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Annotation of loncom/homework/templates/Rnumerical.problem, revision 1.2

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