Analyzing Factors Affecting House Prices In Sidney

Analysis and Results

House prices have not been constant especially in major cities of the world (Dongsheng & Zhong, 2010). They have been seen to fluctuate over a period of time. This has been attributed to a number of factors. Some of these factors include the economy of the geographical location of the house, the demand for housing in a given area, proximity to an urban area just to mention but  a few (Hua, 2008) and (Shisong & Hongmei, 2009). Australia’s cities have not been left behind as their housing sector has also been facing fluctuation in housing prices due to various variables. For example, the real estate market prices in Sidney have been found to be influenced by the following;

• Housing price index of the city (rate of change of prices)
• Annual percentage change (based on previous year)
• Area of land in square meters (on which the house is built)
• Age of the house in years

The above variables together play a major role in determining the market price of houses in the city of Sidney. This research sought to establish a model incorporating the four variables that could be used to estimate the market price of the houses in Sidney. There are other determinants but were considered not significant as far as their influence on house prices was concerned. The age of the house was factored because the older the house the lesser the market price while the newer the house the higher the market price. This situation was more influenced by demand as newer houses attracted more people while old houses attracted less people (Nellis, 2011). Therefore the highly demanded houses automatically led to the soaring of their market prices and vice versa. The size of the land on which the housing is on also played a role (Quigley , 2009). A larger area in meters squared meant higher market price while a smaller area meant a smaller market price. The dependent variable in this research was the market price while the independent variables were housing price index, annual percentage change, area of land in square meters and age of the house in years. The sample size for this research was 15. This was chosen through simple random sampling or probability sampling. This method involves choosing subjects without applying any tricks. It ensures that each and every subject has got an equal chance of being included in the sample. Lastly, it ensures that cases of biasness are minimized that ensuring that the results of the data analysis are accurate and can therefore be used to make conclusion on the whole population.   

1. Scatterplot for dependent variables and each independent variable
2. Market price versus price index scatterplot  

It can be observed that there is a linear relationship between market price and Sidney price index. The relationship is positive indicating that an increase in Sidney price index causes a resultant increase in market price for houses. The R² value is 0.65 meaning that 65% of variation that occurs in market price is as a result of Sidney price index.   

1. Market price versus annual % change scatterplot 

Least square regression equation

It can be observed that there is a linear relationship between market price and annual percentage change. The relationship is positive indicating that an increase in annual percentage change causes a resultant increase in market price for houses. The R² value is 0.16 meaning that 16% of variation that occurs in market price is as a result of annual percentage change.  

1. Market price versus area in meters scatterplot  

It can be observed that there is a linear relationship between market price and area in square meters. The relationship is positive indicating that an increase in land area in square meters causes a resultant increase in market price for houses. The R² value is 0.09 meaning that 9% of variation that occurs in market price is as a result of land area in square meters.  

1. Market Price and age of house scatterplot 

It can be observed that there is a linear relationship between market price and age of house in years. The relationship is positive indicating that an increase in age of house in years causes a resultant increase in market price for houses. The R² value is 0.46 meaning that 46% of variation that occurs in market price is as a result of age of house in years.  

1. The full regression model

The regression equation above is of dependent variable (market price) against the other four independent variables. The y – intercept value is 548.98. This means that the market price of a house in Sidney when all other factors are held constant is 548.98 in thousand dollars.  To add on, a unit change in Sidney price index causes 1.96 units change in market price of the houses. A unit change in land area causes 0.52 unit change in market price. A unit change in annual percentage change causes a negative 5.62 change in market price while a unit change in age of houses in years causes negative 2.49 unit change in market price of houses.

The coefficient of Sidney price index was found to be significant at 95% confidence level since its p-value (0.01) was found to be less than level of significance (0.05). On the other hand, the other estimated coefficients of regression were found not to be significant at 95% confidence level since their p-values were greater than the level of significance (0.05).

The value of the coefficient of determination is 0.71. This indicates that there was a strong correlation between the dependent variable and the independent variables. It also means that 71% of the variation that occurs in the dependent variable (market price) is explained by the independent variables.

Interpretation of 95% confidence interval for each parameter

Interpretation of 95% confidence interval for each parameter

Table 2

The table above shows 95% confidence interval for the parameters listed above. The last two columns give the limits within which the parameters lie at 95% confidence interval. This means that 95 times out of 100 times, the parameters will always lie between the limits shown in the table above.

Linear regression model for relationship between the market price and land size in square meters

Table 3

The regression equation for the above is as below; 

The value of R² is 0.1. This indicates that the relationship between the two variables is not strong. It also means that only 10% of the variation in the dependent variable (market price) is explained by the independent variable (area in square meters).

Comparison of the two models

To choose the best predictor model, the value of R² comes in handy to guide in evaluating the goodness of fit of a given model. The two regression models are as shown below; 

With R² value of 0.1

And; 

With R² value of 0.79

Therefore the model with the best goodness of fit is the second model since it has a greater R² value meaning that much of the variation (79%) in the dependent variable can be explained by the independent variables compared to the first model where only 10% of the variation in the dependent variable could be explained by the independent variables.

Predicting market price of a house given land area is 400 m²

The equation of the relationship is; 

Therefore if land area is 400 m² then the market price is calculated as below; 

Conclusion

Several factors were found to influence the market price of houses in Sidney. Among the factors were size of land in square meters, Sidney price index, annual percentage change and age of the house in years. However, this research established that these factors had different weights in influencing the market price for houses. Annual percentage change was found to be the strongest influencer of the four variables. This was followed by age of the house in years then Sidney price index and lastly area of land in square meters. This was revealed by the coefficients of the variables in the regression model.

Sidney price index had strongest relationship with market price for the houses than the rest of the determinants. The variable that had the least strong relationship with market price for houses was area of land in square meters.   

References

Dongsheng, C., & Zhong, M. (2010). The bad effects of high housing price on urbanization of China. Yangtze Forum, 3, 3-7.

Hua, Z. (2008). An analysis of supply and demand curve of real estate market and its policy implication.. (Vol. 3). Jianghuai Tribune.

Nellis, J. G. (2011). An empirical analysis of determination of house prices in the United Kingdom. Urban Studies. (1 ed., Vol. 19).

Quigley , M. J. (2009). Real estate prices and economic cycles. International Estate Review, 2, 5-8.

Shisong, H., & Hongmei, C. (2009). The mystery of housing price. Beijing: Social Sciences Academic Press.

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