View of /trunk/NationalProblemLibrary/UVA-Stat/setStat212-Homework13/stat212-HW13-10.pg

    1 ## DESCRIPTION
    2 ##  Statistics: Sampling Distributions
    3 ## ENDDESCRIPTION
    4 ##DESCRIPTION
    5 ##KEYWORDS('statistics','hypothesis testing')
    6 ##
    7 ## naw tagged this problem
    8 
    9 ## DBchapter('Hypothesis Testing')
   10 ## DBsection('Common Large-Sample Tests')
   11 ## Date('7/8/2005')
   12 ## Author('Nolan A. Wages')
   13 ## Institution('University of Virgnia')
   14 ## TitleText1('Mathematical Statistics')
   15 ## EditionText1('4')
   16 ## AuthorText1('Wackerly, Mendenhall, Scheaffer')
   17 ## Section1('10.3')
   18 ## Problem1('20')
   19 
   20 
   21 ##ENDDESCRIPTION
   22 
   23 DOCUMENT();        # This should be the first executable line in the problem.
   24 
   25 loadMacros(
   26 "PG.pl",
   27 "PGbasicmacros.pl",
   28 "PGchoicemacros.pl",
   29 "PGanswermacros.pl",
   30 "PGgraphmacros.pl",
   31 "PGnumericalmacros.pl",
   32 "PGstatisticsmacros.pl",
   33 "PGauxiliaryFunctions.pl",
   34 "extraAnswerEvaluators.pl"
   35 );
   36 
   37 
   38 
   39 TEXT(beginproblem());
   40 $showPartialCorrectAnswers = 1;
   41 # install_problem_grader(~~&std_problem_grader);
   42 
   43 $n = random(40,50,1);
   44 $k = random(5,9,1);
   45 $sse = random(1200,1500,1);
   46 $ssr = random(800,900,1);
   47 $sst = $ssr + $sse;
   48 
   49 $r2 = 0.0001*floor(10000*($ssr/$sst) + 0.5);
   50 $multr = 0.0001*floor(10000*sqrt($r2) + 0.5);
   51 $adjr2 = 0.0001*floor(10000*(1 - ( ($sse/($n-$k-1))/($sst/($n-1)) )) + 0.5);;
   52 $obs = $n;
   53 $se = 0.01*floor(100*sqrt($sse/($n-$k-1))+0.5);
   54 
   55 $dfreg = $k;
   56 $dfres = $n-$k-1;
   57 $dftot = $n-1;
   58 
   59 $msr = 0.01*floor(100*$ssr/$dfreg + 0.5);
   60 $mse = 0.01*floor(100*$sse/$dfres + 0.5);
   61 $f = 0.01*floor(100*$msr/$mse + 0.5);;
   62 $fsig = fprob($dfreg,$dfres,$f);
   63 
   64 
   65 BEGIN_TEXT
   66 
   67 Below is partial Excel output from a multiple regression:
   68 \[
   69 \begin{array}{|l|r|r|r|r|r|} \hline
   70 \multicolumn{2}{|c|}{\mbox{Regression Statistics}} & & & & \\ \hline
   71 \mbox{Multiple R} & $multr & & & & \\ \hline
   72 \mbox{R Square}   & $r2    & & & & \\ \hline
   73 \mbox{Adjusted R Square} & $adjr2 & & & & \\ \hline
   74 \mbox{Standard Error} & $se & & & & \\ \hline
   75 \mbox{Observations} & $obs & & & & \\ \hline
   76 &  & & & & \\ \hline
   77 \mbox{ANOVA} & & & & & \\ \hline
   78  & \mbox{df} &\mbox{SS} &\mbox{MS} &\mbox{F} &\mbox{Significance F} \\ \hline
   79 \mbox{Regression} & $dfreg & $ssr & $msr & $f & $fsig\\ \hline
   80 \mbox{Residual} & $dfres & $sse & $mse &   &  \\ \hline
   81 \mbox{Total} & $dftot & $sst &  &   &  \\ \hline
   82 \end{array}
   83 \]
   84 $PAR
   85 Determine each of the following from the output:
   86 $PAR
   87 
   88 \(R^2\) = \{ ans_rule(15) \}
   89 
   90 $PAR
   91 
   92 \(s_{\epsilon}\) = \{ ans_rule(15) \}
   93 
   94 $PAR
   95 
   96 MSR = \{ ans_rule(15) \}
   97 
   98 $PAR
   99 
  100 END_TEXT
  101 
  102 ANS(num_cmp($r2));
  103 ANS(num_cmp($se));
  104 ANS(num_cmp($msr));
  105 
  106 ENDDOCUMENT();       # This should be the last executable line in the problem.