Biased and Inefficient

Quartets of datasets are trendy now, so here’s one for collinearity diagnostics. These four data sets have two candidate predictors \(x\) and \(z\) and outcome \(y\), and have very strong correlation (over 0.95) between \(x\) …

The 1986 Joint Statistical Meetings had a Data Expo where participants were given a dataset to show off visualisation approaches. The “pollen” “data” was a \(3848\times 5\) matrix purporting to be five measurements of 3848 …

The distribution of a \(n\times n\) quadratic form in Gaussian variables, \(X^TAX\) is a linear combination of \(\chi_1^2\) variables: \[Q\sim\sum_{i=1}^n\lambda_iZ^2_i\] where \(\lambda_i\) are the eigenvalues of \(A\Xi\) and \(\Xi\) is the covariance matrix of \(X\). …