ANCOVA & Matrices

Question 1

ANCOVA

Answer 1

Analysis of covariance
1 continuous & 1 categorical variable

Question 2

Multiplication of 2 matrices

Answer 2

Possible if: #columns in A = #rows in B

[n x m] * [m x p] = [n x p]

Question 3

Adding/subtracting matrices

Answer 3

Only possible if objects have same dimension

Question 4

Rules for matrices

Answer 4

• AB =/ BA
• st BA possible but AB not
• A* A^T = symmetric (oben und unten an diagonale gleich)

Question 5

ANCOVA Assumptions

Answer 5

Same as for linear model:
- NV residuals
- independent residuals
- equal variance among groups
NOT: NV explanatory variables (x)

Question 6

Areas where linear algebra (Matrix) is frequently used and powerful

Answer 6

• PCA (principle component analysis)
• for efficient coding / simulations
• to find joint distribution of regression coefficients
  NOT for residual analysis