diff --git a/is/ub9/is9.pdf b/is/ub9/is9.pdf
index d944551..f03aa58 100644
--- a/is/ub9/is9.pdf
+++ b/is/ub9/is9.pdf
Binary files differ
diff --git a/is/ub9/is9.tex b/is/ub9/is9.tex
index c34f421..69c20ec 100644
--- a/is/ub9/is9.tex
+++ b/is/ub9/is9.tex
@@ -9,7 +9,7 @@
 \usepackage{enumerate}
 \usepackage{listings}
 \lstset{language=Python}
-
+\usepackage{ wasysym }
 \usepackage{algpseudocode} %Pseudocode
 \usepackage{dsfont} % schöne Zahlenräumezeichen
 \usepackage{amssymb, amsthm} %noch stärker erweiterte Mathe-Zeichen
@@ -82,7 +82,8 @@
     \Aufgabe{Independence}{50}\\
         \includegraphics[width=0.49\textwidth]{regression.png}
         \includegraphics[width=0.49\textwidth]{residuals.png}\\
-        Da $Y$ qudratisch von $X$ abhängt, vergrößert sich auch die Varianz. Entsprechend werden die Residuen für größere $Y$ ebenfalls größer. %TODO: ?
+        For small values of Y it is overestimated, for larger underestimated. For small X we predict small Y, however there's noise. This leads to the dense population of residuals on y=x.\\
+        Due to the qudratic connection there are more data near zero for a uniformly distributed X than there are further to larger values.\vspace{1cm}\\
     \Aufgabe{Kernels}{50}
         \begin{enumerate}
             \item $k(x_1,x_2)=C= \alpha \cdot k'(x,y)\\
@@ -91,19 +92,19 @@
             \end{pmatrix} \begin{pmatrix}
             1 &1\\1&1
             \end{pmatrix}\begin{pmatrix}
-            x\\y 
-            \end{pmatrix}= x^2+2xy+y^2=(x+y)^2 \geq 0 \forall{x,y}\\$
+            x\\y
+            \end{pmatrix}= x^2+2xy+y^2=(x+y)^2 \geq 0 \forall{x,y}$\checkmark
             \item $k(x,y) =xy\\
-             <x,y> \geq 0 \forall{x,y} $
+             <x,y> \geq 0 \forall{x,y} $\checkmark
             \item No kernel $k(x,y) =\dfrac{1}{2}(x+y)\\
             k(-1,-1) =-1 \ngeq 0\\$
-            But for a Kernel ist has to be:\\
-            $k(x,x) \geq 0 \forall{x} $     
+            But for a Kernel ist has to hold:\\
+            $k(x,x) \geq 0 \forall{x} $\lightning
             \item $k(x,y) = 5x^Ty = 5 \cdot k'(x,y)$ with $k'(x,y) = x^Ty =<x,y>$\\
-            $= \alpha *k'(x,y)$ where $\alpha =5$  
+            $= \alpha *k'(x,y)$ where $\alpha =5$\checkmark
             \item $k(x,y)=(x^Ty+1)^2= (k_1(x,y)+k_2(x,y))^2$\\
             where $k_1(x,y)=x^Ty, k_2(x,y)=1$\\
-            $k_1$ and $k_2$ are proven as kernels in task 2 and 1.
+            $k_1$ and $k_2$ are proven as kernels in task 2 and 1 and summing and multiplying is allowed for kernels. So 5. is also a kernel.\checkmark
         \end{enumerate}
 \end{document}
 
diff --git a/is/ub9/regression.png b/is/ub9/regression.png
index 105a826..58499f0 100644
--- a/is/ub9/regression.png
+++ b/is/ub9/regression.png
Binary files differ
diff --git a/is/ub9/residuals.png b/is/ub9/residuals.png
index c60ca43..0692b9f 100644
--- a/is/ub9/residuals.png
+++ b/is/ub9/residuals.png
Binary files differ
diff --git a/is/ub9/sample.py b/is/ub9/sample.py
index 8ac1fc5..90b9e48 100755
--- a/is/ub9/sample.py
+++ b/is/ub9/sample.py
@@ -3,6 +3,7 @@
 import matplotlib.pyplot as plt
 import random as rand
 from sklearn import svm
+from scipy.optimize import curve_fit
 
 n=500
 
@@ -18,9 +19,19 @@
 X=np.array(X)
 Xt=X.reshape((500,1))
 
-clf=svm.SVR()
-clf.fit(Xt,Y)
-ypred=clf.predict(Xt)
+def func(x,p1,p2,p3,p4,p5):
+  return p1*x**p2+p3*np.exp(x*p4)+p5
+
+popt, pcov = curve_fit(func, X, Y)
+p1 = popt[0]
+p2 = popt[1]
+p3 = popt[2]
+p4 = popt[3]
+p5 = popt[4]
+print(popt)
+ypred=func(X,p1,p2,p3,p4,p5)
+print(np.sum(Y-ypred))
+print(np.mean(Y-ypred))
 
 plt.plot(X,ypred,'rx')