There are two aspects of the modeling that will be evaluated.  One aspect is the predictive ability of the model and the other is the inferences about the causal effect of manganese on cognitive ability.
To evaluate predictive ability, we will assess the root mean square error of the predictions on the test set, which is defined by:
\[ RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(Y_i - \widehat{Y}_i)^2} \]
For this aspect of the modeling you will be allowed to upload predictions on Kaggle and the performance on approximately a random half of the data is given so that you can gauge your performance on out-of-sample data.  The final evaluation will be done on the remaining half so that you do not overfit the test data.
To submit predictions on Kaggle, you should have a CSV file where the first column is the observation ID (ID) and the second column is the corresponding prediction (Y) as you see below.
  The file should include predictions for all 9,588 observations (with matching observation IDs) in the testing set.
ID,Y
1,208.3
2,204.5
3,249.2
etc.
The causal inference aspect will be evaluated by the distance to the causal effect among the test set:
\[ \frac{1}{n_{test}}\sum_{i=1}^{n_{test}} Y_{X_1=17,i}-Y_{X_1=4,i}. \]
Note that the training set and test set are randomly drawn from the same underlying population.  For this aspect of the evaluation you are asked to submit your model and code on canvas at the project deadline.  The performance will then be evaluated based on the submission. Please, refer to the document submitted on canvas for additional questions and information.