Phase 2 Housing project.
| Yussuf Hersi | Bravin Mugangasia | Pauline Wambui | Kibet Kemboi | Brian Kisilu | Ronald Nyagaka
The business problem the client is facing is how to create a successful platform for buying and selling houses in King County. To achieve this goal, the platform needs to provide accurate estimates of house prices, which is crucial for both buyers and sellers.
To accomplish this, the client wants to use a model that can infer the most important features that determine house prices in King County. These features might include factors such as the location of the house, the number of bedrooms and bathrooms, the size of the house, and other relevant factors.
The model needs to be trained on data that accurately represents the real estate market in King County, including historical sales data, current property listings, and other relevant data sources. By using this data, the model can learn to accurately estimate the value of a house based on its features.
Once the model is trained, it can be integrated into the platform to provide buyers and sellers with accurate estimates of house prices, which can help them make informed decisions about buying or selling a property. By providing a reliable and accurate platform for buying and selling houses in King County, the client can establish themselves as a leader in the local real estate market and attract a large and loyal customer base.
- To identify the key features that significantly influence house prices in King County.
- To develop a model that accurately estimates house prices based on the identified features.
- To evaluate the performance of the developed model in estimating house prices in King County.
- Data We utilized the following dataset to help make predictions of house prices in Kings County King County House Data: a dataset that we were provided at the onset of the project. This file contains data for 21,597 homes built in King County, Seattle from 1900 to 2015. Each home in the set contains information regarding features such as number of bedrooms/bathrooms, number of floors, square footage, zip code, condition, and more.
- id
- date
- price
- bedrooms
- bathrooms
- sqft_living
- sqft_lot
- floors
- waterfront
- view
- condition
- grade
- sqft_above
- sqft_basement
- yr_built
- yr_renovated
- zipcode
- lat
- long
- sqft_living15
- sqft_lot15
*Explaratory Analysis
Price Vs Waterfront Box Plot
- This visualization helps to understand the impact of waterfront on the price of the house. The boxplot shows that houses with waterfront tend to have higher prices compared to houses without waterfront.
Average Price Vs View
- The price increases as the view increases, however it seems houses with a good view
2are priced higher than houses with a fair view3
*Price Vs Grade
-
From this we can see that as the grade of the house increases so does the sales price
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The average price of a house with a grade of 13 is the highest
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The average price of a house with a grade of 3 is the lowest
-
Price Vs Conditions
-
From this we can see that price increases as the condition of the house increases
-
However it appears that houses in poor condition are priced higher than those with fair condition
*Price Vs Sqft Living
- The scatter plot shows a positive correlation between the price and the sqft_living
We used three different models for predicting house prices based on various features such as square footage, number of bedrooms and bathrooms, location, etc. The models used are:
The R-squared value (r2_score) is a measure of how well the model fits the data, with values closer to 1 indicating a better fit. In this case, the r2_score is 0.60, which suggests that the model explains 60% of the variability in the target variable.
The mean absolute error (MAE) is a measure of the average magnitude of errors in the predictions made by the model. The lower the MAE, the better the model. The train MAE and test MAE are 153,308 and 155,208, respectively, which are quite large values, indicating that the model is not performing well.
The mean squared error (MSE) is a measure of the average of the squared differences between the predicted and actual values. The train MSE and test MSE are 54,251,508,451 and 54,392,562,865, respectively, which are both quite large.
The root mean squared error (RMSE) is the square root of the MSE, and it measures the average magnitude of the error in the model's predictions. The train RMSE and test RMSE are 232,919 and 233,222, respectively, which are also quite large. Overall, these metrics suggest that the linear regression model is not performing very well in making accurate predictions on the dataset.
An R2 score of 0.5795 indicates that the model explains 57.95% of the variance in the logarithmic actual values.
An MAE value of 0.2727 for train data and 0.2739 for test data suggest that, on average, the model's logarithmic predictions are off by about 27.27% and 27.39% respectively from the logarithmic actual values.
An MSE value of 0.1154 for train data and an MSE of 0.1175 for test data suggest that, on average, the model's logarithmic predictions are off by the squared value of about 11.54% and 11.75% respectively from the logarithmic actual values.
An RMSE value of 0.3396 for train data and 0.3428 for test data suggest that, on average, the model's logarithmic predictions are off by the squared root value of about 33.96% and 34.28% respectively from the logarithmic actual values
The r2_score is 0.669, indicating that the model explains about 66.9% of the variation in the target variable.
