# The Impacts of Open Data and eXplainable AI on Real Estate Price Predictions in Smart Cities
## 4 Discussion
### Private Gross Area  
From the results of the SHAP analysis, private gross area (PGA) exerts the highest average impact on property prices among the features analyzed, with a mean absolute SHAP value of 73,775.16. This prominent position underscores the critical role of a dwelling's size in price determination. This finding validates previous research by [PERSON] et al. (2022) [65], [PERSON] et al. (2020) [31], [PERSON] (2022) [93], [PERSON] et al. (2021) [30], [PERSON] et al. (2022) [32],and [PERSON] et al. (2022) [94], indicating the housing area as a strong predictor for the price of a property. The presence of non-linearities revealed by a broad distribution of PGA's SHAP values in the beeswarm plot, sprawling across both sides of the baseline, reflects a complex relationship with price. Larger properties generally command higher prices, a well-known trend in real estate, but the spread of SHAP values suggests this trend is not universally linear. Smaller properties can similarly fetch high prices, contingent on additional factors. Conversely, a larger area does not unconditionally translate to a premium in price. Indeed, the observable variability along the x-axis of the plot indicates that the influence of PGA on price is subject to inconsistencies. This pattern implies the existence of nonlinear dynamics, where the effect of PGA on the price does not consistently correlate with the area. In some instances, the increment in PGA can lead to a proportionate increase in price predictions. In contrast, the effect may be lesser or inversely related in other instances, potentially influenced by market trends, property location, and desirability. Figure 5 represents a geospatial heatmap of SHAP values for the PGA feature from our XGBoost model for predicting real estate prices. This visualization helps understand which geographic areas have properties where the PGA significantly affects their predicted prices according to the model. Regions with no points or smaller points indicate areas where PGA is less important in predicting real estate prices or has a potentially negative impact. Each point corresponds to a property within the Lisbon area, with its location given by Latitude and Longitude coordinates. The color of a point indicates the SHAP value associated with the PGA feature for that property, with the color scale extending from \(-150\) k to \(250\) k. The negative values on the color scale are essential for understanding the direction of the impact, while the absolute values are used for the size to visualize the magnitude. The size of each point reflects the absolute magnitude of the SHAP value, ensuring visibility for both positive and negative contributions. Figure 5: Geographic distribution of SHAP values for private gross area (PGA) in Lisbon: This map illustrates the influence of the private gross area feature on real estate price predictions across different locations in Lisbon. Each bubble represents a property, with its size proportional to the SHAP value assigned to the PGA feature, indicating the magnitude of impact on the prediction. The color scale ranges from light to dark blue, corresponding to the range of SHAP values from negative to positive. Higher SHAP values (darker blue) suggest a more significant positive impact of PGA on the property’s predicted value, whereas lower values (lighter blue) indicate a lesser or negative impact. This visualization highlights areas where PGA is a stronger predictor of real estate prices and where it may have a reduced or inverse effect. Darker blues represent higher positive SHAP values, denoting a more significant positive impact of PGA on the model's price prediction, particularly noticeable in central Lisbon, which suggests a higher space valuation in these areas. Lighter blues, conversely, indicate negative SHAP values, signaling areas where larger PGAs may not be as valued or could even decrease a property's predicted price. The varying shades of blue indicate that the impact of PGA on the model's predictions is not uniform across Lisbon.