update

doc/src/week35/week35.do.txt

@@ -583,7 +583,18 @@ $n\times p$ matrix $\bm{X}$.
 It is rather straightforward to implement the matrix inversion and obtain the parameters $\bm{\beta}$. After having defined the matrix $\bm{X}$ and the outputs $\bm{y}$ we have 
 !bc pycod 
 # matrix inversion to find beta
+# First we set up the data
 import numpy as np
+x = np.random.rand(100)
+y = 2.0+5*x*x+0.1*np.random.randn(100)
+# and then the design matrix X including the intercept
+#  The design matrix now as function of a fourth-order polynomial
+X = np.zeros((len(x),5))
+X[:,0] = 1.0
+X[:,1] = x
+X[:,2] = x**2
+X[:,3] = x**3
+X[:,4] = x**4
 beta = (np.linalg.inv(X.T @ X) @ X.T ) @ y
 # and then make the prediction
 ytilde = X @ beta