How to graph trendline

[djones]

I have a set of test scores with dates that I can graph. I would like to be able to include a trendline on the graph. What I wrote is not quite right -- the line just follows the original - it's not straight. I would be extremely grateful for any help.

I calculated the slope thus (some subs not included):

#----------------------------------------------------------
#    FOR SLOPE
#----------------------------------------------------------
my $mean_score = &average(\@allscores);
$mean_score= sprintf("%.0f",$mean_score);
my $stdev_score = &stdev(\@allscores);
$stdev_score= sprintf("%.3f",$stdev_score);


my @list_of_x;
my @list_of_y;
my @list_of_z;
my $num_scores = @allscores;

# Get list of x
# since each date is just ... yeah... 1
my $dates = 1;
foreach ($i=0; $i<$num_scores; $i++){
    @list_of_x[$i] = ($dates-$mean_score)/$stdev_score;
    @list_of_x[$i]= sprintf("%.2f",@list_of_x[$i]);
    $dates++;
}
# Get list of y
foreach ($i=0; $i<$num_scores; $i++){
    @list_of_y[$i] = (@allscores[$i]-$mean_score)/$stdev_score;
    @list_of_y[$i]= sprintf("%.2f",@list_of_y[$i]);
}

# Get the list of z-scores
for($i=0; $i<$num_scores; $i++){
    @list_of_z[$i]= (@list_of_x[$i] * @list_of_y[$i]);
    @list_of_z[$i]= sprintf("%.2f",@list_of_z[$i]);
}

# add up the z-scores
my $sigma = 0;
for($i=0; $i<$num_scores; $i++){
    $sigma = ($sigma + @list_of_z[$i]);
}

# get the correlation
my $correl = $sigma/($num_scores-1);

# get the slope
my $stdev_x = &stdev(\@list_of_x);
my $stdev_y = &stdev(\@list_of_y);
my $slope = $correl * ($stdev_x / $stdev_y);
$slope= sprintf("%.2f",$slope);


# add slope to each y ... y is each score
my @trendline;
for($i=0; $i<$num_scores; $i++){
    @trendline[$i] = @allscores[$i]+$slope;
    @trendline[$i] = sprintf("%.4f",@trendline[$i]);
}

#create the data for transfer to the graph program
$trendlineString = join(',',@trendline);

And the graphing script does this:

my @data = ([@alldates],
            [@allScores], 
            [@trendline] 
        );

my $mygraph = GD::Graph::lines->new(600, 300);
$mygraph->set(
    x_label     => 'Assessments',
    y_label     => 'Score',
    title       => 'Progress Monitoring Report for '.$student,
    y_max_value => 100,
    y_min_value => 0,
    show_values => 1,
    # Show the grid
    long_ticks  => 1,
    
    #line_types  => [1, 2, 4],
    line_types  => [1],
    # Set the thickness of line
    line_width  => 4,
    # Set colors for datasets
    #dclrs       => ['blue', 'green', 'red'],
    dclrs       => ['blue','red'],
) or warn $mygraph->error;

$mygraph->set_legend_font(GD::gdMediumBoldFont);

my $myimage = $mygraph->plot(\@data) or die $mygraph->error;

print "Content-type: image/png\n\n";
print $myimage->png;

[frozenwithjoy]

Are you familiar with the the statistical programming language 'R'? Everything you've done and want to do would be just a few lines in R. If you did use R, you can use Statistics::R to run R commands via Perl.

[RichardK]

I'm not sure exactly what your calculation does, but Statistics::Descriptive can calculate a least squares fit, if that's any use to you?

[pvaldes]

use Statistics::R ;
  my $R = Statistics::R->new() ;
  
  $R->startR ;
  $R->send(q`pdf("/tmp/examplot.pdf")`) ;
  $R->send(q`adata <- c(10,20,30,25,24,23,12,7,8,9,10,10,28,29,29,34,3
+8,38,11,14,40,42,41)`) ;
  $R->send(q`bdata <- c(0,3,4,4,1,1,1,7,7,7,1,0,7,4,7,2,1,3,1,0,10,9,1
+1)`) ;
  $R->send(q`plot(adata,bdata, xlab = 'temp', ylab = 'laziness', main 
+= 'silly  experiment')`);
  $R->send(q`lines(lowess(adata,bdata),f = 4/5, col = 'Red')`) ;
  my $ret = $R->read ;
  
  $R->stopR();

system("xpdf /tmp/examplot.pdf") or die $!;