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Bivariate Normal in 3D
Drag to rotate the joint density; change the correlation and see the contours and the regression line.
Day 5: Joint Distributions, Covariance & Correlationsimulated drawsdensity contoursE[Y | X] = ρx
ρ (true)
0.50
sample r
0.52
Var(Y | X)
0.75
1 − ρ²
Left: the joint density surface (drag to rotate). Right: its contour ellipses, 400 draws, and the conditional-mean line E[Y | X = x] = ρx (standardised variables).