Statistics VI - PCA + Meta Exam Questions + Vectors/Matrices Flashcards
What should the PCA be based on if all variables have the same units?
the covariance matrix
What should the PCA be based on if variables have different units?
the correlation matrix
In a PCA of a bivariate distributions: The coordination system is rotated so that …
… the first axis - the first PC - has the largest possible variance.
How come we are allowed to rotate the coordination system in the PCA?
We are allowed to do that, because the total variance is invariant against rotation of data.
The sum of squared distances of a distribution = 3.224.
What is the sum of squared distances after rotating the data in the course of a PCA?
the same: 3.224
The second PC has the ___________ largest variance and is _________ to the first PC.
The second PC has the SECOND largest variance and is ORTHOGONAL to the first PC.
What’s the total variance in the following (graphically akward) covariance matrix?
[0.950 0.647]
[0.647 0.820]
0.950 + 0.820 = 1.770
What multivariate tests should we know?
MANCOVA
MANOVA
Hotelling’s T²
What univariate tests should we know?
student’s t-test
ANOVA
ANCOVA
What is an eigenvector and an eigenvalue?
If A is a square matrix, v != 0 is an eigenvector of A, if
A * v = λ * v
The number λ is called the eigenvalue of A.
List at least 6 tests!
student's t-test Hotelling's T² ANOVA ANCOVA MANOVA MANCOVA
What can the following tests be useful for:
t-test
ANOVA
ANCOVA
t-test: difference btw 2 groups and 1 variable
ANOVA: difference btw several groups, one dependent variable
ANCOVA: difference btw several groups, one dependent variable + controls
What can the following tests be useful for:
Hotelling’s T²
MANOVA
MANCOVA
Hotelling’s T²: difference btw 2 groups and several variables
MANOVA: several dependent variables, groups, interaction among variables
MANCOVA: several dependent variables, groups, interaction among variables + controls
How is the name of a vector usually written in statistics?
bold lowercase letter
How many columns does a vector have?
1
What’s the difference between the vector v and the vector v’?
v is a column vector and
v’ is the transposed version of vector v
In a matrix, what is represented through rows and columns?
rows: cases
columns: variables
How does M’ look like if M =
(2 4 1)
(3 8 4)
(2 3)
(4 8)
(1 4)
What’s the distinct property of a square matrix?
Same amount of rows and columns.
What’s the distinct property of a symmetric matrix?
S = S’
What’s the (main) diagonal of a matrix?
The “row” of numbers from top left to bottom right.
What is an identity matrix (aka. unit matrix)?
An identity matrix is a square matrix with ones on the main diagonal.
Cor(a,b) = 0.8
How large is the explained variance?
0.8² = 0.64 -> 64 %
Cor(a,b) = - 0.3
How large is the explained variance?
- 0.3² = 0.09 -> 9 %
What’s the definition of discrete data?
Discrete Data can only take certain values.
What’s the definition of continuous data?
Continuous Data is data that can take any value (within a range)
What kind of a scale is Kelvin?
ratio scale
What kind of a scale is Celsius?
interval scale
Define precision!
Degree to which repeated measurements show the same results
Define accuracy!
Closeness of measurements of a quantity to the quantity’s actual (true) value.
Define bias!
Difference between the average of the measurements and the reference value.
