How to create a program to compute the Hii of the Hat Marix in matlab?

I'm facing with the problem to compute the Hii of the Hat Matrix at shown in the picture.

Can anyone help me on how to compute? It is supposed to get a single values. However, in my code, it is appeared as 2x2 matrix. Thanks in advance

[Rik]

Have a read here and here. It will greatly improve your chances of getting an answer.

How are we supposed to fix a bug in code we cannot see?

[amj]

This is my code using CSV file:

faithfuldat = xlsread('faithful.csv');
save faithful.mat faithfuldat       % command form

[N,dim]=size(faithfuldat);
fData = faithfuldat;

X_ones =[ones(length(fData(:,1)),1) fData(:,1)];
hii = zeros(N);
for i = 1:N
    hii(i)=X_ones(i,:)'.*(X_ones'*X_ones).*X_ones(i,:)
end

However, i go an error message because the result is 2x2 matrix. I'm supposed to get a single values.

[amj]

This is the code without using csv file:

a = [1 20;1 30;1 40]

for i = 1:length(a)
    disp(a(i,:)'.*(a'*a).*a(i,:))
end

But, the result i got as 2x2 matrix not as expected

[amj]

Thanks Rik Wisselink.. Let me check the link

Answer 1

[the cyclist]

Is this what you want?

x = rand(10,1);

i = 3;
x(i)' .* x'*x .* x(i)

[amj]

Dear The cyclist,

How about if X matrix contains one as

x = [1 20;1 30;1 40] ?

[the cyclist]

I misinterpreted your notation in the example. I believe you can calculate the diagonal element as

a = [1 20;1 30;1 40]
i = 3;
Hii = a(i,:) * inv(a'*a) * a(i,:)'

and the full H matrix as

H   = a * inv(a'*a) * a'

There is probably a more efficient way to calculate that, rather than using the full inverse, but I am too lazy to figure it out.

[amj]

Dear The cyclist,

Let me try.

Thanks you very much