PLS 802

REGRESSION ANALYSIS

Course Handouts

Click on the following links to see the handouts that are available for each course topic. The handouts, themselves, are linked as PDF files.

• Statistical Tables
• Probabilities for the Standard Normal Distribution
• Critical Values for Student's t Distribution
• Critical Values for the F Distribution

• Empirical Relationships Between Variables
• Empirical Relationships Between Variables, I
• Empirical Relationships Between Variables, II
• Empirical Relationships Between Variables, III

• Linear Combinations
• The Mean of a Linear Combination
• The Variance of a Linear Combination
• Calculating the Mean and Variance of a Linear Combination
• Graphing the Linear Relationships in a Linear Combination

• Covariance and Bivariate Relationships
• Covariance and the Relationship Between Two Variables
• The Perils of the Correlation Coefficient

• Using Linear Combinations
• Expected Value of the Sample Mean
• Sampling Variance of the Sample Mean

• Scatterplot Smoothing and Nonparametric Regression
• Slicing a Scatterplot
• Scatterplot Smoothing, I
• Nonparametric Scatterplot Smoothing, II
• Window Width as a Smoothing Parameter
• Bias and Variance in Scatterplot Smoothing
• Scatterplot with a Loess (or Lowess) Smooth

• Demonstration of R Statistical Software
• Using the R Statistical Software Environment for Basic Data Analysis and Graphics
• R Script for Class Demonstration (NOTE: This is the handout, not the script, itself)

• Fitting a Line to Bivariate Data
• Fitting a Line to Bivariate Data
• The Conditions Used to Fit a Line to Data
• Fitting a Line to the Occupational Prestige Data

• The Least-Squares Criterion
• The Fitted Line and the Sum of Squared Residuals
• Deriving the Least Squares Estimates of the Regression Coefficients
• Goodness of Fit for a Bivariate Regression Equation
• Calculating Goodness of Fit for the Linear Relationship Between Income and Prestige

• Graphical Displays for Multivariate Data
• Visualizing Multivariate Data, I
• Trellis Displays for Multivariate Data
• Visualizing Multiple Regression

• The Multiple Regression Model
• Correlation and Structural Relationships
• OLS Estimates of Multiple Regression Coefficients
• R-Squared and Analysis of Variance (ANOVA) in Multiple Regression
• Multiple Regression in R

• Assumptions and Statistical Properties, the Bivariate Regression Model
• Assumptions Required for Statistical Inference in the Bivariate Regression Model
• Expected Value of the OLS Estimator
• The Sampling Variance of the OLS Estimator

• Statistical Inference in the Bivariate Regression Model
• Statistical Inference, Bivariate Regression
• Hypothesis Tests and Confidence Intervals for OLS Regression Coefficients
• Bivariate Inference in R

• Statistical Inference in the Multiple Regression Model
• Assumptions Required for Statistical Inference in the Multiple Regression Model
• Testing the Overall Significance of a Multiple Regression Equation
• F Test for a Set of Independent Variables

• Standardized Regression Coefficients
• Obtaining Standardized Coefficients in R
• The Perils of Standardized Coefficients

• Specification Error
• Specification Error and the OLS Estimator
• The Effects of Specification Error

• Multicollinearity
• The Effects of Multicollinearity, I
• The Effects of Multicollinearity, II
• The Effects of Multicollinearity, III
• Collinearity and Variance Inflation
• Multicollinearity and the State Policy Priorities Data
• Collinearity and Variance Inflation

• Residual Plots
• Residual Plots

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