Let’s say you have inputs and outputs given by:

### Inputs

- Matrix/Array of predictors (
`X`

X) - Matrix/Array of predictor uncertainties (
`Xsd`

\sigma_X) - Vector of response values (
`y`

y) - Vector of response uncertainties (
`ysd`

\sigma) - Matrix/Array of new predictors (
`X2`

X_2) - (Optional) Matrix/Array of new predictor uncertainties (
`Xsd2`

\sigma_{X2})

### Outputs

- Vector of new responses (
`ypred`

y_{pred}) - Vector of new response uncertainties (
`ysd2`

\sigma_2) - (Optional) predictor covariance matrix (
`cov`

\Sigma_2)

How do you get something like this (or even something along the way to this)?