The reproducible example to fix the discussion:

```
from sklearn.linear_model import RidgeCV
from sklearn.datasets import load_boston
from sklearn.preprocessing import scale 

boston = scale(load_boston().data)
target = load_boston().target

import numpy as np
alphas = np.linspace(1.0,200.0, 5)
fit0 = RidgeCV(alphas=alphas, store_cv_values = True, gcv_mode='eigen').fit(boston, target)
fit0.alpha_
fit0.cv_values_[:,0]

```

The question: what formula is used to compute `fit0.cv_values_`?

Edit:
=====

@Abhinav Arora answer below seems to suggests that `fit0.cv_values_[:,0][0]`, the first entry of `fit0.cv_values_[:,0]` would be 

```
(fit1.predict(boston[0,].reshape(1, -1)) - target[0])**2

```

where `fit1` is a ridge regression with alpha = 1.0, fitted to the data-set from which observation `0` was removed.

Let's see:

1) create new dataset with first row of original dataset removed:

```
from sklearn.linear_model import Ridge
boston1 = np.delete(boston, (0), axis=0)
target1 = np.delete(target, (0), axis=0)

```

2) fit a ridge model with alpha = 1.0 on this truncated dataset:

```
fit1 = Ridge(alpha=1.0).fit(boston1, target1)

```

3) check the MSE of that model on the first data-point: 

```
(fit1.predict(boston[0,].reshape(1, -1)) - target[0])**2

```

it is `array([ 37.64650853])` which is not the same as what is produced by the `fit0.cv_values_[:,0]`, ergo:

```
fit0.cv_values_[:,0][0]

```

which is `37.495629960571137`

What gives?