Climate change greatly affects farming by reducing crop yields, thereby challenging sustainable farming. Real-time data and analytics help identify key factors to boost crop yield and support smart farming through better decision making. To study how different factors affect crop yield, this paper considers various parameters, namely, temperature, precipitation, CO₂ emissions, extreme weather, use of fertilizers/pesticides, irrigation, soil health, economic factors, and location, and their influence on the crop yield is estimated. The Pearson Correlation Coefficient (PCC) is commonly used to find relationships between variables, but it only detects linear connections. Since climate factors often change in complex, nonlinear ways, this paper suggests a hybrid approach that combines the PCC with the XGBoost machine learning method for better analysis. In the proposed hybrid model, XGBoost identifies which factors are most important, while the PCC measures their impact on crop yield, thereby performing an effective correlation analysis. Simulations show that 'economic impact' has the strongest direct influence on crop yield, with a correlation coefficient of 0.73. Further, it is also noticed that the combination of 'average temperature' and 'economic impact' has the highest indirect influence, with a correlation of 0.2. The proposed hybrid model performs better than the standard PCC method, achieving an R-squared of 0.57, RMSE of 0.62, and MAPE of 29.14%, compared to PCC’s R-squared of 0.55, RMSE of 0.71, and MAPE of 31.48%. This study uses the 'climate change impact on agriculture' dataset from Kaggle and supports UN Sustainable Development Goals (UN SDGs 13 and 15) for promoting sustainable farming.