Why is it necessary to set “.prototype.constructor” of a constructor function?

In the section about inheritance in the MDN article Introduction to Object Oriented Javascript, I noticed they set the prototype.constructor:

// correct the constructor pointer because it points to Person
Student.prototype.constructor = Student;  

Does this serve any important purpose? Is it okay to omit it?

It's not always necessary, but it does have its uses. Suppose we wanted to make a copy method on the base Person class. Like this:

// define the Person Class  
function Person(name) {
    this.name = name;
}  

Person.prototype.copy = function() {  
    // return new Person(this.name); // just as bad
    return new this.constructor(this.name);
};  

// define the Student class  
function Student(name) {  
    Person.call(this, name);
}  

// inherit Person  
Student.prototype = Object.create(Person.prototype);

Now what happens when we create a new Student and copy it?

var student1 = new Student("trinth");  
console.log(student1.copy() instanceof Student); // => false

The copy is not an instance of Student. This is because (without explicit checks), we'd have no way to return a Student copy from the "base" class. We can only return a Person. However, if we had reset the constructor:

// correct the constructor pointer because it points to Person  
Student.prototype.constructor = Student;

...then everything works as expected:

var student1 = new Student("trinth");  
console.log(student1.copy() instanceof Student); // => true