The train MAE is 141902.51 and the test MAE is 143141.58. This means that, on average, the model's predictions are off by about $141,902.51 in the training data and $143,141.58 in the test data.
The train MSE is 44468558642.63 and the test MSE is 45132115646.34. The MSE is larger than the MAE because it penalizes larger errors more heavily.
The train RMSE is '''210875.69''' and the test RMSE is 212443.21. The RMSE is in the same units as the target variable, and it can be interpreted as the average absolute difference between the actual and predicted values, after taking into account the scale of the target variable.
In summary, these metrics can be used to evaluate the performance of the model. In this case, the model has a decent r2_score, but its MAE and RMSE indicate that there is still room for improvement in the model's predictive accuracy.
This model has a lower R-squared value, which indicates that the model is not able to explain as much variance in the data as the other models. The R-squared value of 0.60 suggests that the model explains 60% of the variance in the data, which is lower than the other two models.
The MAE values for both the train and test sets are around 155,000, which is higher than the other two models, indicating that this base model's predictions are, on average, off by a larger margin. The MSE values are also higher than the other models, indicating that the model's predictions may be quite far off for some instances. The RMSE values are also higher than the other models, indicating that the errors are larger.
The mean_diff value for this base model is around 32%, which is higher than the other two models, indicating that the model's predictions are off by a larger margin. The percentage difference for each individual instance is also higher, ranging from 20% to ```44%.
In conclusion, this base model's performance is lower than the other two models, as indicated by the lower R-squared value, higher MAE, MSE, and RMSE values, and higher mean_diff. Therefore, there is room for improvement, and we should explore other models to improve the performance of our prediction model.
This is a log transformation model output, and it is difficult to compare it with the previous results as they are from a different type of model. However, we can analyze the performance of this log transformation model using the provided output.
The R-squared value of 0.58 suggests that the model explains 58% of the variance in the data, which is lower than the R-squared value of the previous model. It indicates that the model may not be able to capture all the underlying patterns in the data.
The Mean Absolute Error (MAE) for both the train and test sets is around 0.27, which means that on average, the model's predictions are off by 0.27 units. The Mean Squared Error (MSE) values for the train and test sets are in the order of 0.11, indicating that the model's predictions may be quite far off for some instances. The Root Mean Squared Error (RMSE) values are around 0.34 for both the train and test sets.
Looking at the mean_diff, which is the mean of the percentage difference between the actual and predicted values, it is around 2%, indicating that the model's predictions are off by 2% on average. The percentage difference for each individual instance is also quite low, ranging from 1.5% to 4.3%.
In conclusion, the performance of this log transformation model is reasonable, but there is still room for improvement. The lower R-squared value suggests that the model may not be able to capture all the underlying patterns in the data. However, the lower mean_diff values suggest that this model may be better suited for this particular dataset, and further analysis is required to draw a definitive conclusion.
Based on the given output, the model seems to have performed reasonably well in predicting the target variable. The R-squared value of 0.67 suggests that the model explains 67% of the variance in the data, which is not bad, but there is still room for improvement.
The Mean Absolute Error (MAE) for both the train and test sets is around $140,000, which means that on average, the model's predictions are off by $140,000. The Mean Squared Error (MSE) values for the train and test sets are in the order of billions, indicating that the model's predictions may be farther off for some instances. The Root Mean Squared Error (RMSE) values are around $210,000 and $212,000 for the train and test sets, respectively.
Looking at the mean_diff, which is the mean of the percentage difference between the actual and predicted values, it is around 30%, indicating that the model's predictions are off by 30% on average. The percentage difference for each individual instance is also quite high, ranging from 19% to 39%.
In conclusion, the model's performance is decent, but there is certainly room for improvement. The high MAE, MSE, and RMSE values indicate that the model's predictions may be quite far off for some instances. Additionally, the high percentage difference for each individual instance suggests that the model may benefit from more fine-tuning or feature engineering.
Based on the performance metrics reported, the Log Transformation Model and Polynomial Model outperformed the Base Model. However, further improvements can be made by exploring other models, feature engineering, or hyperparameter tuning.
As a recommendation, it would be useful to perform further analysis to identify the features that are driving the model's predictions and consider incorporating new features that may improve the model's performance. It would also be worth experimenting with different machine learning algorithms or hyperparameter tuning to see if the model's performance can be improved. Finally, it may be useful to gather more data to train the model and increase the size of the training set to get more accurate predictions.
Discussing possible future steps for improving the models, such as incorporating new data, refining the feature set, or exploring new algorithms or ensembles.