# RECORD 0795e1f2569ab3c9b87c0451960aa54739093319 # TITLE: PERFORMANCE OF MULTIPLE LINEAR REGRESSION AND NONLINEAR NEURAL NETWORKS AND FUZZY LOGIC TECHNIQUES IN MODELLING HOUSE PRICES # YEAR: 2012.0 VENUE: nan DOI: 10.3844/jmssp.2012.419.434 # AUTHORS: Siti Amri; Gurudeo Anand Tularam # PAGES: 16 CANDIDATE TABLE PAGES (1-based): [1] # ABSTRACT: House price prediction continues to be important fo r government agencies insurance companies and real estate industry. This study investigates the perfor mance of house sales price models based on linear a nd non-linear approaches to study the effects of selec ted variables. Linear stepwise Multivariate Regress ion (MR) and nonlinear models of Neural Network (NN) and Adaptive Neuro-Fuzzy (ANFIS) are developed and compared. The GIS methods are used to integrate the data for the study area (Bathurst, Australia). While it was expected that the nonlinear methods wo uld be much better the analysis shows NN and ANFIS are only slightly better than MR suggesting q uestions about high R 2 often found in the literature. While structural data and macro-finance variables m ay contribute to higher R 2 performance comparison was the goal of this study and besides the Australi an data lacked structural elements. The results sho w that MR model could be improved. Also, the land value and location explained at best about 45% of the sale price variation. The analysis of price forecasts ( within the 10% range of the actual prediction) on average revealed that the non-linear models perform ed slightly better (29%) than the linear (26%). Th e inclusion of social data improves the MR prediction in most of the suburbs. The suburbs analysis shows the importance of socially based locations and also variance due to types of housing dominant. In general terms of R 2 , the NN model (0.45) performed only slightly bette r than ANFIS 0.39) and better than MR (0.37); but the linear MRsoc performed bett er (0.42). In suburb level, the NN model (7/15) performed better than ANFIS (3/15) but the linear M R (5/15) was better than ANFIS. The improved linear MR (6/15) performed nearly as well as the no n-linear NN. Linear methods appear to just as precise as the the more time consuming non linear methods in most cases for accounting for the differences and variation. However, when a much more in depth analysis is required non linear methods may prove to be more valuable. More research is nee ded in the area of house price modelling including more structural elements, modern buyer beliefs and the nature and type of risks noted in modern times. ===== PAGE 1 (score 12, numeric-paren 3, table-words 3, var-words 3) ===== Journal of Mathematics and Statistics 2012, 8 (4), 419-434 ISSN 1549-3644 © 2012 Science Publications doi:10.3844/jmssp.2012.419.434 Published Online 8 (4) 2012 (http://www.thescipub.com/jmss.toc) Corresponding Author: Gurudeo Anand Tularam, Senior Lecturer in Mathematics and Statistics, Science Environment Engineering and Technology (ENV) Griffith University Brisbane, Australia 419 Science Publications JMSS Performance of Multiple Linear Regression and Nonlinear Neural Networks and Fuzzy Logic Techniques in Modelling House Prices Siti Amri and Gurudeo Anand Tularam Centre for Environmental Futures, Faculty of Science, Environment, Engineering and Technology (ENV), Griffith University, Australia Received 2012-06-14, Revised 2012-09-08; Accepted 2012-12-18 ABSTRACT House price prediction continues to be important for government agencies insurance companies and real estate industry. This study investigates the performance of house sales price models based on linear and non-linear approaches to study the effects of selected variables. Linear stepwise Multiple Regression (MR) and nonlinear models of Neural Network (NN) and Adaptive Neuro-Fuzzy (ANFIS) are developed and compared. The GIS methods are used to integrate the data for the study area (Bathurst, Australia). While it was expected that the nonlinear methods would be much better the analysis shows NN and ANFIS are only slightly better than MR suggesting questions about high R2 often found in the literature. While structural data and macro-finance variables may contribute to higher R2 performance comparison was the goal of this study and besides the Australian data lacked structural elements. The results show that MR model could be improved. Also, the land value and location explained at best about 45% of the sale price variation. The analysis of price forecasts (within the 10% range of the actual prediction) on average revealed that the non-linear models performed slightly better (29%) than the linear (26%). The inclusion of social data improves the MR prediction in most of the suburbs. The suburbs analysis shows the importance of socially based locations and also variance due to types of housing dominant. In general terms of R2, the NN model (0.45) performed only slightly better than ANFIS 0.39) and better than MR (0.37); but the linear MRsoc performed better (0.42). In suburb level, the NN model (7/15) performed better than ANFIS (3/15) but the linear MR (5/15) was better than ANFIS. The improved linear MR (6/15) performed nearly as well as the non- linear NN. Linear methods appear to just as precise as the more time consuming non linear methods in most cases for accounting for the differences and variation. However, when a