Submissions are evaluated by a standardized weighted mean squared error.

We chose this metric for the following reasons:
- Standardization ensures the MSE scores all have the same scale. This ensures comparability between the MSE scores for the individual targets
- Weighting allows us to weight all four cultivar regression targets such that our average considers them to be a single target.
- Simplifies intuitive understanding of the metric. Assuming test data is from the same distribution as the training data, blindly guessing the training set mean results in a score of approximately 1.0, with 0.0 being a perfect score.

Given following parameters:

$$N = \mathtt{Number\, of\, samples}$$
$$T = \mathtt{Number\, of\, targets}$$
$$w_j = \mathtt{Target\, weight}$$
$$\sigma_j= \mathtt{Target\, standard\, deviation\, (from\, training\, set)}$$

We score all submissions using the following formula:

$$\frac{1}{N}\sum_j^T \frac{w_j}{{\sigma_j}^2} \sum_i^N (y_{i,j} - \hat{y_{i,j}})^2$$

We using the following target weights:

| target        | GrainWeight | Gsw    | PhiPS2 | Fertilizer | Heerup | Kvium  | Rembrandt | Sheriff |
|---------------|-------------|--------|--------|------------|--------|--------|-----------|---------|
| $$w_j$$       | 1.0         | 1.0    | 1.0    | 1.0        | 0.25   | 0.25   | 0.25      | 0.25    |

## Submission File
For each ImageId in the test set, you must predict a probability for all 8 target variables. The file should contain a header and have the following format:

    ImageId,GrainWeight,Gsw,PhiPS2,Fertilizer,Heerup,Kvium,Rembrandt,Sheriff
    00002,6355.478,0.05804877,0.5530334,0.5786164,0.25786164,0.22012578,0.27044025,0.25157234
    00004,6355.478,0.05804877,0.5530334,0.5786164,0.25786164,0.22012578,0.27044025,0.25157234
    00005,6355.478,0.05804877,0.5530334,0.5786164,0.25786164,0.22012578,0.27044025,0.25157234
    etc.