显示表单提交后选择的单选按钮

我是PHP的新手，目前正在做一项调查。用户通过单选按钮选择表格中问题的答案。每个问题有4种可能性，并分组在每个问题下。提交表单时，页面应显示每个组上的哪个按钮被选中。目前的代码是：

<form action="thankyou.php" method="post">
  <p>How easy would you say it is to create new carers?</p>
   <input type="radio" name="rgroup1" value="rg1v1"> Excellent
   <input type="radio" name="rgroup1" value="rg1v2"> Good
   <input type="radio" name="rgroup1" value="rg1v3"> Average
   <input type="radio" name="rgroup1" value="rg1v4"> Poor</br>
  <p>How easy is it to generate a report?</p>
   <input type="radio" name="rgroup2" value="rg2v1"> Excellent
   <input type="radio" name="rgroup2" value="rg2v2"> Good
   <input type="radio" name="rgroup2" value="rg2v3"> Average
   <input type="radio" name="rgroup2" value="rg2v4"> Poor</br>
  <p>How easy is it to add and alter timesheets?</p>
   <input type="radio" name="rgroup3" value="excellent"> Excellent
   <input type="radio" name="rgroup3" value="good"> Good
   <input type="radio" name="rgroup3" value="average"> Average
   <input type="radio" name="rgroup3" value="poor"> Poor</br>
  <p>How good would you rate the Packages Of Care functions? </p>
   <input type="radio" name="rgroup4" value="excellent"> Excellent
   <input type="radio" name="rgroup4" value="good"> Good
   <input type="radio" name="rgroup4" value="average"> Average
   <input type="radio" name="rgroup4" value="poor"> Poor</br>
  <p>Question 5</p>
   <input type="radio" name="rgroup5" value="excellent"> Excellent
   <input type="radio" name="rgroup5" value="good"> Good
   <input type="radio" name="rgroup5" value="average"> Average
   <input type="radio" name="rgroup5" value="poor"> Poor</br>
   </br>
      Please  Enter Your Comments Below:
   </br></br>
        <textarea name="comments" width="100px" rows="4" cols="50" wrap="wrap"></textarea>
   </br></br>
        <input type="submit">
   <br/><br/>
</form>

我的"谢谢你.PHP"页面的PHP是：

<?php 
switch($_POST['rgroup1']) {
    case "rg1v1":
        $value = "Radio Group 1 - Value 1 was selected.";
        break;
    case "rg1v2":
        $value = "Radio Group 1 - Value 2 was selected.";
        break;
    case "rg1v3":
        $value = "Radio Group 1 - Value 3 was selected.";
        break;
    case "rg1v4":
        $value = "Radio Group 1 - Value 4 was selected.";
        break; 
        default:
        $value = "No radio has been selected for Radio Group 1";
}
switch($_POST['rgroup2']) {
    case "rg2v1":
        $value2 = "Radio Group 2 - Value 1 was selected.";
        break;
    case "rg2v2":
        $value2 = "Radio Group 2 - Value 2 was selected.";
        break;
    case "rg2v3":
        $value2 = "Radio Group 2 - Value 3 was selected.";
        break;
    case "rg2v4":
        $value2 = "Radio Group 2 - Value 4 was selected.";
        break; 
        default:
        $value = "No radio has been selected for Radio Group 2";
}
switch($_POST['rgroup3']) {
    case "rg3v1":
        $value3 = "Radio Group 3 - Value 1 was selected.";
        break;
    case "rg3v2":
        $value3 = "Radio Group 3 - Value 2 was selected.";
        break;
    case "rg3v3":
        $value3 = "Radio Group 3 - Value 3 was selected.";
        break;
    case "rg3v4":
        $value3 = "Radio Group 3 - Value 4 was selected.";
        break; 
        default:
        $value = "No radio has been selected for Radio Group 3";
}
switch($_POST['rgroup4']) {
    case "rg4v1":
        $value4 = "Radio Group 4 - Value 1 was selected.";
        break;
    case "rg4v2":
        $value4 = "Radio Group 4 - Value 2 was selected.";
        break;
    case "rg4v3":
        $value4 = "Radio Group 4 - Value 3 was selected.";
        break;
    case "rg4v4":
        $value4 = "Radio Group 4 - Value 4 was selected.";
        break; 
        default:
        $value = "No radio has been selected for Radio Group 4";
}
switch($_POST['rgroup5']) {
    case "rg5v1":
        $value5 = "Radio Group 5 - Value 1 was selected.";
        break;
    case "rg5v2":
        $value5 = "Radio Group 5 - Value 2 was selected.";
        break;
    case "rg5v3":
        $value5 = "Radio Group 5 - Value 3 was selected.";
        break;
    case "rg5v4":
        $value5 = "Radio Group 5 - Value 4 was selected.";
        break; 
        default:
        $value = "No radio has been selected for Radio Group 5";
}

echo $value;
echo $value2;
echo $value3;
echo $value4;
echo $value5;
?>

我收到一个错误，说我没有定义值2、3、4和5的变量，我不知道为什么。