note1 - STAT5044: Regression and Anova Inyoung Kim Outline...

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STAT5044: Regression and Anova Inyoung Kim
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Outline 1 Introduction to regression and anova
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Statistics Descriptive statistics: summarization of populations, e.g, mean, variance, 5 number summary Statistical Inference: estimation and testing, e.g, maximum likelihood estimator(MLE), least square estimator (LSE), confidence interval, F test, t-test.
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Objective of Statistics Objective: using data, Describe a population, study relationships Estimate quantities of interest Test hypotheses about quantities of interest
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Looking at Data Single population: boxplots, stem and leaf, histograms, normality and q-q plots Multiple populations: side by side boxplots, scatterplots, residual analysis
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Relationship among variables Regression and ANOVA are methods that are used to analyze linear models A linear statistical model is a statistical model that has a deterministic component that may be expressed as a linear function of parameters and an additive error term.
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Examples of Linear models Regression y i = β 0 + β 1 x i + ε i y i = β 0 + β 1 ln ( x i )+ ε i g ( y i ) = β 0 + β 1 x i + ε i ANOVA y i = μ + ε i y ij = μ i + ε ij = μ + α i + ε ij y ijk = μ ij + ε ijk = μ + α i + β j +( αβ ) ij + ε ijk
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Not a linear model y i = β 0 + e - β 1 x i + ε i A model is not a linear model if it cannot be expressed as a model that is linear in the parameters with an additive error
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A simple linear model Single group: y i = μ + ε i Two groups: y ij = μ i + ε ij = μ + α i + ε ij Parameter: a numerical characteristic of a population or model ( ) Estimator: a statistic (numerical characteristic of the sample) that is used to provide an estimate for a parameter Estimate: numerical value for an estimator Data: n observations or n i from group i ˆ μ = ¯ y = 1 n i y i ˆ μ i = ¯ y i = 1 n i j y ij
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A simple linear model Single group: y i = μ + ε i Two groups: y ij = μ i + ε ij = μ + α i + ε ij Parameter: a numerical characteristic of a population or model (unknown) Estimator: a statistic (numerical characteristic of the sample) that is used to provide an estimate for a parameter Estimate: numerical value for an estimator Data: n observations or n i from group i ˆ μ = ¯ y = 1 n i y i ˆ μ i = ¯ y i = 1 n i j y ij
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Course structure Regression: continuous variables e.g., simple linear regression, Multiple regression How to fit a model, estimate parameters, and to test How to check assumptions in model using residuals Categorical data: dummy variables, discrete variables Generalized linear model: dummy variables, discrete variables Mixed models Linear mixed effects model: continuous variable Generalized mixed effects model: dummy variables, discrete variables (Not COVER IN THIS CLASS)
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note1 - STAT5044: Regression and Anova Inyoung Kim Outline...

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