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#+TITLE:    
#+AUTHOR:    FOSSEE
#+EMAIL:     
#+DATE:    

#+DESCRIPTION: 
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#+LANGUAGE:  en
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* 
#+begin_latex
\begin{center}
\vspace{12pt}
\textcolor{blue}{\huge Least Square Fit}
\end{center}
\vspace{18pt}
\begin{center}
\vspace{10pt}
\includegraphics[scale=0.95]{../images/fossee-logo.png}\\
\vspace{5pt}
\scriptsize Developed by FOSSEE Team, IIT-Bombay. \\ 
\scriptsize Funded by National Mission on Education through ICT\\
\scriptsize  MHRD,Govt. of India\\
\includegraphics[scale=0.30]{../images/iitb-logo.png}\\
\end{center}
#+end_latex
* Objectives
  At the end of this tutorial, you will be able to,

 - Generate the least square fit line for a
   given set of points.
* Pre-requisite
  Spoken tutorial on -
  - Using plot interactively.
  - Loading data from files.
  - Getting started with arrays.
* Exercise 1
  - Generate a least square fit line for l v/s t^2 using the data in the file
    'pendulum.txt'.
* Summary
  In this tutorial,we have learnt to,

  - Generate a least square fit using matrices.
  - Use the function ``lstsq()`` to generate a least square fit line. 
* Evaluation
  1. What does ones_like([1, 2, 3]) produce

   - array([1, 1, 1])
   - [1, 1, 1]
   - [1.0, 1.0, 1.0]
   - Error
   
  2. The plot of ``u`` vs ``v`` is a bunch of scattered points that show a
     linear trend. How do you find the least square fit line of ``u`` v/s ``v``.

* Solutions
  1. array([1, 1, 1])

  2. A = array(u, ones\_like(u)).T
     result = lstsq(A, v)
     m, c = result[ 0 ]
     lst\_line = m * u + c
* 
#+begin_latex
  \begin{block}{}
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  \textcolor{blue}{\Large THANK YOU!} 
  \end{center}
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\begin{block}{}
  \begin{center}
    For more Information, visit our website\\
    \url{http://fossee.in/}
  \end{center}  
  \end{block}
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