Predicting Housing Prices with Machine Learning Models
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Overview of Housing Prices in Ames, IA
Machine learning modeling to predict housing prices in Ames, Iowa utilizing advanced regression techniques
Project Description
- Ask a home buyer to describe their dream house, and they probably won't begin with the height of the basement ceiling or the proximity to an east-west railroad. But this playground competition's dataset proves that much more influences price negotiations than the number of bedrooms or a white-picket fence.
- With 79 explanatory variables describing (almost) every aspect of residential homes in Ames, Iowa, this competition challenges you to predict the final price of each home.
Acknowledgments
- The Ames Housing dataset was compiled by Dean De Cock for use in data science education. It's an incredible alternative for data scientists looking for a modernized and expanded version of the often-cited Boston Housing dataset.
Dataset
- We utilized a a database from 2006-2010 including 1460 observations, each representing a home and 79 features, describing different areas of the house such as the interior and exterior, parking lot, housing surroundings, etc.
Objectives & Goals
- For the purpose of this project, we acted as a fictional data science company focused on data mining and consulting. Our goal was to build a unique housing pricing prediction model in order to predict the fair market value assessment for homes in Ames, Iowa. Additionally, we wanted to identify which features had the largest impact on the predictions of the home sale price in order to understand on what areas of the home would increase or decrease the value of the home.
Exploratory Housing Prices Data Analysis
Extensive graphical exploratory data analysis (EDA) was carried out to investigate the relationship between the explanatory variables (features) and the response variable, sale price. The relationship between Sale Price and Year Built is shown in Figure 1.
Figure 1. Representative EDA visualizing relationship between house Sale Price and Year Built
Furthermore, numerical EDA demonstrated the correlation (Spearman's) between the variables (Figure 2). Features such as Overall Quality and Above Ground Living Area were highly correlated with Sale Price, in contrast with the Month or Year Sold, which showed near zero correlation with Sale Price.
Figure 2. Correlation (Spearman’s) between selected features
Housing Prices Data Pre-Processing
- Once we did some EDA and became familiar with the features in our dataset, we then looked at the missing values in our dataset. We had at least 36 features with missing values and they were either imputed with the mean or mode of their respective columns. One thing to note was that imputation in both the training and test datasets used fill values only from the training data set to avoid data leakage.
- Next, we made sure to use the encoding function on ordinal values so that the model would be compatible and understand the different ordered values. There were 12 features that were suitable for encoding to ordinal.
- Then, we also made sure to either dummify or label encode for categorial features. This was an important step because we wanted to make sure we were using the correct data set for the correct models. We had used the linear models for the dataset that was dummified and tree based models for the dataset that was label encoded.
- Lastly, we did some feature transformation, for example the log Sale Price to generate a more normal distribution. Then, we used these new features for the the linear models as it met the assumptions of regression models and ultimately improved its performance.
Figure 3. Summary of dataset pre-processing
Feature Engineering
- From what we observed from the EDA, we created 5 different new features as this would reduce dimensionality and to better predict our target variable.
- Total Outdoor SF: 5 features into 1
- Total Baths: 4 features into 1
- House Age: YearSold - YearBuilt
- Remodel/Addition Age: YearSold - YearRemodAdd
- Garage Age: YearSold - GarageYearBuilt
- To simplify the large number of features, we removed features with correlation values less than 0.3 compared with Sale Price and features with >90% having the same value. For example, the feature Electrical System had values of either circuit breakers or fuses. The vast majority of the houses had modern circuit breakers, and thus this feature was removed.
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Correlation < 0.3 with Sale Price
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Features with > 90% of the same level (Electrical System)
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Redundant features (GarageArea, GarageCond)
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- Lastly, we also removed features with trends that were highly independent of the Sale Price. For example, features such as month sold and year sold.
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Features with trends that were independent of Sale Price (MonthSold and YearSold)
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Machine Learning Models to Analyze Housing Prices Data
- We explored two types of models: linear regression models and ensemble tree-based regression models.
- For linear models we took the log value of our target variable Sale Price and had dummified the predictors as mentioned previously in the pre-processing section. Then we used this data on models such as multiple linear regression and regularization models such as ridge, lasso, and elastic-net.
- For tree-based models we encoded the features into a numerical format rather than dummifying the variables. Then, we used this dataset for models such as random forest, gradient boosting, and XGBoost.
Linear Regression Models
- Multiple Linear Regression
- Regularization
Ensemble Models
- Random Forest
- Gradient Boosting
- XGBoost
Model Performance
- We fit each of the models and then compared the train and test set errors in to order measure the fit and tuned hyperparameters as needed. Then, we evaluated the performance between models using the metric root mean squared error.
Figure 4. Model performance RMSE values
Feature Importance
- Below are the two feature importance graphs from our highest performing models. Although, they don't convey exact similarities in the order of the features, we saw that several features were important in both models such as Overall Quality, Above Ground Living Area, Garage Cars, Kitchen Quality, Fireplace Quality, and Central Air.
- We also observed that the two engineered features Total Basement SF and Total Baths were both ranked top 10 in our best performing models. This was interesting to see because it confirmed the multicollinearity we found among the original features and the correlations between the combined variables and sale price.
Figure 5. Top ten important features for two best performing models, Gradient Boosting and XGBoost
Insights & Conclusions About Ames' Housing Prices
Our models predicted Ames' home prices with an average error of ~$25,000 to $32,000.
Figure 6. Comparison of actual and predicted house prices with respect to age for XGBoost model. Pink histogram bars represent the count of homes by year in the training data.
Model fidelity comparisons revealed a distinct dependence on age, which was directly related to the number of houses used to train the model for a given year.
Future Work on Housing Prices
About Authors
Ryan Kniewel
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Marcus Choi
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