Using Data to Predict Housing Prices in Ames, Iowa
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Housing Prices in Ames, IA - Background
Based on data there are many qualities of a residential home that determine its worth and price outside of just the number of rooms and square footage. Taking a closer look at 81 residential variables from Ames, Iowa between 2006 to 2010, we were able to use various machine learning methods to determine features of a home in this region that are important to predict sale prices. In this regression analysis, the R2 value across select regression models helped determine which model best fit the dataset and predicted housing prices.
About the Housing Prices Data
The dataset includes several residential features, from ordinal numeric values like OveralQual and GrLivArea to different string variables. In all, after combining the test and training data, over 2900 observations were used for fitting various models.
Exploring the Housing Prices Data
Applying a correlation heatmap to the data reveals which features are most correlated to the sale price (SalePrice) and which are least correlated. The heat map below shows the 10 features most correlated to SalePrice. There's no great surprise here. The top 10 are the primary features people look for in a home they're considering buying. So, it's no wonder that they would most likely affect sale prices. Converting the full heatmap to a bar chart, we can also see the features least correlated to the price like BsmtFinSF2, BsmthHalfBath, and MiscVal.
As noted, the overall quality (OverallQual) greatly affects the sale price. The higher the OverallQual, the higher the price, as shown on the box plot below.
Data Pre-processing
Missing Data
A number of features were identified with significant amounts of missing data. The row Id and features with more than 80% missing values, including PoolQC, MiscFeature (with its counterpart, MiscVal), Alley, and Fence were deleted from the dataset.
Other features with missing values were imputed based on their data type. Categorical features were imputed with “None.” Numerical features were imputed with zeros. Features including LotFrontage, MSZoning, Utilities, Electrical, KitchenQual, SaleType, Functional, Exterior1st, and Exterior2nd were imputed with the mode.
One difference between the simple and advanced dataset include whether GarageCars, GarageArea, and MasVnrArea had a “None” or zero imputation, as both imputation methods yielded different R2 values.
Feature Engineering
To further improve the data set, several features were transformed to yield meaningful insight. For example, several quality and condition string features--including ExterQual, ExterCond, BsmtQual, BsmtCond, HeatingQC, KitchenQual, GarageQual, GarageCond--had values that were converted to ordinal numerical values (e.g. {None: 0, Po: 1, Fa: 2, TA: 3, Gd: 4, Ex: 5}). Other categorical variables were converted to ordinal values as well, as seen below:
- LotShape - {IR3: 1, IRF2: 2, IRF1: 3, Reg: 4}
- BsmtExposure - {None: 0, No: 1, Mn: 2, Av: 3, Gd: 4}
- BsmtFinType1 and BsmtFinType2 - {None: 0, Unf: 1, LwQ: 2, Rec: 3, BLQ: 4, ALQ: 5, GLQ: 6}
- Functional - {None: 0, Sal: 1, Sev: 2, Maj2: 3, Maj1: 4, Mod: 5, Min2: 6, Min1: 7, Typ: 8}
- GarageFinish - {None: 0, Unf: 1, RFn: 2, Fin: 3}
- PavedDrive - {N: 0, P: 1, Y: 2}
- CentralAir - {N: 0, Y: 1}
- LandSlope - {Gtl: 1, Mod: 2, Sev: 3}
Feature Selection
For the linear regression model, an F-Test revealed six coefficients that were statistically insignificant. We opted to drop these features from the linear regression model.
Since the F-test also revealed GrLivArea as having statistical significance, outliers were filtered out for all models.
Model Assessment for Housing Prices Data
Linear Models
SalePrice distribution is right skewed as shown below. To improve model fit, SalePrice was made normally distributed with log transformation. ElasticNet with alpha 0.001 and rho 0.6 performed the best of all the linear models.
Advanced Regression Models
The two advanced regression models tested were random forest and gradient boosting regression. Both algorithms are more robust compared to linear regression. While random forest uses a bagging method to take aggregates of random samples of small subsets of data, gradient boosting converts weak learners into stronger ones and subsequently improves each tree. After obtaining the best parameters of each model using grid search cross-validation, gradient boosting yielded the best R2 score compared to all models tested.
Housing Prices Conclusion
As mentioned previously, gradient boosting yielded the best R2 score, compared to the linear regression and random forest model, with a test R2 value of 0.924. Based on the gradient boosting model, the top housing variables that are important when predicting sale price are HeatingQC and Street. In all, feature engineering played a key role in improving the accuracy score for each model. Simpler regression models, like multiple linear regression, achieved lower accuracy or R2 scores compared to gradient boosting. Therefore, the advanced gradient boosting regression model is the best model to use when determining important features that predict house prices.
Future Directions
In order to improve the model, we would like to continue exploring methods that can minimize overfitting, including cross-validation and parameter tuning. Since there are still a number of data manipulations that can be done and explored, further feature engineering is another possibility, along with improving feature selection for each model.
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Kristin Teves
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