gra 6020 multivariate statistics
DESCRIPTION
GRA 6020 Multivariate Statistics. Ulf H. Olsson Professor of Statistics. Multivariate Statistics. 1) Examining relationships with respect to a single variable Univariate Analysis Univariate Distributions 2) Examining relationships with respect to two or more variables simultaneously - PowerPoint PPT PresentationTRANSCRIPT
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GRA 6020Multivariate Statistics
Ulf H. Olsson
Professor of Statistics
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Ulf H. Olsson
Multivariate Statistics
• 1) Examining relationships with respect to a single variable
• Univariate Analysis• Univariate Distributions
• 2) Examining relationships with respect to two or more variables simultaneously
• Multivariate Analysis• Multivariate Distributions
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Ulf H. Olsson
Statistical Models
• Statistical models are mathematical representations of population behavior; they describe salient features of the hypothesized process of interest among individuals in the target population. When you use a particular statistical model to analyze a particular set of data, you implicitly declare that this population model gave rise to these sample data.
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Ulf H. Olsson
True Process
TheoreticalDomain
Empirical Domain
Making Sense
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Ulf H. Olsson
Relationships (Stochastic)
1131211 SavingsLoanBranchonSatisfacti
221 onSatisfactiLoyalty
Loyalty
Branch
Loan
Savings
Satisfaction
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Ulf H. Olsson
Univariate Normal Distribution•
•
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Ulf H. Olsson
Bivariate normal distribution
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Ulf H. Olsson
Standard Normal density functions
2
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1)(
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eu
)2()1(2
1
2
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)1(2
1),(
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),....,('
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21
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1
n
nn
uuu
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u
uu
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Ulf H. Olsson
Regression Analysis/OLS-Regression
ikikiii xxxy .....2211
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Ulf H. Olsson
Factor Analysis
pq
pi
x iqqi
,...,3,2,1
.....2211
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Ulf H. Olsson
Structure Equation Modeling
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Ulf H. Olsson
Regression Models
•All variables, both ys and xs, are directly observed
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Ulf H. Olsson
Factor Models
•Observed variables are ”linked” to latent variables (factors)
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Ulf H. Olsson
Structural Equation Models
•Regression models where all variables are latent (factors)