much more in depth analysis is required non linear methods may prove to be more valuable. More research is needed in the area of house price modelling including more structural elements, modern buyer beliefs and the nature and type of risks noted in modern times. Keywords: Neural Network (NN), Adaptive Neuro-Fuzzy (ANFIS), Multiple Regression (MR), Global Financial Crisis (GFC), International Monetray Fund (IMF), Statistics 1. INTRODUCTION Housing investment is an important investment in Australia and worldwide and it is the means through which many have increased their wealth in the past. It is probably not possible for house prices to increase without bounds and as such the investment choice has been questioned causing a number of commentators (Stapledon, 2009) predicting a price decreases in not too distance future if only to stabilize the market. Whatever the market place does, it is nonetheless important to study the growth of house prices to predict prices for the use of real estate ===== PAGE 2 (score 7, numeric-paren 0, table-words 0, var-words 7) ===== Siti Amri and Gurudeo Anand Tularam / Journal of Mathematics and Statistics 8 (4) (2012) 419-434 420 Science Publications JMSS agents, insurance companies and government departments. Government agencies and councils can use the predicted prices to determine future rates payable amounts and use them to conduct forward planning such as budgeting for the corridors of growth in cities and so on. In 2008, the International Monetray Fund (IMF) reported that the Australian house price was overpriced by around 20% (IMF, 2008). Given that house prices have softened in many overseas countries it is not surprising then that Australians are debating whether similar corrections may occur here. After the Global Financial Crisis (GFC) in 2007-8 the Australian government provided a number of stimulus measures and one of them to the housing industry; namely, the First Home Owners Grant that has allowed the Australian housing market to remain relatively strong. This has caused some heating of the market and the government acted swiftly increasing cash rates in order to slow the market and this has indeed slowed the growth rate and economy significantly in Australia. Since there has been over 70% owners occupiers in Australia, there is a vested interest in a strong housing market (ABS, 2009). In addition, the market has been favourably aided by government policy of negative gearing for investors to be active. The capital gains made in the past and the above mentioned tax policy have led to a significant increase in private investors. Evidence of this is noted in the proportion of investors taking out new housing loans increasing from 11-27% between 1990- 2008 (ABS, 41020) but this appears to be slowing caused by many factors such as the global financial crisis and increasing interest rates. Nonetheless, significant increase in rental prices continue to lure new investors into the market. As noted there is a need to estimated house prices but this is a challenge due to incomplete and “noisy” data of the market (Prasad and Richard, 2006). The data used in house price estimation is often based on historical sales records representing a small percentage of the total housing stock in a given area. Newly constructed homes also dominate the sales market and often there is lack of details regarding improvements or renovations as well as those pertaining to structural data. In this regard, the price reporting from previous sales records may not represent the true value of housing market appreciation. This suggests that the price patterns for many areas may be inaccurate due to a lack of appropriate sample information. The housing system is a complex system. Housing data is complex and is kept in multiple data bases that is subject to ever changing financial and urban environment. However, there are some important factors impacting on prices such as accessibility, neighbourhood- quality, environmental, structural and speculation to name a few (Yates, 2002). Buyer’s decision to pay above average prices for property in a premium location adds to the complexity in the development of accurate models. The local level factors include population demand, migration and other social variables, and the global level factors such as government policies and mortgage interest rates all have an impact on house price estimation (Fig. 1). 1.1. Modelling of House Prices While there has been work done on house price modelling much is yet to be understood about house price fluctuations, patterns and growth (Farlow, 2004). The models can be grouped as those that use urban economics perspective focusing mainly on spatial; and those that use macroeconomic or financial economics. The latter focusing on housing as an asset using optimal methods in a consumption type model for example. Authors have used models based on heterogeneous assets labelled hedonic regression and also time series related models (Cannaday et al., 2005; DEWHA, 2008; Nagaraja et al., 2011; Shiller, 1993) while others use spatiotemporal models (Holly et al., 2010; Yu et al., 2007); Some have used the Torbin’s Q model when others use genetic algorithmic type models (Wilson et al., 2004). Amri and Bossomaier (2003) have attempted an agent based model but much work is yet undone in this area. Fig. 1. Complex housing system