## ECON 370 LAB 5:  CROSS-VALIDATION 
## NAME:  
## DATE:  


# preliminaries ----------------------------------------------------------------



# load data --------------------------------------------------------------------


# setup --------------------------------------------------------------------

## define datasize as the number of rows in your data set


## add a row data_id that is indicates the row number in the original data set


# define max_order, the maximum number of polynomial terms to consider (set it to 8)


# define num_folds (we'll use 10)


# create a fold_id vector that is max_order copies of 1 followed by max_order copies of 2, etc... 
#   up to the final fold


# create a poly_id (for the number of polynomial terms used) that is a sequence from 1 to max_order 
#   repeated num_fold times in a column vector


# create 3 blank (NA) vectors train_mse, test_mse, and check_mse that are max_order * numbfolds by 1


# set the seed and randomly assign each observation to a fold


# now do the cross-validation, looping through the folds

  
  # split into training (fold != n) and test (fold == n) data sets 
  
  # loop through the number of polynomial terms to include (1 up to max_order)
  
    # run ols on the training data including i polynomial terms of log gdp
    
    # define j to indicate the row where you will write the MSEs
    
    # update train_mse in row j
    
    # calculate the MSE in the test data, write it to row j of test_mse
    
  # calculate the MSE in the training data using your test data formula, write it to row j of check_mse
  
  
# define kcv, a data frame or tibble containinf fold_id, poly_id, train_mse, test_mse, and check_mse
# group the data by poly_id to calculate the mean k-fold CV test MSE for each number of polynomial terms

# make a scatter plot of the degree of polynomial on the x-axis and the test MSE on the y-axis
# save your graph as a pdf