W10 - MULTIVARIATE DATA

Question 1

What kind of variables could we used in a multivariate data analysis

Answer 1

Dependent or independent variables

Question 2

What defines a multivariate dataset

Answer 2

p > 1

Question 3

What is a 11 x 5 dimensional data? Give an example

Answer 3

11 objects and 5 variables
Eg. 11 species of plants and 5 leaf morphology variables

Question 4

What do the matrix values tell us

Answer 4

It defines the position of n points in p dimensional space
(N = Objects, P = Variables)

Question 5

What three parameters does a cross product and sum square matrices describes?

Answer 5

Means (centroid)
Variance
Covariance

Question 6

Define data variation and how it is quantified

Answer 6

Data variation explains the amount of different values we can observe for an object as they do not always have the same values
It is quantified by the sum of squares

Question 7

Define data association and how it is quantified

Answer 7

Variables collected for the same object share patterns of deviation from the mean
It is quantified by the sum of cross-product or covariance

Question 8

How does a covariance plot differ from regression plot?

Answer 8

It is not a run over rise plot - we are interested in the shared variation between variables.
Either variable can be plotted on the horizontal axis

Question 9

Name the following matrices of covariance
(x1 x2)
(x3 x4)

Answer 9

(var1 cov1,2)
cov2,1 var2)
OR
(sum sqr sum cross)
sum cross sum sqr)

Question 10

What does the three parameters in the sum of cross-product tell us when a cloud is plotted?

Answer 10

Mean tells us the position
Variance tell us the size
covariance tells us the shape

Question 11

What is the trace?

Answer 11

sum of variances in a variance-covariance matrix.
It is the sum of diagonal elements

Question 12

Why is trace useful?

Answer 12

Helps us to understand the distribution of variance across multiple dimensions when dealing with high dimensional datasets.

Question 13

What is the numeral range of corelation coefficients?

Answer 13

Ranges from -1 to +1 with 0 being no corelations

Question 14

What is the coefficient of determination?

Answer 14

Corelation squared = % of variation shared between variables
Interpreted the same was as Rsqr in regression analysis
For example a value of 0.83 means 83 percent of a variable is explained by the other variable