1.1 Introduction

Zillow has realized that its housing market predictions aren’t as accurate as they could be because they do not factor in enough local intelligence. Our group has been selected to build a better predictive model of home prices for San Francisco. Because there are so many variables and elements to influence home value in San Francisco, it is such a tough task to perform prediction. Even though it may takes substantial times and energy to gather and process raw data, it will still be interesting to take this challenge.

As far as this project, we will bring geospatial analysis and machine learning techniques together to generate our model. The goal of geospatial prediction is to borrow the experience from one place and test the extent to which that experience generalizes to another place. The machine learning process will be divided into four steps. Below is a brief discussion on each step of the process.

• Data wrangling: The first step of the process is to gather and compile the appropriate data, often from multiple disparate sources, into one consistent dataset.This means the analyst has to understand the nature of the data, how it was collected and how to massage the raw data into useful predictive features.

• Exploratory analysis: Thoughtful exploratory analyis often leads to more useful predictive models. Additionally, more reasonable exploratory research will make the analysis more interpretable for non-technical clients.

• Feature engineering: Feature engineering is the vital point to differ a great model from a good one. Features are the variables used to predict the outcome of interest - in this case home prices. The more the analyst can convert data into useful features, the better her model will perform. There are two key considerations for doing this well.

• Feature selection: In a geospatial prediction project, it is possible to contain hundreds of features in the dataset. It is much wiser to select useful features in a model instead of implementing all of them. The feature selection process is the process of whittling down all the possible features into a concise and parsimonious set that optimizes for accuracy and generalizability.

• Model estimation and validation: In this project, we will develope a a home price prediction algorithm by using linear regression models. To aviod bias and inaccuracy, we will perform plenty of methods to validate a machine learning model for accuracy and generalizability in the following report.

Generally, the home value model we built can predict approximately 85 percent of the total homes from 2012-2015. The error is about 180,000 dollars. Considering the situation of home prediction difficulty, we think this model is well-performed.

2. Data

3.Feature Engineering and Selection

In this project, we are using Ordinary Least Square (OLS) as the model to estimate house prices. OLS is able to find the linear relationship between the dependent variable, which in this case is the house sale price, and the predictors, which are the variables mentioned above in the data collection section. The feature engineering is done in the following steps.

1. In order to construct and choose the most effective features, we ran an OLS linear regression model for all the predictors to test the fitness of the model. The output gives both the p-value and the coefficient for each variable. The p-value reflects the significance of the coefficient, in other words, the probability of having the coefficient assuming there is no correlation between the independent and the dependent variables. Typically, we want p-value to be smaller than 0.05. R-squared is also calculated, which demonstrates the amount of variance in the dependent variable that is explained by the predictors. A larger R-squared means a better estimation of the model and is desired.

2. We compare the p-values of the variables to check their significances in relation to the house price. This gives us a direction of what variables to keep or change. After removing or adding variables, we ran OLS model again to compare the R-squared value. Multiple trials are done to select the best set of predictors.

3. A series of feature engineering is done throughout the trial process. We have log-transformed the price related to the predictors in order to make them better fit for the linear model. We also have made several variables into categories, since continuous variables do not always have the most predictive power. For example, in a demand perspective, a potential mansion purchaser would not care about the exact numbers of the rooms, therefore, a house with 6 or 7 bedrooms might not influence the final house price that much.

4. We also have used the stepwise regression using the stepAIC function in the MASS package, which automatically finds the best set of predictors with the least R-squared value. However, since we have more model validation in the next step, we only used this function result as a reference.

4.Model Estimation and Validation

##   intercept     RMSE  Rsquared      MAE   RMSESD RsquaredSD    MAESD
## 1      TRUE 299118.1 0.8165478 203908.9 38288.06 0.04399277 18957.19

## 
##  Monte-Carlo simulation of Moran I
## 
## data:  filter(sp.test, !is.na(SalePrice.Error))$SalePrice.Error 
## weights: spatialWeights.test  
## number of simulations + 1: 1000 
## 
## statistic = 0.016313, observed rank = 944, p-value = 0.056
## alternative hypothesis: greater

5. Conclusion

We would highly recommend our model to Zillow, as it has a very small error in predicting house prices. Even though it is less representative in higher home value communities, the model still has great MAE, MAPE and r-squared. As we disccussed before, the model can be improved in multiple ways.Additionally, Non-linear models other OLS can be considered for better fit.