<p>Due to rapid economic growth, India is the world's third-largest emitter of carbon, with a high reliance on fossil fuels. Simultaneously, the country has been on an unparalleled course of renewable energy development, making serious strides through its National Solar Mission and its Paris Pledge. This study examines the linkages among renewable energy use, fossil fuel use, and carbon emissions in India between 1991 and 2024. Ordinary Least Squares (OLS) and Bayesian linear regression provide the study with a powerful tool, offering a comparative framework with particular emphasis on the benefits of frequentist and probabilistic approaches. Based on the findings, a 1 percent increase in the use of renewable energy consumption has reduced carbon dioxide emissions by approximately 1.20 percent, whereas a 1 percent increase in the use of fossil fuel consumption has increased carbon dioxide emissions by about 1.51 percent. Despite OLS's definite elasticity estimates, the Bayesian approach provides better insights (a posterior distribution and credible intervals), as it captures uncertainty. The two models are verified by diagnostic tests, but Bayesian methods offer additional advantages, including the ability to handle small samples and to handle multicollinearity. The findings reveal that, despite the effectiveness of renewable energy in reducing emissions, India's carbon trajectory is determined by the massive expansion of fossil fuel production. The study concludes that the decarbonization goal should be achieved through increased use of renewable energy and active measures to reduce fossil fuel dependence, including the introduction of carbon taxes, emissions limits, and investment in clean technologies.</p>