Submitting an html with php and saving to MySQL Db using Ajax and jQuery?

This is my first time creating a php form and so I've been reading and copying a ton of tutorials, but none really seem to cover everything from start to finish so I'm piecemealing different people's decisions into one file and it isn't really working.

I think I understand what I've been learning so far, I just don't know enough about how to troubleshoot this php and find out where it's going wrong. Here's the HTML:

<section class="content">
  <form method="POST" action="" enctype="multipart/form-data" name="form">
    <p>Please remember, these results are saved into the database and will be shown to other users. So please do not include any identifying or personal information.</p>
    <label>
      <input type="text" id="object" placeholder="Name an object" required="required" />
      <i class="fa fa-wrench"></i>
    </label>
    <label>
      <input type="text" id="location" placeholder="Name a location" required="required" />
      <i class="fa fa-map-marker"></i>
    </label>
    <label>
      <input type="text" id="person" placeholder="Name a person" required="required" />
      <i class="fa fa-user"></i>
    </label>
    <button type="submit">Submit</button>
  </form>
</section>
<section class="result">
  <div class="return"><?php echo $result; ?></div>
  <h2>See how other people have responded.</h2>
  <div class="previous"></div>
</section>

The js:

<script type="text/javascript">
  $(function(){
    $("button").click(function(e){
      e.preventDefault();
      $.post("phptest.php", {$("form").serialize()}, function(res){
        $(".return").html(res);
        $(".content").hide();
        $(".result").show();
      });
    });
  });
</script>

Here is the php:

<?php
  $mysqli = new mysqli('mysite.com', 'myuser', 'mypass', 'mydb');
  if($mysqli->errno) {
    printf("Connection To Database Failed:<br/> %s", $mysqli->error());
    die();
  };
  $query = "INSERT INTO test_table (person, object, location) VALUES ('{$person}', '{$object}', '{$location}')";
  $stmt = $mysqli->stmt_init();
  $stmt->prepare($query);
  $stmt->bind_param('sss', $person, $object, $location);
  $person = $_POST['person'];
  $object = $_POST['object'];
  $location = $_POST['location'];
  $results = $mysqli->query($query);
  $stmt->execute();
  $stmt->close();
  $mysqli->close();
?>
<?php
  $mysqli = new mysqli('mysite.com', 'myuser', 'mypass', 'mydb');
  if($mysqli->errno) {
    printf("Connection To Database Failed:<br/> %s", $mysqli->error());
    die();
  };
  $query = "SELECT person, object, location FROM test_table WHERE person = ?";
  $stmt = $mysqli->stmt_init();
  $stmt->prepare($query);
  $stmt->bind_param('sss', $person, $object, $location);
  $stmt->execute();
  $result = $stmt->get_result();
  while($row = $result->fetch_assoc()) {
    printf('<strong>%s</strong> is a person. <strong>%s</strong> is an object. <strong>%s</strong> is a location.', $row['person'], $row['object'], $row['location']);
  $stmt->close();
  $mysqli->close();
?>

Now I have rewritten this as I understood the tutorials and taken what the tutorials were saying and tried to apply it to my use case, so anything wrong with the above is my own fault and not the case that I'm following bad advice.

GOAL:

1. Submit an html form for the fields
2. Add them to the db
3. Return the results of the submission to the page where <div class="return">
4. Return the previous 10 results of prior submissions where <div class="previous"> (hence the i<11 part)