Goals for this Module
Computing Probability
Joint Events
Conditional Probability
Independence
Computing Probability
James H. Steiger
Sequences
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October 17, 2003
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Introduction to Linear Regression Part 2
James H. Steiger
Department of Psychology and Human Development
Vanderbilt University
James H. Steiger (Vanderbilt University)
Linear Regression 2
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Introduction to Linear Regression Part 2
James H. Steiger
De
Subscript and Summation
Notation
James H. Steiger
Single Subscript Notation
Most of the calculations we perform in
statistics are repetitive operations on lists of
numbers. For example, we compute the
sum of a set of numbers, or the sum of the
squares of
Summation Algebra Proofs
James H. Steiger
Sum of Deviation Scores
Prove that, in any list of numbers, the sum
of the deviation scores is zero, that is,
N
N
dx= ( X
i
= 1= 1
i
i
i
X ) 0
=
Linear Transformation Rule for
Means
If, a group of Xs with mean X
The Laws of Linear Combination
James H. Steiger
Goals for this Module
In this module, we cover
What is a linear combination? Basic definitions and
terminology
Key aspects of the behavior of linear combinations
The Mean of a linear combination
The Variance
Understanding p Values
James H. Steiger
Vanderbilt University
James H. Steiger Vanderbilt University
Understanding p Values
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Introduction
Introduction
In this module, we introduce the notion of a p value, a concept widely
used (and abused) in statis
The Foundation of Probability
Theory
James H. Steiger
Probabilistic Experiment
A Probabilistic Experiment is a situation in
which
More than one thing can happen
The outcome is potentially uncertain
The Sample Space
The Sample Space of a probabilistic
expe
Introduction
The Grouped Frequency Distribution Table
The Frequency Histogram
The Cumulative Frequency Distribution Plot
The Cumulative Relative Frequency Plot
The Stem-Leaf Diagram
The Box-and-Whisker Plot
The Q-Q plot
Univariate Descriptive Statistics f
Misconceptions, Problems, and Fallacies
in Correlational Analysis
James H. Steiger
Department of Psychology and Human Development
Vanderbilt University
James H. Steiger (Vanderbilt University)
Misconceptions, Problems, and Fallacies
1 / 32
Introduction to
Goals for this Module
The Keep It Alive . . .
Counting Rules and . . .
Sequential Probabilities, Counting Rules,
and Combinatorics
James H. Steiger
October 27, 2003
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Two Uses for R
Simple Listwise Transformations
Using Functions within Expressions
Dening and Building a Function Library
The Maximum Possible Z -Score
Expected Value of the Maximum
Answering Theoretical Questions with R
James H. Steiger
Department of Psyc
Goals for this Module
Random Variables
Discrete Probability . . .
Expected Value of a . . .
Functions of a . . .
Random Variables, Probability
Distributions, and Expected Values
James H. Steiger
Variance of a . . .
Random Vectors . . .
Covariance and . .
Introduction to Linear Regression
James H. Steiger
Department of Psychology and Human Development
Vanderbilt University
James H. Steiger (Vanderbilt University)
Introduction to Linear Regression
1 / 46
Introduction to Linear Regression
1
2
Introduction
Fi
Introducing R and RStudio
James H. Steiger
Vanderbilt University
James H. Steiger Vanderbilt University
Introducing R and RStudio
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Introduction
Introduction
In this module, we get started in R and RStudio by illustrating a few key
points and demonst
Introduction
Discrete and Continuous Probability Distributions
Quantiles
Distribution Calculations in R
p-Value Calculation
Probability Distributions A First Look
James H. Steiger
Department of Psychology and Human Development
Vanderbilt University
James