The project encompasses a multifaceted approach to analyze and predict purchase prices through rigorous data manipulation, visualization, normalization, and advanced modeling techniques.

Data Manipulation and Visualization: We initiated our project by acquiring raw data and subjecting it to meticulous manipulation to ensure its suitability for analysis. Following this, we employed various data visualization techniques to gain insights into patterns, trends, and relationships within the dataset. Visualizations were instrumental in understanding the data's characteristics and identifying potential factors influencing purchase prices.

Data Normalization: Normalization is crucial for standardizing data, ensuring uniformity, and enhancing the effectiveness of predictive models. We employed normalization techniques to scale the data appropriately, mitigating biases and ensuring optimal performance across different modeling algorithms.

Predictive Modeling: We utilized multiple predictive models to forecast purchase prices, each offering unique insights and advantages:

1. Linear Regression: Leveraging linear regression, we aimed to establish a linear relationship between independent variables and purchase prices, providing a baseline prediction model.

2. Random Forest: By employing the Random Forest algorithm, we capitalized on its ability to handle complex datasets and capture nonlinear relationships, thus improving prediction accuracy.

3. LSTM Model: Long Short-Term Memory (LSTM) networks were employed to analyze sequential data and capture temporal dependencies within the dataset, offering enhanced prediction capabilities for time-series data like purchase prices.

4. ARIMA Model: The Autoregressive Integrated Moving Average (ARIMA) model, known for its effectiveness in time-series forecasting, was employed to capture trends, seasonality, and other temporal patterns in purchase prices.

Evaluation and Comparison: Each model was evaluated based on various metrics such as Mean Squared Error (MSE), and Mean Absolute Error (MAE). These metrics facilitated a comprehensive comparison of model performance, allowing us to identify the most effective approach for predicting purchase prices.