In addition to showing sufficient parameter recovery (
Figure 2—figure supplement 2), we probed the correlation among estimated linear regression coefficients. Even if the true coefficients were not correlated, estimated coefficients may show artificial dependencies due to correlations present in the design matrix. To investigate this possibility, we generated synthetic data using
y =
X∗
b + ε∗
p, as before. This time, we set all values in
b to the same value of 100. Critically, we added Gaussian noise drawn from
N(0,5) to each linear regression coefficient separately. We repeated this procedure 100 times for each subject and calculated the correlation between estimated linear regression coefficients for the five regressors within a given subject. We set
p and λ to 50 and 0.0005, respectively, as in the previous simulation. We averaged obtained correlation matrices across all subjects. We found that the correlation across estimated linear regression coefficients (
B) was lower than expected, given correlations present in design matrix (
A). Again, we confirmed that linear regression coefficients were recoverable for all regressors (
C; scatter plots showing results from all subjects; R corresponds to Pearson’s R between estimated and true linear regression coefficients).