Multiple Linear Regression Analysis for Pricing Properties: Research, Variable Selection, Hypotheses

Business Scenario

Business Scenario

 

Following the preliminary analysis of the data employing descriptive statistics and graphical presentations (Assignment 1), further analysis is required with the aims of helping Happy Homes Ltd in the pricing of properties to be sold, and planning for improved sales performance in the property market going forward.  To provide realistic advice, it is necessary to understand which factors are related to SalesPrice and how strongly they are related. 

The dataset ‘HouseSales.xls’ contains the relevant data, and the explanation of all variables is in the ‘HouseSales_Variable Listing.docx’ file.  The dataset contains 345 cases (properties), and there are 32 property-related variables.  The latter includes a unique ID for each property (PropID) and a variable recording the price for which the property had been sold (SalesPrice) in pounds (£).    

You are to employ Multiple Linear Regression to analyse the data, identifying variables that act directly as predictors, or antecedents of SalesPrice.  It is part of your task to decide which variables to include as predictors in the regression analysis, bearing in mind the guidance below.  

Analysing the data requires the statement of hypotheses to be tested.  These hypotheses will be formulated based upon a review of some of the relevant literature on house pricing/ housing market, including in particular, peer-reviewed literature, but also where relevant e.g. industry reports.  These sources of literature are also needed when interpreting the findings.   

 
N.B.  5 marks will be allocated for layout, spelling, and grammar.

Section 1: Research Question(s) and Variable Selection and Hypotheses

1. As in all reports, you need to set out clear questions that you are investigating into in your report.  Please clearly state the broader research questions in the introduction of the report.  For example, what area-related factors most affect…, or alternatively, are good predictors of SalesPrice?  

Note that students are expected to provide enough broader questions to cover all the main predictors in the final model (with a minimum of 2). So 2 - 5 questions are required, but 2 is often sufficient.  Answering one of the latter questions will therefore, possibly (though not necessarily), Simply analysing data for more than one variable that falls under the broader category (e.g. there is more than one area-related variable covered by the example question above, but you may have only one such variable in the final model).   
(5 marks) 

2. Based on your knowledge and review of the literature on house pricing/ the housing market, and citing sources in your justification for choosing each predictor, formulate hypotheses (null and alternative for each) between each of the 5 predictor/ independent variables and the outcome/ dependent variable SalesPrice.

Section 2: Data Analysis

3. Produce descriptive statistics for each variable you have selected in Task 2.  Nominal and Ordinal variables also require a full frequency table in the report (Interval or Ratio variables do not require a frequency table in the report).  

Also, and as appropriate, produce measures of correlation/ association i.e. Pearson’s r (Pr), between the variables you have selected in Task 2

and SalesPrice. (10 marks)

4. Produce a multivariate regression model focusing on the relationships between the 5  predictor variables and SalesPrice. You may include additional control variables, up to a maximum of 8 variables in the model (if e.g. you are trying to increase R Square)

5. Discuss and interpret (citing supporting literature) the descriptive statistics and the measures of association/ correlation in Task 3 above. (10 marks)

6. Discuss and interpret the findings of the model in Task 4 above. Does the model support your hypotheses?  (20 marks)

7. Illustrate how your model could be used for price setting by Happy Homes Ltd, by giving an example of predicting the price for an imagined property that is being placed on the market. (5 marks)

8. Critically reflect on the factors that might limit the prediction accuracy of your regression model. Thus e.g., when one uses the regression model to predict the price of a property, what are the caveats and cautions?  What other factors would you suggest HappyHomes Ltd takes into account when using the model for making such predictions and for helping with  planning for improved performance in the housing market?