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: $data=&cas('R',"set.seed($seed);x<-1:$n;w<-1+sqrt(x)/2;data.frame(x=x,y=$offset+$slope*x+rnorm(x)*w);");
9: # separate into an x and a y vector
10: @datatable=split(/\s+/gs,$data);
11: for ($i=0;$i<2*$n;$i+=2) {
12: push(@x,$datatable[$i]);
13: push(@y,$datatable[$i+1]);
14: }
15: $datax=join(',',@x);
16: $datay=join(',',@y);
17: # calculate the right answer using R
18: ($intercept,$slope)=split(/\s+/,&cas('R',"x<-c($datax);y<-c($datay);dataset<-data.frame(x=x,y=y);fm<-lm(y~x,data=dataset);array(coef(fm),dim=2);"));
19: $answer="$slope*x+$intercept";
20: </script>
21: <gnuplot width="400" solid="0" plotcolor="monochrome" gridlayer="off" bmargin="default" font="9" alttag="dynamically generated plot" bgcolor="xffffff" texfont="22" transparent="off" plottype="Cartesian" rmargin="default" gridtype="Cartesian" minor_ticscale="0.5" fontface="sans-serif" grid="on" align="right" texwidth="93" height="300" border="on" samples="100" fgcolor="x000000" major_ticscale="1" tmargin="default" lmargin="default" fillstyle="empty">
22: <curve linestyle="points" linetype="solid" color="x000000" pointtype="3" limit="closed" pointsize="2" linewidth="1">
23: <data>@x</data>
24: <data>@y</data>
25: </curve>
26:
27: </gnuplot>
28:
29: <startouttext />
30: Consider the data set
31: <pre>$data</pre>
32:
33: Give a linear function approximating the data.<br />
34: <tt>y(x)=</tt>
35: <endouttext />
36: <formularesponse answer="$answer" samples="x@1:$n#20">
37: <responseparam name="tol" default="2%" description="Numerical Tolerance" type="tolerance" />
38: <textline size="25" readonly="no" />
39:
40: </formularesponse>
41: </problem>
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