Turn on thread page Beta
    • Thread Starter
    Offline

    4
    ReputationRep:
    By using matrix A, derive the result x = \dfrac{COV(x,y)}{VAR(x)} (Covariance and Variance) , c = \bar{y} - m\bar{x} using generalised inverse methods, i.e.

    m =(A^T A)^-1 A^t \gamma where m = \begin{pmatrix} m \\ c \end{pmatrix}
    Any ideas on how I'd go about doing this?
    Offline

    14
    ReputationRep:
    (Original post by Jagwar Ma)
    By using matrix A, derive the result x = \dfrac{COV(x,y)}{VAR(x)} (Covariance and Variance) , c = \bar{y} - m\bar{x} using generalised inverse methods, i.e.

    m =(A^T A)^-1 A^t \gamma where m = \begin{pmatrix} m \\ c \end{pmatrix}
    Any ideas on how I'd go about doing this?
    A little bit of context would help here! I presume that you're trying to derive the least squares estimator in linear regression and that you really mean

     \displaystyle m = \dfrac{COV(x,y)}{VAR(x)}

    Is that right?

    If so, this is pretty standard bookwork, and you can find some hints in places like this.
    • Thread Starter
    Offline

    4
    ReputationRep:
    (Original post by Gregorius)
    A little bit of context would help here! I presume that you're trying to derive the least squares estimator in linear regression and that you really mean

     \displaystyle m = \dfrac{COV(x,y)}{VAR(x)}

    Is that right?

    If so, this is pretty standard bookwork, and you can find some hints in places like this.
    Sorry, the actual question is:
    "We have showed on the least-squares worksheet that the best fit straight line through the data is given by

     \displaystyle m = \dfrac{COV(x,y)}{VAR(x)}, c = \bar{y} - m\bar{x}

    By using the matrix A, derive this result using generalised inverse methods.

    A = \begin{pmatrix} x1 & x2 & x3 \\1 & 1 & 1 \end{pmatrix}
    • Thread Starter
    Offline

    4
    ReputationRep:
    Any ideas anybody?
    Offline

    14
    ReputationRep:
    (Original post by Jagwar Ma)
    Any ideas anybody?
    To give you an answer suitable for your needs, it would really help to have some context: what have you been taught about generalized inverses, for example? Which course does this question come from?

    The theory of how the generalized inverse minimizes squared error can be found here, for example -- or here, with a little more focused context for the problem in hand.
    • Thread Starter
    Offline

    4
    ReputationRep:
    (Original post by Gregorius)
    To give you an answer suitable for your needs, it would really help to have some context: what have you been taught about generalized inverses, for example? Which course does this question come from?

    The theory of how the generalized inverse minimizes squared error can be found here, for example -- or here, with a little more focused context for the problem in hand.
    I'm doing a data modelling course and have been set a problem sheet. This is just one of the questions from the sheet. I can't really provide more context then that..All I can say is that the questions I'm set are often rather obtusely written and aren't stuff you can simply look up..it's a common theme my lecturer likes to abide by so that problem sheets are particularly challenging.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 31, 2016
The home of Results and Clearing

1,063

people online now

1,567,000

students helped last year

University open days

  1. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
  2. Bournemouth University
    Clearing Open Day Undergraduate
    Wed, 22 Aug '18
  3. University of Buckingham
    Postgraduate Open Evening Postgraduate
    Thu, 23 Aug '18
Poll
A-level students - how do you feel about your results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.