Defining Relationships in Laravel

I'm new to understanding relationships and understanding the MVC. It really helps if you could guide me why I'm receiving this error, and how I could solve this in the future.

SQLSTATE[23000]: Integrity constraint violation: 1452 Cannot add or update a child row: a foreign key constraint fails (`guest_log`.`logs`, CONSTRAINT `fk_logs_Dept1` FOREIGN KEY (`department_to_visit`) REFERENCES `departments` (`dept_id`) ON DELETE NO ACTION ON UPDATE NO ACTION) (SQL: insert into `logs` (`guest_id`, `guest_id_number`, `purpose`, `department_to_visit`, `date_time_in`, `updated_at`, `created_at`) values (2, 123, abc, 0, 2018-12-22 10:29:29, 2018-12-22 10:29:29, 2018-12-22 10:29:29))

Here is the SQL for department, logs and guest

-- ----------------------------
-- Table structure for logs
-- ----------------------------
DROP TABLE IF EXISTS `logs`;
CREATE TABLE `logs` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `guest_id` int(11) NOT NULL,
  `guest_id_number` datetime NOT NULL,
  `date_time_in` datetime NOT NULL,
  `date_time_out` datetime DEFAULT NULL,
  `purpose` varchar(45) COLLATE utf8mb4_unicode_ci NOT NULL,
  `department_to_visit` int(11) DEFAULT NULL,
  PRIMARY KEY (`id`,`guest_id`),
  KEY `fk_logs_guests1_idx` (`guest_id`),
  KEY `fk_logs_Dept1_idx` (`department_to_visit`),
  CONSTRAINT `fk_logs_guests1` FOREIGN KEY (`guest_id`) REFERENCES `guests` (`id`) ON DELETE NO ACTION ON UPDATE NO ACTION,
  CONSTRAINT `fk_logs_Dept1` FOREIGN KEY (`department_to_visit`) REFERENCES `Dept` (`dept_id`) ON DELETE NO ACTION ON UPDATE NO ACTION
) ENGINE=InnoDB DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_unicode_ci;


-- ----------------------------
-- Table structure for guests
-- ----------------------------
DROP TABLE IF EXISTS `guests`;
CREATE TABLE `guests` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `first_name` varchar(255) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `middle_name` varchar(255) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `last_name` varchar(255) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `gender` varchar(6) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `email` varchar(45) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `tel_no` varchar(45) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `mobile_no` varchar(45) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `company` varchar(255) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `photo` varchar(500) COLLATE utf8mb4_unicode_ci DEFAULT NULL,
  `created_at` timestamp NULL DEFAULT NULL,
  `updated_at` timestamp NULL DEFAULT NULL,
  PRIMARY KEY (`id`),
  UNIQUE KEY `id_UNIQUE` (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=4 DEFAULT CHARSET=utf8mb4 COLLATE=utf8mb4_unicode_ci;

 Table structure for Departments
-- ----------------------------
DROP TABLE IF EXISTS 'Departments'
CREATE TABLE `Deptartments` (
  `dept_id` int(5) NOT NULL AUTO_INCREMENT,
  `dept_code` varchar(30) CHARACTER SET latin1 DEFAULT NULL,
  `dept_description` varchar(75) CHARACTER SET latin1 NOT NULL,
  `dept_assign` enum('Academic','Admin') CHARACTER SET latin1 NOT NULL DEFAULT 'Academic',
  `is_deleted` enum('Yes','No') CHARACTER SET latin1 DEFAULT 'No',
  PRIMARY KEY (`dept_id`)
) 

Here is the model for Logs, department and Guest.

class Log extends Model
{
    protected $fillable = ['guest_id','guest_id_number','date_time_in','date_time_out','purpose','department_to_visit'];

}

class Department extends Model
{
    protected $fillable = ['dept_id','dept_code', 'dept_description', 'dept_assign'];


}
class Guest extends Model
{
    protected $fillable = ['first_nane',
                            'middle_name',
                            'last_name',
                            'gender',
                            'email',
                            'tel_no',
                            'mobile_no',
                            'company',
                            'photo'
        ];
}

And this is the part that gets the error when form is submitted

 {!! BootForm::inline(['route'=>['logs.store'],'method'=>'POST']) !!}

        {!! BootForm::select('guest_id', 'Guest Name',\App\Guest::pluck('full_name','id')->toArray() ,null, [])!!}


        {!! BootForm::tel('guest_id_number','ID Number',null, ['required']) !!}
        {!! BootForm::select('department_to_visit','Department to Visit', \App\Department::pluck('department_to_visit','dept_id'),null,[]) !!}
        {!! BootForm::text('purpose',null,null,['required']) !!}

        {!! BootForm::submit('Save') !!}

        {!! BootForm::close() !!}

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