Angular overrides the "selected" property when you bind the select to a model. If you inspect the rendered DOM you will find that a new item has been added:

<option value="? undefined:undefined ?"></option>

In order to automatically select the third option you need to pre-populate the model in scope. There are a few ways to do this, including wrapping the select in a controller:

<div ng-controller="MyCtrl">
    <select id="myselection" ng-model="selectedColors">
        <option value="1">Red</option>
        <option value="2">Blue</option>
        <option value="3">Green</option>
    </select>
<div>Selected Colors: {{selectedColors }}</div>

And then defining that model in the controller.

var myApp = angular.module('myApp', [])
    .controller('MyCtrl', ['$scope', function ($scope) {
    $scope.selectedColors = 2;
}]);

Here's a running example.

http://jsfiddle.net/93926/

Alternatively, you could just initialize it using ng-init such as in this example:

<div ng-init="selectedColors=3">

http://jsfiddle.net/9JxqA/1/

EDIT: Removed the selected property in the first example, it's no longer needed.

By adding option with empty value to select and initializing selectedColors to empty string(ng-init="selectedColors=''"), we can see 'select Color' option on top instead of having first color to be selected defaultly:

<div>
<select id="myselection" ng-init="selectedColors=''" ng-model="selectedColors">
    <option value="">Select Color</option>
    <option value="1">Red</option>
    <option value="2">Blue</option>
    <option value="3">Green</option>
</select>
<div>Selected Colors: {{selectedColors }}</div>

Try it on Fiddle http://jsfiddle.net/CodecPM/qxyckf7u/

You need to do only two things 1)ng-init="days='noday'" 2)ng-selected="true"

 <select class="filtersday" ng-init="days='noday'" ng-model="days">
 <option ng-selected="true" value="noday">--Select Day--</option>

You should use single quote to work per

<select ng-model="liveDataType" ng-init="liveDataType='1'" class="form-control input height" required>
    <option value="1">Running data</option>
    <option value="2">Rest Data</option>
    <option value="3">All Data</option>
</select>

Use ng-selected="true"

Check the below code:

<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.2.23/angular.min.js"></script>
<select ng-model="foo" ng-app >
    <option value="1">1</option>
    <option ng-selected="true" value="2">2</option>
    <option value="3">3</option>
    <option value="4">4</option>
    <option value="5">5</option>
</select>