Exploratory Data & Correlation Analysis
Quantifying relationships between environmental factors and river discharge response.
Scientific Interpretation of Correlation Findings
Pearson correlation $r \approx 0.947$ confirms Rainfall is the primary linear driver of river discharge. The positive slope demonstrates strong hydrological precipitation-runoff generation.
Soil moisture exhibits modest direct linear correlation ($r \approx 0.151$). However, in the quadratic model, its interaction with rainfall ($\beta_12$) proves vital for amplifying flood peaks during saturated conditions.
Runoff coefficient acts as an empirical catchment multiplier ($r \approx 0.175$). Combined interactions ($\beta_13, \beta_23$) elevate the overall volume yield of the river basin.
Multicollinearity Check: Inter-factor correlations (X1 ↔ X2, X1 ↔ X3, X2 ↔ X3) are all below |r| < 0.13, confirming that independent predictors operate without collinear interference.