"The shape of the input features: $\frac{442,10}{?}$

$,$

"The shape of the output varaible: $\frac{442,}{?}$

$"$# Load the diabetes dataset $\frac{?}{?}$

$",$

"diabetes$\_x,$ diabetes $y=$ datasets.Load$\_$diabetes$($return$\_$X$\_$y$=$True$)|n",$

"print$(\text{'}$The shape of the input features:$\text{'},$ diabetes$\_$X$.$ shape$)$ In$",$

"print$(\text{'}$The shape of the output varaible:$\text{'},$ diabetes y$.$shape$)"$

$"$# Use only one feature $\frac{?}{?}$

$",$

"diabetes$\_$X$\_$one $=$ diabetes$\_$X$[$:$,$ np$.$newaxis, $2]\frac{?}{?}$

$",$

"print$($diabetes$\_$X$\_$one.shape$)"$

$"$## Dataset split $|n,$

$"$In$",$

"Now, we split the dataset into two parts: training set and test set. $1n",$

$"$In$",$

$"-$ training set: $422$ samples $\frac{?}{?}$

$,$

$"-$ test set: $20$ samples $"$

"Assume that we have a hypothesis $$$h_{-}\{||\}(x)=||$ theta$\_+||$ theta$\_1$ x$.$ $$\frac{\text{\$}}{?}$

$,$

$"$In$",$

"Your tasks: In$",$

$"$In$",$

$,$

$"|n",$

$"[$IMPORTANT$]$ Do not just call the least square function from libraries, for example, $1n",$

"scipy.optimize.least$\_$squares from scipy. Doing so will result in $0$ point. Using helping functions such as numpy.linalg.inv is okay. In$",$

$"$In$",$

$"1n",$

$"[$NOTE$]$ Notice that the loss function is mean$-$squared error. In$",$

$"1n",$

$"-[3$pts$]$ derive the analytical expression of the gradient if the loss is defined as $1n,$

theta $|\frac{|}{2^{{?}^{{?}^{?}}}}2,$$$$|n^{\text{'}\text{'}},$

$"$In$",$

$"$To check whether your computation is correct, consider using an API such as Scikit learn linearregression."