From d64a0b1e22ae338314ad535ee12ada730bb914dd Mon Sep 17 00:00:00 2001
From: Ole Schulz-Trieglaff <ole.st@gmx.de>
Date: Sat, 28 Feb 2015 00:06:02 +0000
Subject: [PATCH 1/3] Linear regression in R, to get optimal solution

---
 01-Simple-Linear-Regression/linreg.R | 12 ++++++++++++
 1 file changed, 12 insertions(+)
 create mode 100644 01-Simple-Linear-Regression/linreg.R

diff --git a/01-Simple-Linear-Regression/linreg.R b/01-Simple-Linear-Regression/linreg.R
new file mode 100644
index 0000000..7ebca2c
--- /dev/null
+++ b/01-Simple-Linear-Regression/linreg.R
@@ -0,0 +1,12 @@
+x <- read.table("ex2x.dat")
+y <- read.table("ex2y.dat")
+
+ft <- lm(y[,1]~x[,1])
+ft
+anova(ft)
+
+png(file="age_vs_weight.png",height=600,width=600);
+plot(x[,1],y[,1])
+abline(ft)
+dev.off()
+

From 503e3e05b7497881201d525a819b67d74dd783fc Mon Sep 17 00:00:00 2001
From: Ole Schulz-Trieglaff <ole.st@gmx.de>
Date: Sat, 28 Feb 2015 00:15:25 +0000
Subject: [PATCH 2/3] Gradient descent implemented using numpy

---
 .../linreg.gradient.py                        | 40 +++++++++++++++++++
 1 file changed, 40 insertions(+)
 create mode 100644 01-Simple-Linear-Regression/linreg.gradient.py

diff --git a/01-Simple-Linear-Regression/linreg.gradient.py b/01-Simple-Linear-Regression/linreg.gradient.py
new file mode 100644
index 0000000..ce4bc64
--- /dev/null
+++ b/01-Simple-Linear-Regression/linreg.gradient.py
@@ -0,0 +1,40 @@
+#!/usr/bin/python
+
+import numpy as np
+
+def gradDescent(x, y, theta, alpha, m, nIter):
+    loss = 0
+    for i in range(0, nIter):
+        h = np.dot(x, theta)
+        loss = (h-y)
+        gradient = np.dot(x.transpose(), loss) / m
+        theta = theta - alpha * gradient
+
+    cost = np.sum(loss ** 2) / (2 * m)
+    print("After %d iterations, cost is %f" % (nIter, cost))
+    return theta
+
+y = np.loadtxt('data/ex2y.dat')
+x = np.loadtxt('data/ex2x.dat')
+
+on = np.ones(np.shape(x))
+# append ones for offset
+x  = np.column_stack((on,x))
+
+m,n     = np.shape(x)
+numIter = 10000
+
+# starting values
+theta = np.array([5,5])
+# learning rate
+alpha = 0.05
+
+# gradient descent
+theta = gradDescent(x, y, theta, alpha, m, numIter)
+print "theta=",theta
+
+# analytical solution
+t1 = np.linalg.inv(np.dot(x.transpose(),x))
+theta2 = np.dot(np.dot(t1,x.transpose()),y)
+print "theta2=",theta2
+

From 0b0c6c151ddc0bfe54cbb77560492f29f16dcdd2 Mon Sep 17 00:00:00 2001
From: Ole Schulz-Trieglaff <ole.st@gmx.de>
Date: Sat, 28 Feb 2015 00:17:45 +0000
Subject: [PATCH 3/3] Adding ref to machine learning coursera class

---
 01-Simple-Linear-Regression/linreg.R           | 4 ++--
 01-Simple-Linear-Regression/linreg.gradient.py | 1 +
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/01-Simple-Linear-Regression/linreg.R b/01-Simple-Linear-Regression/linreg.R
index 7ebca2c..7fa4805 100644
--- a/01-Simple-Linear-Regression/linreg.R
+++ b/01-Simple-Linear-Regression/linreg.R
@@ -1,5 +1,5 @@
-x <- read.table("ex2x.dat")
-y <- read.table("ex2y.dat")
+x <- read.table("data/ex2x.dat")
+y <- read.table("data/ex2y.dat")
 
 ft <- lm(y[,1]~x[,1])
 ft
diff --git a/01-Simple-Linear-Regression/linreg.gradient.py b/01-Simple-Linear-Regression/linreg.gradient.py
index ce4bc64..2a7834c 100644
--- a/01-Simple-Linear-Regression/linreg.gradient.py
+++ b/01-Simple-Linear-Regression/linreg.gradient.py
@@ -2,6 +2,7 @@
 
 import numpy as np
 
+# Implementation based on Ex. 1 in https://www.coursera.org/course/ml
 def gradDescent(x, y, theta, alpha, m, nIter):
     loss = 0
     for i in range(0, nIter):