Dear all,

I am stuck in the following problem when I am doing my master thesis, and I failed to find any solution online by myself and thus your help will be really appreciated. Thanks for your reading and help in advance.

As the below sample dataset shows, I have collected five variables measuring subjects' mental health. Then, I need to derive an index that incorporates these five variables. To do so, previous literature suggests that I need to firstly get the covariance matrix of these five variables. Let's call it Mat_A. Then, for each subject, I need to do a calculation like: (a 1*5 vector of ones) multiply with (a 5*5 matrix) multiply with (a 5*1 vector of the outcomes of the five variables.)

As for the above operation, I have several operation problem:
  1. How can I save the covariance matrix with codes automatically, instead of entering the numbers one by one by hands?
  2. How can I do the above matrix multiplication to get the index? Sharing the codes will be the best for me.
Thanks for your help again, and look forward to your replying.
subject Q1 Q2 Q3 Q4 Q5 Index
1 3 3 1 2 4
2 3 2 2 5 5
3 4 4 2 4 6
4 7 6 6 7 8
5 8 7 3 7 4
6 4 8 6 5 6
7 1 2 3 2 1
8 3 3 2 2 3
9 5 4 1 7 6
10 5 6 7 8 7
Best regards,
Wu