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Paul Rubin's interface to R.

Works now. However, it needs additional Perl libraries, which are currently
commented out. Also, an R-package needs to be installed.

    1: <problem>
    2: <script type="loncapa/perl">
    3: $seed=&random(1,500,1);
    4: $n=&random(15,25,1);
    5: $offset=&random(2,5,0.1);
    6: $slope=&random(0.6,2.5,0.1);
    7: # construct a data set using R
    8: # dump is for debugging, print to screen to see data structure
    9: ($data,$dump)=&cas_hashref('R',"set.seed($seed);x<-1:$n;w<-1+sqrt(x)/2;data.frame(x=x,y=$offset+$slope*x+rnorm(x)*w);");
   10: @x=&cas_hashref_array($data,'x');
   11: @y=&cas_hashref_array($data,'y');
   12: $datax=join(',',@x);
   13: $datay=join(',',@y);
   14: # calculate the right answer using R
   15: ($answerdata,$dump)=&cas_hashref('R',"x<-c($datax);y<-c($datay);dataset<-data.frame(x=x,y=y);fm<-lm(y~x,data=dataset);");
   16: $answer=&cas_hashref_entry($answerdata,'coefficients','x').'*x+'.&cas_hashref_entry($answerdata,'coefficients','(Intercept)');
   17: </script>
   18: 
   19: <startouttext />
   20: Consider the plotted data set.<br />
   21: <endouttext />
   22: <gnuplot width="400" solid="0" plotcolor="monochrome" gridlayer="off" bmargin="default" font="9" alttag="dynamically generated plot" bgcolor="xffffff" texfont="22" transparent="off" plottype="Cartesian" rmargin="default" gridtype="Cartesian" minor_ticscale="0.5" fontface="sans-serif" grid="on" align="left" texwidth="93" height="300" border="on" samples="100" fgcolor="x000000" major_ticscale="1" tmargin="default" lmargin="default" fillstyle="empty">
   23:     <curve linestyle="points" linetype="solid" color="x000000" pointtype="3" limit="closed" pointsize="2" linewidth="1">
   24:         <data>@x</data>
   25:         <data>@y</data>
   26:     </curve>
   27:     
   28: </gnuplot>
   29: 
   30: <startouttext />
   31: <br />
   32: Give a linear function approximating the data.<br />
   33: <tt>y(x)=</tt>
   34: <endouttext />
   35: <formularesponse id="11" answer="$answer" samples="x@1:$n#20">
   36:     <responseparam name="tol" default="2%" description="Numerical Tolerance" type="tolerance" />
   37:     <textline size="25" readonly="no" />
   38:     
   39: </formularesponse>
   40: </problem>