The Application of Ridge Approach to the Modeling of Urban Housing Prices in Iran

Housing is one of the basic and vital needs of individual and social life. In development economics, the importance of housing is so high that it is one of the indicators of development and development of countries. Using simple multivariate regression methods, this research was conducted to investigate the performance and the effect of macroeconomic variables including household income per capita, total stock index, inflation rate, urban household consumption price and the number of residential building mortalities on the behavioral pattern of housing prices in the country. This study aims to examine the performance and impact of macroeconomic variables on the pattern of housing prices in the country, using regression methods. Variables such as family income, the stock price index, inflation, the consumer price of urban households and the number of residential building permission were regarded as a regression variables. Simple and multivariate linear regression analysis showed that positive serial correlation respectively and severe multi-collinearity and lack of confidence in the ability of these models are coming down. The results showed that the variable of building permission has no significant linear relationship with housing prices and the variable of inflation rate will have a significant linear relationship with housing price only if the data of 1393 were removed. Then, in the range of 0.01 to 0.52 charting ridged was found that the regression coefficients multivariate models 0.08 and 0.1 are stable. So by adopting a structured exercise, regression models were reproduced by regression coefficients real numbers. It turns out that in a compound model, family income, the consumer price of urban households, inflation rate and total stock index affected the urban housing price of Iran as equal as 0.349, 0.348, 0.288, and 0.0612 respectively. The results of this study showed that since the macro-economic variables usually do not have orthogonality condition and have a linear relationship, it is necessary to use ridge regression to present real models having the extrapolate ability. Moreover, unrealistic estimates of regression coefficients provide regression variables.
Extended Abstract
1-Introduction
Housing is one of the basic and vital needs of individual and social life. In development economics, the importance of housing is so high that it is one of the indicators of development and development of countries. The long-term analysis of the housing market in Iran suggests severe fluctuations in the variables of this sector, including housing prices, fee and investment. These fluctuations had the greatest impact on the final cycle of housing, households, and these price changes, in addition to instability in planning, have provoked a negative psychological wave for people. Accordingly, the purpose of this research is to fit the model that can be efficient and with the use of variables, be able to predict the changes in the price of housing over time with the least error. Housing price fluctuations seem to be influenced by several factors in which there is a direct correlation between increased revenues and construction costs and rising housing prices (Wang & Zhang, 2014). Determining the contribution of each factors affecting housing prices, authorities can take an action to balance suppliers and applicants, which results in sustainability and rational development of housing prices in urban areas. Therefore, the comparative analysis of regression and ridge models, the identification of the instability and the falsehood of the factors determining the price of housing in the models are examined. This process will ultimately lead to the use of an appropriate model to increase the reliability and stability of these coefficients. Thus, a more realistic understanding of how urban housing prices behave in relation to macroeconomic variables can be achieved.                    
2-Materials and Methods
Statistical methods such as Pearson correlation coefficient, simple linear regression, multivariable regression and ridge regression were used to investigate the reaction of housing prices to independent variables. In this regard, at first, household income per capita data, total stock index, inflation rate of urban households, number of residential construction projects pertaining to the entire city of the country, as independent variable, and the housing price index of all cities in the country, as a dependent variable, from 2002-2014, were gathered from the Archives of the Center Statistics and Central Bank of Iran (2016).
3-Results and Discussion
In spite of having significant coefficient, simple regression models are not trustworthy enough. As a matter of fact, there was a positive serial correlation between the residuals of these models, which indicates that there are other variables playing a decisive role in the housing market model.                                                                                                                            
Subsequently, using a multi-variable regression model, a model of housing price index was developed by adopting a combination of macroeconomic variables including household income per head, total stock index, inflation rate, urban household consumption price, and the number of residential construction mortgages. The results of the multivariate regression model, as in previous studies, showed that the combination of macro variables could significantly explain the behavioral pattern of urban housing prices in Iran (Soheilie et al., 2012). Housing price volatility is affected by several factors. As household income per head increases, housing prices also increases, which indicates a direct correlation between the independent variables and the function. The existence of such a connection is also seen in previous studies (Wang and Zhang, 2014; Ho et al., 2006). It is worth noting that these coefficients are not reliable. As all indexes, including the inflation index of variance, showed that due to the large error of the governor, regression coefficients (beta), the proposed model  has no predictive capability and these coefficients are false. In order to solve this problem, ridge regression analysis was used. Coherency metrics such as Tolerance and ..., also showed the stability and reliability of this coefficient. However, the results of multiple coherency measures in the model show the stability of the coefficients obtained for all independent variables by the ridge model. In this way, the damaged model managed to estimate the values of these coefficients successfully by interacting with multiple interactions, while decreasing the error width of the governor's coefficients. Indeed, the results of this study emphasize the use of the ridge model in studies on modeling and predicting housing prices.
4-Conclusion
The housing market is affected by macroeconomic variables, which is due to the volatility of these variables in its price pattern. Accordingly, this study was conducted to model the price of urban housing market throughout the country using regression methods The regression coefficients of ridge models are more realistic than the least squares method and have good extroversion, so that the inverse and false role played by the stock price index in two least squares regression models has now become a direct and actual role in ridge models. Generally, the results of this study, based on the used statistical measures, showed that the application of the ridge method by interfering multiple interactions between independent variables not only can estimate the stable values of the coefficients of influence, but also has a significant statistical significance to model housing price