Boston Home Prices Prediction

Introduction

Zillow, as one of the largest real estate online database, has seen a remarkable growth in recent years. However, its housing market predictions are found to be not as accurate as they could be. Home price prediction is a tricky task, because so many factors might influence the home prices, and it is hard to figure out the relationship between these factors and home prices.
To provide better home valuation service for Zillow’s users, we built a predictive model of home prices for Boston using OLS regression, based on machine learning algorithms. For dependent variable, we used log-transformed sale price of 1286 properties in Boston. For independent variables, We introduced 36 predictors into the model, and took into consideration different aspects that were expected to be associated with home prices. Through out-sample prediction and cross-validation, we could ensure that the model is robust and relatively accurate.
Our final model could account for 81% variations in the log-transformed sale price. In training set, the root mean square error (RMSE) and mean absolute percent error (MAPE) are around 0.15 to 0.17 and 12%-13% respectively. The relatively low RMSE and MAPE indicate that it is a good model. In test set, we have computed Global Moran’s I and have found that there is no significant spatial auto-correlation, which means that the model will not perform better or worse in some specific areas.

1.Data

The dataset we used basically consists of two parts: Boston_Midterm_Dataset, a dataset which includes the information of the properties, and data from online open data portals,like Open Data Boston, MassGIS, and Social Explorer (ACS 5-year estimated, 2015). We used the log-transformed sale price as the dependent variable. For independent variables, we have 37 predictors in total, which fall into five categories: internal predictors, demographic predictors, spatial predictors, spatial lag, and interactions.
Internal Predictors
Attributes of the property itself
Demographic Predictors
Demographic profile on block group level
Spatial Predictors
Distance to amenities and disamenities
Spatial Lag
Average sale price and price per square foot of nearby properties
Interactions
Interactions of some predictors

Low income is defined as the percent of area median income (% AMI) no greater than 0.8.

2.Method

Our methods could be discussed from three steps: data wrangling, building the model, and testing the model.
In the step of data wrangling, first, we determined our dependent variable. To meet the regression assumption, we used log-transformed sale price (dollar) as our final dependent variable. Second, we selected different types of predictors, which were expected to be associated with the dependent variable, and not highly correlated with each other. Third, we cleaned the data, removing outliers. The major tool for data wrangling is ArcGIS and R. Then, we used OLS linear regression for building the model. Finally, we tested the model by k-fold cross validation (k=100) to make sure that our model was generalizable. Also, we checked that there was little spatial autocorrelation in our model.

3.Results

Here is the regression formula:

formula<- LnSalePrice ~ LAND_SF + LnLivingArN + R_FULL_BTH + 
           R_HALF_BTH + R_FPLACE + R_TOTAL_RM + Dis_Hosp + Dis_PolSta + 
           Dis_OS2 + Dis_OS3 + Dis_OS3_p2 + Dis_3bus + Dis_Sub + Dis_Sub_p2 + 
           Dis_MR + Dis_River + Dis_River_p2 + Dis_DT + Dis_DT_p2 + Dis_Univ+
           Dis_SpZone + Dis_20crime + Dis_20inter + Dis_20bldgpmt + 
           Dis_20rest + Dis_tourism +LnIncome+BachelorP + VacancyR + SP_lag5 + 
           SP_lag20 + AP_lag5 + AP_lag20 + Bac_Univ_Inter + LowInc_Area_Inter + 
           LowInc_Room_Inter + LowInc_Crime_Inter

4.Discussion

Generally speaking, it is an effective model. For one thing, it could account for 81% of variations in the log-transformed sale price. For another, the model is generalizable, which means that it performs similarly well across neighborhoods. According to the regression results, we have found some interesting predictors. First, all variables concerning internal attributes are significant.
Second, many spatial predictors related to distance are effective predictors of home prices. This is within our expectation. Large-size open spaces are usually neighborhood parks and golf course, which will add value to nearby properties. The proximity to subway is also an important factor people take into consideration when they are buying a house. Another significant predictor is the proximity to business or mixed-use zoned areas, because they are usually dynamic and full of potential. So, it could add value to the nearby properties.
Third, the demographic profile is vital in predicting home prices as well. The income per capita is a good predictor of home prices.
Last, the variables of nearby property values, namely spatial lag, make difference to the model. When people buy a house, they usually buy a neighborhood indeed.
To test the effectiveness and generalizability of the model, we did out-sample prediction, using 25% randomly selected test set. Also, we performed cross-validation on the model, and the results are good. The MAPE of both training set and test set is relatively small. The standard deviation of the MAE in cross-validation is small, which indicates that the model is generalizable. According to the spatial auto-correlation test and MAPE map by neighborhood, our model generally performs similarly well on different areas (neighborhoods).
But there is still some little difference in the performance of model across neighborhoods. Through spatial cross-validation, we have found that the model predicts particularly well when holding out poor neighborhood (built the model using the remaining neighborhoods, and predicted for the poor). The possible reason could be that the data size is not big enough, because all three neighborhoods we selected out only had around 50 observations. Another possible reason might be that there were some factors the rich cared about very much but we overlooked.

5.Conclusion

We highly recommend that Zillow should use our model, which will generate considerable benefits to Zillow, because our model is effective and generalizable. But the model could still be improved in three aspects. First, if the model is applied to other cities, models might need to be changes according to the city condition. Second, we should use larger dataset and include more observations if possible. Third, we might consider more factors that the rich care about when they purchase a property to improve its performance on different neighborhoods.