STAT 701 -- EXAM 2 REVIEW SHEET

I. Advanced Regression Ideas
 A. Polynomial Regression
  1. Determining whether polynomial regression is needed
  2. Centering predictor variables
  3. Polynomial regression with two predictors
  4. Extrapolation in polynomial regression
 B. Interaction Models
  1. Basic meaning of interaction between two predictors
  2. Interaction plots
  3. F-test for whether interactions are significant
 C. Model Building
  1. Confirmatory and Exploratory Observational Studies
  2. Criteria for choosing "best" model
    a. Adjusted R^2
    b. C_p criterion
  3. Stepwise regression Methods
  4. "All-possible-subsets" approach
 D. Diagnostic Measures
  1. Added-variable (Partial Regression) Plots
  2. Outliers and Influential Cases
    a. (Internally) Studentized Residuals
    b. Leverage Values (Hat diagonal elements)
    c. Cook's Distance
    d. DFFITS
    e. The various rules of thumb
  3. What to do about Outliers/Influential Points

II. Single-Factor ANOVA Model
 A. Difference between Regression Models and ANOVA models
  1. Factors (how they differ from predictors in regression)
  2. Levels of a Factor
  3. Experimental Units, Observational Units, Subjects
 B. ANOVA Model Assumptions
 C. Cell-Means Model and Notation
  1. Relationship to "general linear model" form
  2. Fitted Values and Residuals in the ANOVA Model
 D. Analysis of Variance for a Single-Factor Study
  1. SSTO, SSTR, SSE
    a. What type of variability does each SS measure?
    b. Variability AMONG treatment means vs. variability WITHIN treatments
  2. Degrees of Freedom for each SS
  3. MSTR and MSE and their expected values
  4. ANOVA F-test for Equality of Factor Level Means
    a. Null and alternative hypotheses
    b. Test statistic value
    c. What does the F-test result help you to conclude?
  5. Factor Effects Model and alternate formulation of F-test H_0
 E. Investigation of Differences Among Treatment Means
  1. When do we investigate the treatment means further?
  2. Simple plots (bar graph, main effects plot)
  3. Inference about an Individual Population Treatment Mean
    a. CI for an Individual Population Treatment Mean
    b. t-test about an Individual Population Treatment Mean
  4. Inference about a PAIR of Population Treatment Means
    a. CI for the Difference between Two Population Treatment Means
    b. t-test Comparing Two Population Treatment Means
 F. Contrasts
  1. Formal Definition of a Contrast
  2. How a Contrast can help us compare various Population Treatment Means
  3. CI and t-test about a contrast
 G. Simultaneous Inference
  1. Why we must account for simultaneous inferences
    a. Data snooping
    b. Family significance level, family confidence level
  2. Tukey's Multiple Comparison Procedure
    a. Simultaneous CIs for ALL Pairwise Differences between Two Population Treatment Means
    b. Simultaneous Tests comparing ALL Pairs of Population Treatment Means
  3. Other Multiple Comparison Procedures
    a. Scheffe method and Bonferroni method
    b. When are these methods preferred?
 H. Checking Model Assumptions in ANOVA
  1. Residual Plot (vs. Fitted Values)
  2. Normal Q-Q plot of residuals
  3. Testing Equal-Variance Assumption Using Brown-Forsythe Test
  4. Possible Remedy for Violation