The Residual Analysis Tool is an interactive and data-driven solution designed to help analysts, researchers, and decision-makers evaluate the quality of regression models by analyzing residuals. This tool allows users to input observed and predicted values from a regression model and perform diagnostic checks such as residual plots, normality tests, and heteroscedasticity detection. It provides actionable insights into model assumptions (e.g., linearity, homoscedasticity, normality) and helps stakeholders improve their regression models.

Key Features:

1. Dynamic Input Fields: Users can input observed and predicted values for up to five variables.
2. Residual Diagnostics: Automatically compute residuals, standardized residuals, and diagnostic metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R-squared.
3. Interactive Charts: Visualize residuals using scatter plots, histograms, Q-Q plots, and residual vs. fitted value plots for enhanced clarity.
4. Assumption Testing: Perform tests for normality (e.g., Shapiro-Wilk test) and heteroscedasticity (e.g., Breusch-Pagan test).
5. Scenario Testing: Allow users to adjust inputs dynamically to explore how changes in data affect residual diagnostics.
6. PDF Export Functionality: Generate downloadable reports summarizing residual analysis results for presentations or sharing with stakeholders.
7. Modern and Stylish Design: A sleek interface with vibrant colors, animations, and clear typography to enhance user engagement.
8. Fully Responsive: Optimized for all devices, ensuring seamless functionality on desktops, tablets, and mobiles.
9. Self-Contained Container: The tool operates within its own container, ensuring no interference with the page header or footer.

Use Cases:

• Researchers validating regression models for academic studies.
• Data scientists diagnosing issues in predictive models for business applications.
• Academics teaching regression diagnostics and model improvement techniques.

How It Works:
Users input observed and predicted values for a regression model. The tool computes residuals, standardized residuals, and diagnostic metrics such as MSE, RMSE, and R-squared. It also generates visualizations (e.g., residual plots, Q-Q plots) and performs statistical tests for normality and heteroscedasticity. Results are displayed in tables and visualizations, allowing users to interpret model performance. Users can customize inputs dynamically, analyze scenarios, and download detailed reports in PDF format for further analysis or sharing with stakeholders.