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doc/src/How2ReadData/How2ReadData.do.txt

@@ -140,8 +140,24 @@ formats, ipython notebooks, latex files, pdf files etc with minimal edits.
 !split
 ===== Simple linear regression model using _scikit-learn_ =====
 We start with perhaps our simplest possible example, using _scikit-learn_ to perform linear regression analysis on a data set produced by us. 
-What follows is a simple Python code where we have defined  function $y$ in terms of the variable $x$. Both are defined as vectors of dimension $1\times 100$. The entries to the vector $\hat{x}$  are given by random numbers generated with a uniform distribution with entries $x_i \in [0,1]$ (more about probability distribution functions later).
-The Numpy functions are imported used the  
+What follows is a simple Python code where we have defined  function $y$ in terms of the variable $x$. Both are defined as vectors of dimension $1\times 100$. The entries to the vector $\hat{x}$  are given by random numbers generated with a uniform distribution with entries $x_i \in [0,1]$ (more about probability distribution functions later). These values are then used to define a function $y(x)$ (tabulated again as a vector) with a linear dependence on $x$ plus a random noise added via the normal distribution.
+
+
+The Numpy functions are imported used the _import numpy as np_ statement and the 
+random number generator for the uniform distribution is called using the function
+_np.random.rand()_, where we specificy that we want $100$ random variables. 
+Using Numpy we define automatically an array with the specified number of elements, $100$ in our case.
+Using the Numpy function _randn()_ we can compute random numbers with the normal distribution (mean value equal to zero and variance set to one) and produce the values of $y$
+assuming a linear dependence as function of $x$
+!bt
+\[
+y = 2*x+N(0,1),
+\]
+!et
+where $N(0,1)$ represents random numbers generated by the normal distribution. 
+From _scikit_learn_ we import then the _LinearRegression_ functionality and make a prediction $\tilde{y} = \alpha + \beta x$ using the function _fit(x,y)_
+
+We make also a prediction
 !bc pycod
 # Importing various packages
 import numpy as np
@@ -149,7 +165,7 @@ import matplotlib.pyplot as plt
 from sklearn.linear_model import LinearRegression
 
 x = np.random.rand(100,1)
-y = 4+3*x+np.random.randn(100,1)
+y = 2*x+np.random.randn(100,1)
 linreg = LinearRegression()
 linreg.fit(x,y)
 xnew = np.array([[0],[2]])
@@ -164,6 +180,7 @@ plt.title(r'Random numbers ')
 plt.show()
 !ec
 
+Add paly around with various forms, also relative error, plot that and other ways to estimate by the eye the qaulity of the fit
 
 !split
 ===== Introduction to Jupyter notebook and available tools =====