Performing montecarlo simulation of regression coefficients
Steps: Random Sampling: Randomly select 100 pairs of discharge ( Q ) and suspended sediment concentration ( C ) from the dataset. Convert these values to their logarithmic forms: log(Q) and log(C) . Compute the Slope (b) of the Regression Line: Calculate the covariance between log(Q) and log(C). Calculate the variance of log(Q). Compute the slope as: b = Cov ( log Q , log C ) Var ( log Q ) b = \frac{\text{Cov}(\log Q, \log C)}{\text{Var}(\log Q)} b = Var ( log Q ) Cov ( log Q , log C ) Compute the Intercept (logA) of the Regression Line: Compute the mean of log(C) and log(Q). Calculate the intercept using the equation: log A = Mean ( log C ) − ( b × Mean ( log Q ) ) \log A = \text{Mean}(\log C) - (b \times \text{Mean}(\log Q)) log A = Mean ( log C ) − ( b × Mean ( log Q )) Compute the Coefficient of Determination ( R 2 R^2 R 2 ): Compute the Pearson correlation coefficient r r r between log(Q) and log(C): r = Cov ( log Q , log C ) σ log Q ⋅ σ log C r = \fra...