This repository contains a collection of advanced statistical modeling and data analysis scripts developed in R. The projects demonstrate proficiency in hypothesis testing, regression analysis, econometric diagnostics, and simulation methods.
- Description: Developed an asymptotic Likelihood Ratio test to distinguish between two Beta distributions. Analytically derived the Fisher Information and calculated the minimax sample size.
- Key Techniques: Monte Carlo simulations (10,000 iterations) to refine the asymptotic decision thresholds and calculate empirical statistical power.[cite: 9]
- File:
monte_carlo_hypothesis_testing.R
- Description: Diagnosed a failed multiple regression model that suffered from severe multicollinearity between predictors (study hours and pages read).[cite: 7]
- Key Techniques: Scatterplot matrix diagnostics, Feature Engineering (created a
ReadingSpeedmetric), and robust model fitting. The engineered feature successfully transformed a statistically insignificant model into a highly predictive one.[cite: 7] - File:
regression_multicollinearity_fix.R
- Description: Addressed severe heteroscedasticity and right-skewness in real household survey data by transitioning to log-log econometric models.[cite: 5]
- Key Techniques: Logarithmic transformations, residual diagnostics (Q-Q plots, histograms), and Chow Test application to detect structural breaks across demographic groups.[cite: 5, 6]
- File:
log_log_regression_chow_test.R
- Language:
R - Libraries:
car,stats, base R graphics.