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    <p>So, here's the php implementation of your algorithm that uses Dawkins' weasel to reduce the error gradually until the desired threshold.</p> <pre><code>&lt;?php function sqrMeanDeviation($array, $avg) { $sqrMeanDeviation = 0; for($i=0; $i&lt;count($array); $i++) { $dev = $array[$i] - $avg; $sqrMeanDeviation += $dev * $dev; } return $sqrMeanDeviation; } // z values are non-0 an can value between [-abs_z_bound, abs_z_bound] function random_z_element($abs_z_bound = 1) { $a = (mt_rand() % (2*$abs_z_bound) ) - ($abs_z_bound-1); if($a &lt;= 0) $a--; return $a; } // change z a little function copy_z_weasel($old_array_z, $error_probability = 20 /*error possible is 1 in error_probability*/, $abs_z_bound = 1) { $new_z = array(); for($i = 0; $i &lt; count($old_array_z); $i++) if(mt_rand() % $error_probability == 0 ) $new_z[$i] = random_z_element($abs_z_bound); else $new_z[$i] = $old_array_z[$i]; return $new_z; } function correlation_error($array_y, $array_x, $avg_x, $sqrMeanDeviation_x, $correlation) { // checking correlation $avg_y = array_sum($array_y)/count($array_y); $sqrMeanDeviation_y = 0; $covariance_xy = 0; for($i=0; $i&lt;count($array_x); $i++) { $dev_y = $array_y[$i] - $avg_y; $sqrMeanDeviation_y += $dev_y * $dev_y; $dev_x = $array_x[$i] - $avg_x; $covariance_xy += $dev_y * $dev_x; } $correlation_xy = $covariance_xy/sqrt($sqrMeanDeviation_x*$sqrMeanDeviation_y); return abs($correlation_xy - $correlation); } function ySeries($array_x, $low_bound, $high_bound, $correlation, $threshold) { $array_y = array(); $avg_x = array_sum($array_x)/count($array_x); $sqrMeanDeviation_x = sqrMeanDeviation($array_x, $avg_x); // pre-compute beta $beta_x_sQMz = $sqrMeanDeviation_x * sqrt( 1 / ($correlation*$correlation) - 1 ); $best_array_z = array(); $n = 0; $error = $threshold + 1; while($error &gt; $threshold) { ++$n; // generate z $array_z = array(); if(count($best_array_z) == 0) for($i=0; $i&lt;count($array_x); $i++) $array_z[$i] = random_z_element(); else $array_z = copy_z_weasel($best_array_z); $sqm_z = sqrMeanDeviation($array_z, array_sum($array_z)/count($array_z) ); // this being 0 implies that for every beta correlation(x,y) = 1 so just give it any random beta if($sqm_z) $beta = $beta_x_sQMz / $sqm_z; else $beta = 10; // and now we have y for($i=0; $i&lt;count($array_x); $i++) $array_y[$i] = $array_x[$i] + ($array_z[$i] * $beta); // now, change bounds (we could do this afterwards but we want precision and y to be integers) // rounding $min_y = $array_y[0]; $max_y = $array_y[0]; for( $i=1; $i&lt;count($array_x); $i++ ) { if($array_y[$i] &lt; $min_y) $min_y = $array_y[$i]; if($array_y[$i] &gt; $max_y) $max_y = $array_y[$i]; } $range = ($high_bound - $low_bound) / ($max_y - $min_y); $shift = $low_bound - $min_y; for( $i=0; $i&lt;count($array_x); $i++ ) $array_y[$i] = round($array_y[$i] * $range + $shift); // get the error $new_error = correlation_error($array_y, $array_x, $avg_x, $sqrMeanDeviation_x, $correlation); if($new_error &lt; $error) { $best_array_z = $array_z; $error = $new_error; } } echo "Correlation ", $correlation, " approched within " , $new_error, " in ", $n ," iterations.\n"; return $array_y; } ?&gt; </code></pre>
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    1. POHow to calculate a random series of values (B) that have a given correlation with a given series (A)
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    1. COThanks! But what I don't understand ... you speak off an average difference of 0.001 ... I get many differences between -0.1 and 0.8 on a requested correlation of 0.7. How is such a difference with your results possible? I'm using your code with `$array_x = array(5,3,6,7,4,2,9,5); $low_bound = 100; $high_bound = 130; $correlation = 0.7;` Any ideas? Is it possible to enhance the algorithms accuracy or let the function repeat itself if the correlation has a difference above a certain threshold, say 0.05?
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    2. COI am surprised by the variance of the error (the value abs($correlation_xy - $correlation)) but I did only a quick testing, with a big number of random input values (array_x and correlation) and the average error was low. That's why I suggested you add a loop to control the maximum error. But I'll edit to include that since I like Alex's idea.
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