cleaning up typos

doc/src/Projects/2021/Project1/Project1.do.txt

@@ -111,22 +111,22 @@ analysis using polynomials in $x$ and $y$ up to fifth order. Find the
 variances, evaluate the Mean Squared error (MSE)
 
 !bt 
-\[ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n}
+\[ MSE(\bm{y},\tilde{\bm{y}}) = \frac{1}{n}
 \sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2, 
 \] 
 !et 
 
-and the $R^2$ score function.  If $\tilde{\hat{y}}_i$ is the predicted
+and the $R^2$ score function.  If $\tilde{\bm{y}}_i$ is the predicted
 value of the $i-th$ sample and $y_i$ is the corresponding true value,
 then the score $R^2$ is defined as
 
 !bt
 \[
-R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2},
+R^2(\bm{y}, \tilde{\bm{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2},
 \]
 !et
 
-where we have defined the mean value  of $\hat{y}$ as
+where we have defined the mean value  of $\bm{y}$ as
 
 !bt
 \[
@@ -142,6 +142,7 @@ splitting training data provided by the library _Scikit-Learn_ (make
 sure you have installed it).  This function is called
 $train\_test\_split$.  _You should present a critical discussion of why and how you have scaled or not scaled the data_.
 
+
 It is normal in essentially all Machine Learning studies to split the
 data in a training set and a test set (eventually  also an additional
 validation set).  There
@@ -228,7 +229,7 @@ Note also that when you calculate the bias, in all applications you don't know t
 The aim here is to write your own code for another widely popular
 resampling technique, the so-called cross-validation method.  Again,
 before you start with cross-validation approach, you should scale your
-data.
+data if you think this is needed.
 
 Implement the $k$-fold cross-validation algorithm (write your own
 code) and evaluate again the MSE function resulting