How is the coefficient of determination (R^2) calculated from a simple linear regression model?

Write the formula for Pearson correlation coefficient

r = Σ((xi - x̄)(yi - ȳ)) / (√Σ(xi - x̄)² * √Σ(yi - ȳ)²)

How does the Root Mean Square Error (RMSE) quantify the difference between predicted values and observed values in regression analysis?

RMSE measures the average magnitude of prediction errors in regression, squaring and averaging residuals

Write the formula for Mahalanobis distance

D^2 = (x - μ)^T Σ^(-1) (x - μ)

Write the formula for covariance between X and Y

Cov(X, Y) = Σ((Xi - X̄)(Yi - Ȳ)) / (n - 1)

What expected calibration error (ECE) measures: gap between confidence and accuracy

ECE quantifies the discrepancy between a model's predicted confidence and its actual accuracy

Write the formula for PageRank equation

Pr(A) = (1-d) + d * Σ(Pr(W)/L(W)) for all outbound links W leading to page A