Bivariate Normal Regression

Linear Regression and Residual Standard Deviation (RSD)

Simulation demonstrating the 68-95 rule with RSD

Within ±1 RSD

--%

Expected: ~68%

Within ±2 RSD

--%

Expected: ~95%

Regression Line

±1 RSD

±2 RSD

Correlation: 0.70

-0.99 0 +0.99

Sample Size (n): 200

20 260 500

Actual sample correlation: r = -

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What is RSD?

RSD (Residual Standard Deviation) measures the typical vertical distance of data points from the regression line. Under normality assumptions, approximately 68% of points fall within ±1 RSD and 95% within ±2 RSD from the regression line.