part of the page limit, for either part B or C as separate files. Ensure that the page setup of your submitted document is A4 Portrait, with an appropriate format so that it is easily readable if printed. Use line spacing of at least 1.5. Please name your file “Family Name_First Name_Part_A/B/C_Campus” For example; Jayne _Nicola_Part_A_Lismore.

len1994288

5/24/2018 1:43:46 AM

Penalties For - Incorrect Sample - If you use a sample that does not correspond to the last digit of your student ID number, to be entered on the cover sheet, a maximum of two marks may be deducted, as this causes the marker extra work and frustration. Incorrect Format - If the page setup of your submitted Word file is not as required (that is, A4 Portrait, with appropriate format so that it is easily readable if printed), with at least 1.5 line spacing or your project is not submitted as a single Word document a maximum of two marks may be deducted, as this causes the marker extra work and frustration. In addition, if your file is not named as requested or the required cover sheets are not included or correctly completed a maximum of two marks may also be deducted, as this can cause the marker extra work and frustration.

len1994288

5/24/2018 1:43:39 AM

Marking Criteria – Part A - Read the marking criteria carefully and consider them when preparing your Part A Submission. See the marking and feedback sheet, page 3 Part A coversheets, for allocation of marks. Note: Later in Part B you will use these criteria to self-mark Part A of the project. Marking Criteria – Part B - Read these marking criteria carefully and consider them when preparing Part B. See the marking and feedback sheet, page 4 of Part B coversheets, for allocation of marks. Marking Criteria – Part C - Read these marking criteria carefully and consider them when preparing Part C. See the marking and feedback sheet, page 3 Part C coversheets, for allocation of marks.

len1994288

5/24/2018 1:43:32 AM

Part B Submission - You should submit one word document consisting of Part B coversheets – first four pages, including completed self-marking sheet for Part A with reflection. Copy of your Part A submission. Written answer as components of a report for Part B - this should follow the format given on page 5 of Part B coversheets. Appendices for Part B, which contain full statistical working for the required statistical tasks.

len1994288

5/24/2018 1:43:26 AM

Notes: You may need to transform or manipulate your sample data, before using Excel for the required statistical calculations. Use Excel for statistical calculations. You do not need to repeat any Excel calculations by hand. However, make sure that you define your random variables and include any steps not given by Excel. For example, in a hypothesis test include the null and alternative hypotheses, along with the decision to reject or not reject the null hypothesis. Mention any assumptions you need to make. Comment on why the test or confidence interval has been chosen. Make sure you interpret confidence intervals and write a conclusion to hypothesis tests.

len1994288

5/24/2018 1:43:20 AM

Notes: You may need to transform or manipulate the given data, before using Excel for the corresponding statistical calculations. Use Excel for the statistical calculations. You do not need to repeat any Excel calculations by hand. However, make sure that you define your random variables and include any steps not given by Excel. For example, in a hypothesis test include the null and alternative hypotheses, along with the decision to reject or not reject the null hypothesis. Mention any assumptions you need to make. In Question 2 fit a linear model even if from your scatter plot you decide that a non-linear relationship better fits the data or that no apparent relationship exists. However, mention this in your written answer and/or corresponding appendix.

len1994288

5/24/2018 1:43:14 AM

In Question 3 while there may be interaction between independent variables, you are not required to add interaction terms to your model or test for interaction. Similarly, in Question 3 while there may be collinearity of pairs of independent variables, you are not required to consider this or calculate a variance inflation factor (VIF). Comment on why a test has been chosen. Make sure you write conclusions to hypothesis tests. As a result of the best model determined in Question 3, you may need to develop an additional multiple regression equation with two independent variables or an additional simple linear regression equation. Alternatively, the best model may be the simple linear regression model developed in Question 2 or the multiple regression model with three independent variables developed in Question 3.

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