Figure 2. The effect of collinearity on model parameter estimates.

We simulated 10,000 iterations of a model y ∼ x1 + x2, where x1 had a positive effect on y (β_x1 = 1, vertical dashed line). x2 is collinear with x1 with either a moderate (r = 0.5). (A) or strong correlation (r = 0.9). (B) With moderate collinearity, estimation of β_x1 is precise, but certainty of the sign of β_x2 is low. When collinearity is strong, estimation of β_x1 is far less precise, with 14% of simulations estimating a negative coefficient for the effect of x1. For more elaborate versions of these simulations, see Freckleton (2011).