jQuery: Get and Set a Radiobutton Value

HTML

<script src="https://code.jquery.com/jquery-2.2.4.min.js"></script>
<h2>Select a Pet</h2>

<div>
  <input name="petu" type="radio" value="dog" /><span>Dog</span>
  <input name="petp" type="radio" value="cat" /><span>Cat</span>
  <input name="petl" type="radio" value="fish" /><span>Fish</span>
</div>

<fieldset>
  <legend>Select a Pet with jQuery</legend>
  <button id="selectDog">Select Dog</button>
  <button id="selectCat">Select Cat</button>
  <button id="selectFish">Select Fish</button>
</fieldset>

<div>
  <button id="getPetValue">Get Pet Value</button>
</div>

<h2>Results</h2>

<div id="results">

</div>

<div style="position: absolute;bottom: 5px;">
Read about this Fiddle at: <a href="http://jsdev.wikidot.com/howto:7" target="_blank">How To: jQuery - Get and Set a Radiobutton Value</a>
</div>

CSS

body > div, fieldset {
  margin-bottom: 20px;
}

fieldset {
  display:inline-block;
  border: 1px solid lightgrey;
}

button {
  margin-right: 10px;
}

#results {
  min-height: 50px;
  border: 1px solid lightgrey;
  padding: 5px;
}

JavaScript

$(function () {
	var $checkbox = $("#checkbox");
  var $results = $("#results");
  var count = 1;
  
	$("#selectDog").on("click", function () {
  	var $radiobutton = $("input[value='dog']");
  	$radiobutton.prop("checked", true);
  });

	$("#selectCat").on("click", function () {
  	var $radiobutton = $("input[value='cat']");
  	$radiobutton.prop("checked", true);
  });

	$("#selectFish").on("click", function () {
  	var $radiobutton = $("input[value='fish']");
  	$radiobutton.prop("checked", true);
  });

  $("#getPetValue").on("click", function () {
  	var pet = $("input[name='pet']:checked").val();
    var message = "";
    if (typeof pet === "undefined") {
    	message = "A pet has not been selected";
    } else {
    	message = "The pet that is currently selected is: " + pet;
    }
    $("#results").prepend("<div>" + count++ + ". " + message);
  });
});