## DESCRIPTION
##  Statistics: Sampling Distributions
## ENDDESCRIPTION
##DESCRIPTION
##KEYWORDS('statistics','hypothesis testing')
##
## naw tagged this problem

## DBchapter('Hypothesis Testing')
## DBsection('Common Large-Sample Tests')
## Date('7/8/2005')
## Author('Nolan A. Wages')
## Institution('University of Virgnia')
## TitleText1('Mathematical Statistics')
## EditionText1('4')
## AuthorText1('Wackerly, Mendenhall, Scheaffer')
## Section1('10.3')
## Problem1('20')


##ENDDESCRIPTION

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGgraphmacros.pl",
"PGnumericalmacros.pl",
"PGstatisticsmacros.pl",
"PGauxiliaryFunctions.pl",
"extraAnswerEvaluators.pl"
);



TEXT(beginproblem());
$showPartialCorrectAnswers = 0;
install_problem_grader(~~&std_problem_grader);

$x[1] = random(-3,-1,1);
$x[2] = random(0,3,1);
$x[3] = random(4,6,1);

$y[1] = 3 + random(-3,-1,1);
$y[2] = 6 + random(0,3,1);
$y[3] = 9 + random(4,6,1);

$xbar = ($x[1]+$x[2]+$x[3])/3;
$ybar = ($y[1]+$y[2]+$y[3])/3;

$sx = sqrt( (($x[1]-$xbar)**2 + ($x[2]-$xbar)**2 + ($x[3]-$xbar)**2)/2 );
$sy = sqrt( (($y[1]-$ybar)**2 + ($y[2]-$ybar)**2 + ($y[3]-$ybar)**2)/2 );

$cov = ( ($x[1]-$xbar)*($y[1]-$ybar) + ($x[2]-$xbar)*($y[2]-$ybar) 
                + ($x[3]-$xbar)*($y[3]-$ybar) )/2;
                
$b1 = round($cov/$sx**2);
$b0 = round($ybar - $b1*$xbar);

$sse = ($y[1] - ($b0+$b1*$x[1]))**2 + ($y[2] - ($b0+$b1*$x[2]))**2
                + ($y[3] - ($b0+$b1*$x[3]))**2;

BEGIN_TEXT

Suppose that the line \(\hat{y} = $b0 + $b1 x\) is 
fitted to the data points ($x[1],$y[1]), ($x[2],$y[2]), and ($x[3],$y[3]).  
Determine the sum of the squared residuals.
$PAR

Sum of the Squared Residuals = \{ ans_rule(15) \}

$PAR

END_TEXT

ANS(num_cmp($sse));


ENDDOCUMENT();       # This should be the last executable line in the problem.