1 / 26

Welcome to MAR 6658

Welcome to MAR 6658. Course Title Quantitative Methods in Marketing IV: Psychometric and Econometric Techniques Prerequisites MAR 6507 or instructor permission Instructor Charles Hofacker Meeting Tue 1:00-5:00 Contact Info Email : chofack @ cob.fsu.edu Office : RBB 255

Download Presentation

Welcome to MAR 6658

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Welcome to MAR 6658 Course Title Quantitative Methods in Marketing IV: Psychometric and Econometric Techniques Prerequisites MAR 6507 or instructor permission Instructor Charles Hofacker Meeting Tue 1:00-5:00 Contact Info Email: chofack @ cob.fsu.edu Office: RBB 255 Hours: T/ R 11:00-12:00 Grades Two exams plus homework

  2. Ready to Get Going?

  3. Vectors and Transposing Vectors An m element column vector A q element row vector Transpose the row Transpose the column

  4. A Matrix Is A Set of Vectors • X is an n · m matrix • First subscript indexes rows • Second subscript indexes columns

  5. The Transpose of a Matrix Note that (X')' = X

  6. The Dot Subscript Reduction Operator - Rows We can display an intermediate amount of detail by separately keeping track of each row: So the matrix X becomes

  7. The Dot Subscript Reduction Operator – Columns Or we can keep track of each column of X: So that X is

  8. The Equals Sign A = B iff aij = bij for all i, j. The matrices must have the same order.

  9. Some Special Matrices Diagonal Scalar cI Unit 1

  10. More Special Matrices Null Symmetric Identity

  11. Matrix Addition • Adding two matrices means adding corresponding elements. • The two matrices must be conformable.

  12. Commutative: A + B = B + A Associative: A + (B + C) = (A + B) + C Identity: A + 0 = A Properties of Matrix Addition

  13. Vector Multiplication Vector multiplication works with a row on the left and a column on the right. • There are a lot of names for this: • linear combination • dot product • scalar product • inner product

  14. Orthogonal Vectors Two vectors x and y are said to be orthogonal if x =[2 1]

  15. Scalar Multiplication Associative: c1(c2A) = (c1c2)A Distributive: (c1 + c2) A = c1A + c2A

  16. Matrix Multiplication

  17. Partitioned Matrices Visually, matrices act like scalars And here is a little example

  18. The Cross Product Matrix B Keeping track of the columns of X

  19. The Cross Product Matrix 2 Keeping track of the rows of X

  20. Properties of Multiplication • Scalar Multiplication: • Commutative: cA = Ac • Associative: A(cB) = (cA)B = c(AB) • Matrix Multiplication: • Associative: (AB)C = A(BC) • Right Distributive: A[B + C] = AB + AC • Left Distributive: [B + C]A = BA + CA • Transpose of a Product(BA)' = A'B' • IdentityIA = AI = A

  21. The Trace of a Matrix Tr[AB] = Tr[BA] . The theorem is applicable if both A and B are square, or if A is m · n and B is n · m Note that for a scalar s, Tr s = s.

  22. Solving a Linear System Consider the following system in two unknowns: The key to solving this is in the denominator below:

  23. An Inverse for Matrices ax = y a-1ax = a-1y 1x = a-1y x = a-1y Ax = y A-1Ax = A-1y Ix = A-1y x = A-1y • Scalars: One Equation and • One Unknown • Matrices: N Equations and • N Unkowns We just need to find a matrix A-1 such that AA-1 = I.

  24. The Inverse of a 2 · 2

  25. The Inverse of a Product Inverse of a Product: (AB)-1 = B-1A-1

  26. Quadratic Form (Bilinear form is where the pre- and post-multiplying vectors are not necessarily identical)

More Related