Ch 3: Characterizing and Displaying Multivariate Data Flashcards
density function f(y)
the relative frequency of occurrence of the random variable y
µ
population mean
E (y)
the expected value of y
ȳ
sample mean
E (ȳ) =
µ
var (ȳ) =
σ2/n
E (ay) =
aE(y) = aµ
Vay (y) =
σ2 = E(y - µ)2
S2
Sample variacne
E (S2) =
σ2
Standard deviation
the square root of either the population variance or sample variance
Bivariate Random Variable (x, y)
if two variables x and y are measured on each research unit (object or subject)
population covariance
Cov (x, y) = σxy = E[ (x-µx) (y-µy) ]
s
Sample standard deviation
Orthogonal
Variables with zero sample covariance
Correlation
Standardized covariance: to find a measure of linear relationship that is invariant to changes of scale, standardized the covariance by dividing by the standard deviations of the two variables
Population correlation
ρxy
Sample correlation
rxy
ȳ bold
the sample mean vector
ȳ1 bold
the mean of the n observation on the first variable
Y bold
Data matrix
S bold
Sample covariance matrix
Covariance matrix
variance matrix, variance-covariance matrix, dispersion matrix
Σ bold
Population covariance matrix
R bold
Sample correlation matrix
P bold
Population correlation matrix
Generalized sample variance | S |
A single numerical value for the overall multivariate scale
Total sample variance tr(S)
the trace of S
Imputation
filling the missing data
