检查功能点的位置

Question

I have a points and I want to draw a best fit hyperbolic function for this points.
Now I want to make a Quality checker. Any ideas?
My idea was to check where is the point against the function. ( Like if the point is over / under or on the function )
prescription function is : fn(x)=A1+(A2/A3*(x+A4))
My first idea for this was:

function checkQuality($points,$m,$k,$A1,$A4){
    $over = 0;
    $under= 0;
    $on = 0;
    $radius = 3;

    foreach ($points as $point){
        $status = ($A1+($m/($k*($point['x']+$A4)))-$point['y']);
        if($status < $radius && $status > -$radius){
            $status = 0;
        }
        if($status > 0){
            $over++;
        }else if($status <1 && $status >= 0){
            $on++;
        }else if($status < 0){
            $under++;

        }
    }
    if($under < $over){
        $percentChange = ($under !== 0 ? ($under / $over) : 0) * 100;
    }else{
        $percentChange = ($over !== 0 ? ($over / $under) : 0) * 100;
    }

    return ['on'=>$on,'over'=>$over,'under'=>$under,'percent'=>$percentChange];
}

But the result is not so accurate.

Here I post how its look like. The green curve is manualy set and the blue one is generated ( Where I'm using the quality check for check how is good and if is bad try generate better curve ) -> the Green curve is better than the blue

(The values in the inputs are for green curve)

here is code where I'm using the Quality check for imagine why I want to have the most possible accurate checker:

  for($i = 0; $i < 10000 ; $i++){
        $new_m += 0.2;
        $actual = $this->checkQuality($points['points'],$new_m,$ob['k'],0,0);
        if($actual['percent'] > $prev['percent']){
            $prev['percent'] = $actual['percent'];
            $prev['m'] = $new_m;
            $newQuality = $actual;
        }else if($i>0 && $actual['percent'] < $prev['percent']){
            break;
        }
    }