Studying Data to Predict Housing Prices
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Purchasing a home is a major life event for many people, and rightfully so. It's a massive investment and there can be a lot of risk if you don't know enough about the market. With this in mind, wouldn't it be amazing to have an inside look at what features are most important when determining home prices? If a buyer had access to this data, they could realize what every house on the market is truly worth and would be able to quickly identify homes that are overvalued, or undervalued; ensuring they make out with the best bang for their buck. My team and I examined these details through the Ames, Iowa housing data set on Kaggle.
The objective of this closed Kaggle competition was to create the best possible housing price predictive score, however, my team and I were also focused on exploring the data and interpreting different machine learning models in order to improve our own knowledge about their inner workings. In light of this, we decided to dig deeply into easy-to-interpret models by using Lasso, Ridge, and Multiple Linear Regression as opposed to something more complicated like XGBoost.
The details of our data exploration, feature engineering, and machine learning techniques are described below.
Data Exploration and Feature Engineering
The data Kaggle provided was pre-split into a training set and a test set. The training set was comprised of 79 features (51 categorical/28 numerical) and 1460 observations. The test set was nearly identical except that it contained one less observation.
The first thing my team and I noticed was the sparse data (large amount of NaNs and 0 values) as well as the numerous sub-categories. We quickly realized that most of the NAs were there simply because the home didn't have a certain feature (such as a fireplace). We were able to quickly impute these with a value such as "no fireplace." We then decided to visualize all of the quantitative features (as seen below) to gain a better understanding of the data and easily determine whether or not they are continuous or discrete.
This visualization made it very apparent that many of the quantitative features were also extremely skewed and this needed to be dealt with. After applying a log transformation, the skewness dropped considerably for each of the applicable features and our predictive power increased. Below is an example of how sales price was improved post log transformation.
Lastly, we had to deal with the remaining categorical variables. Each of these were ‘dummified’ (or one hot encoded) in order to transform them into numerical values so we could give our model as much information as possible.
As mentioned in the introduction, our goal was to aim for a combination of interpretability and predictive power. For this reason, and because the data was very linear, we decided to compare Lasso, Ridge, and Multiple Linear Regression. Our first step was to ensure we could cross-validate, so we split the training data into an 80%/20% split. Once we trained the model, we used the untouched 20% to assess our predictions and gauge how powerful our model was.
After the data wrangling that we performed above, our Ridge and Lasso regressions performed very well. Unsurprisingly, they outperformed a standard Multiple Linear regression by a significant amount. What was surprising is that our Ridge regression outperformed our Lasso regression. This may be because each feature holds weight in predicting the sales price. The Lasso method tends to completely eliminate the weights of the least important features (ie. sets them to zero) which may have actually been relevant.
Interpreting The Model's Data
Here is where a linear regression model's interpretability comes into play. Below is a comparison of the most important features between our Ridge and Lasso regressions.
As we can see, the amount of square feet on the 1st floor is pivotal in both the Lasso and Ridge regressions. Unsurprisingly, this is followed by the total above-ground living area. Another noteworthy finding is that different neighborhoods appear to both negatively and positively weight heavily on each model. This makes sense as there are always more/less desirable neighborhoods in every part of the United States.
Data Results/Next Steps
With our first machine learning project under our belts, we are pretty proud of what we were able to accomplish. Is there room for improvement? Of course. However, the plot below is a clear indicator that we were able to respectfully predict home prices in Ames, Iowa.
For future work, our model clearly needs to improve when dealing with homes of higher value. This may be solved through further feature engineering, or perhaps different forms of predictive modeling. Ensembling is probably the most attractive method that we weren't able to take advantage of. All in all, we accomplished what we set out to do, and will certainly only improve from here.