using filters laravel models

i want to make a filter by shops.

Controller:

function filter(Request $request){
        $goods = Good::select('shop_id')->where('shop_id', '=', $request->id)->get();
        $shops = Shop::all ();
        return view('filter')->with(['goods' => $goods, 'shops' => $shops]);
    }

Migrations:

Schema::create('goods', function (Blueprint $table) {
                $table->increments('id');
                $table->string('name');
                $table->integer('amount');
                $table->integer('shop_id');
                $table->timestamp('onPurchase');
                $table->timestamps();
        });
      
Schema::create('shops', function (Blueprint $table) {
                $table->increments('id');
                $table->string('name');
                $table->string('adress')->nullable();
                $table->timestamps();
        });

Form to get id:

<form action = "" method="post">
                                
        <select name="id">
                @foreach ($shops as $shop)
                        <option value=""> </option>
                @endforeach;
        </select>
        <br><br>
        <input type="submit" class="btn btn-primary" value="Pasirinkti">
</form>

It wont print the list based on selected ID that i get via $_POST. Any help appreciated.

via Benua