# LaTeX2HTML 2008 (1.71)
# Associate images original text with physical files.


$key = q/theta_0=theta_1=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\theta_0=\theta_1=0$">|; 

$key = q/(x^{(i)},y^{(i)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$(x^{(i)}, y^{(i)}$">|; 

$key = q/xin{mathbbR}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$x \in {\mathbb R}^2$">|; 

$key = q/theta=vec{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\theta = \vec{0}$">|; 

$key = q/x_0=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$x_0 = 1$">|; 

$key = q/alpha=0.07;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\alpha = 0.07$">|; 

$key = q/theta_1=0.4057;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\theta_1 = 0.4057$">|; 

$key = q/theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\theta$">|; 

$key = q/n=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$n=1$">|; 

$key = q/{eqnarraystar}theta_0&=&0.7502theta_1&=&0.0639{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="\begin{eqnarray*}
\theta_0 &amp;=&amp; 0.7502 \\\\
\theta_1 &amp;=&amp; 0.0639
\end{eqnarray*}">|; 

$key = q/m=50;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$m = 50$">|; 

$key = q/thetain{mathbbR}^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\theta \in {\mathbb R}^n$">|; 

$key = q/h_theta(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$h_\theta(x)$">|; 

$key = q/theta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\theta_0$">|; 

$key = q/theta_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\theta_j$">|; 

$key = q/{displaymath}J(theta)=frac{1}{2m}sum_{i=1}^{m}left(h_{theta}(x^{(i)})-y^{(i)}right)^{2}nonumber{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="\begin{displaymath}
J(\theta)=\frac{1}{2m}\sum_{i=1}^{m}\left(h_{\theta}(x^{(i)})-y^{(i)}\right)^{2} \nonumber
\end{displaymath}">|; 

$key = q/theta_0=0.0745;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\theta_0 = 0.0745$">|; 

$key = q/J(theta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$J(\theta)$">|; 

$key = q/thetain{mathbbR}^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\theta \in {\mathbb R}^2$">|; 

$key = q/theta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\theta_1$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$x$">|; 

$key = q/{eqnarraystar}theta_0&=&0.0745theta_1&=&0.3800{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="\begin{eqnarray*}
\theta_0 &amp;=&amp; 0.0745 \\\\
\theta_1 &amp;=&amp; 0.3800
\end{eqnarray*}">|; 

$key = q/{displaymath}h_{theta}(x)=theta^Tx=sum_{i=0}^ntheta_ix_i,nonumber{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="\begin{displaymath}
h_{\theta}(x) = \theta^Tx = \sum_{i=0}^n \theta_i x_i, \nonumber
\end{displaymath}">|; 

$key = q/{displaymath}theta_j:=theta_j-alphafrac{1}{m}sum_{i=1}^m(h_{theta}(x^{(i)})-y^{(i)})x_j^{(i)};;;;;mbox{(forall{j{)}nonumber{par{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="\begin{displaymath}
\theta_j := \theta_j - \alpha \frac{1}{m} \sum_{i=1}^m (h_{\...
...{(i)}) x_j^{(i)} \;\;\;\;\;\mbox{(for all $j$)} \nonumber
\par
\end{displaymath}">|; 

1;

