MBA 8370/8380 Course Companion
Preface
About this book…
Acknowledgements
MBA 8370
1
Introduction
1.1
The “Big Picture” of Statistics
1.2
The Vocabulary of Statistics
1.3
Descriptive Measures
1.3.1
Central Tendency
1.3.2
Variation
1.3.3
Measures of shape
1.3.4
Covariance and Correlation
2
Data Collection and Sampling
2.1
Sampling Distributions
2.2
Sampling Bias - two examples
2.2.1
Dewey Defeats Truman?
2.2.2
98.6?
2.3
Sampling Methods
2.3.1
Simple random sampling
2.3.2
Systematic Sampling
2.3.3
Stratified Sampling
2.3.4
Cluster Sampling
2.4
Sampling in Practice
2.5
Sampling and Sampling Distributions
2.5.1
An Application
3
Getting Started with R
3.1
The R Project for Statistical Computing
3.2
Before you Install… Posit (RStudio) Cloud?
3.3
Downloading and installing R
3.3.1
Choosing a
Mirror
3.3.2
Download and install the correct version
3.3.3
Downloading and installing RStudio
3.4
Taking Stock
3.5
Coding Basics
3.5.1
Installing
Packages
3.5.2
Assigning Objects
3.5.3
Listing, Adding, and Removing
3.5.4
Importing Data
3.5.5
Manipulating Data
3.5.6
Subsetting Data
3.6
Data Visualization
3.6.1
Histograms
3.6.2
Line, bar, and Scatter Plots
3.6.3
Boxplots
3.6.4
Much more out there
4
The Central Limit Theorem
4.1
The CLT (Formally)
4.2
Application 1: A Sampling Distribution with a Known Population
4.3
Application 2: A Sampling Distribution with an Unknown Population
4.3.1
The Sample
4.4
The Punchline
5
Confidence Intervals
5.1
A Refresher on Probability
5.1.1
Application 1
5.1.2
Application 2
5.2
Deriving a Confidence Interval
5.2.1
Application 3
5.2.2
What if we want to change confidence?
5.2.3
What happens to the size of the confidence interval when we increase our
confidence
?
5.3
What to do when we do not know
\(\sigma\)
5.3.1
Student’s t distribution versus Z distribution…
5.3.2
Application 4
5.4
Determining Sample Size
5.5
Concluding Applications
5.5.1
Light Bulbs (Last Time)
5.5.2
Returning to the Philadelphia School Policy Application
6
Hypothesis Tests
6.1
Anatomy of a Hypothesis Test
6.2
Steps to a hypothesis test
6.3
Two methods for conducting a hypothesis test (when
\(\sigma\)
is known)
6.3.1
Rejection Region Method
6.3.2
P-value Approach
6.4
Two-sided vs One-sided Test
6.5
Conducting a hypothesis test (when
\(\sigma\)
is unknown)
6.6
Appendix: A note on calculating P-values
6.6.1
The Problem
6.6.2
How to calculate p-values
MBA 8380
7
Simple Linear Regression
7.1
A Simple Linear Regression Model
7.1.1
What does a regression model imply?
7.1.2
The
REAL
Simple Linear Regression Model
7.2
Application: Predicting House Price Based on House Size
7.3
Ordinary Least Squares (OLS)
7.3.1
B.L.U.E.
7.4
Decomposition of Variance
7.4.1
The
\(R^2\)
7.4.2
What is a
good
\(R^2\)
?
7.4.3
Standard Error of the Estimate
7.5
Assumptions of the Linear Regression Model
7.5.1
Linearity
7.5.2
Independence of Errors
7.5.3
Equal Variance
7.5.4
Normality of Errors
7.6
A Concluding Application
7.7
Appendix: Statistical Inference
7.7.1
Confidence Intervals (around population parameters)
7.7.2
Hypothesis Tests
7.7.3
Confidence Intervals (around forecasts)
7.8
Up Next…
8
Multiple Linear Regression
8.1
Application: Explaining house price in a multiple regression
8.1.1
The Importance of “Controls”
8.2
Adjusted
\(R^2\)
8.2.1
Abusing an
\(R^2\)
8.2.2
An
Adjusted
\(R^2\)
8.3
Statistical Inference
8.3.1
Recalling the Concept of Statistical Inference
8.3.2
Confidence Intervals (around population parameters)
8.3.3
Hypothesis Tests
8.3.4
Confidence Intervals (around forecasts)
8.4
A Concluding Application
Interpretation
Confidence Intervals
Hypothesis Tests
Forecasts
9
Collinearity
9.1
An Application
9.2
What does Collinearity do to our regression?
9.3
How to test for Collinearity?
Correlation Coefficients
Variance Inflation Factors (VIFs)
9.3.1
An Application:
9.4
How do we remove Collinearity?
Sometimes removing collinearity might involve multiple rounds
9.5
A Concluding Application
10
Qualitative (Dummy) Variables
10.1
Intercept dummy variable
10.2
Slope dummy variable
10.3
What if there are more than two categories?
10.4
A Concluding Application
10.5
Another Concluding Application
Make a
Nominal
Series a
Real
Series
Remove a Trend
Remove Seasonality
11
Functional Forms
11.1
Derivatives
11.2
Why consider non-linear relationships?
11.3
The Log transformation
The derivative of the log function
Log-log and Semi-log models
Application
11.4
The Quadratic transformation
Application
11.5
The Reciprocal transformation
Application
11.6
Conclusion
11.7
A Concluding Application
A Residual Analysis
Log Transformation
Quadratic Transformation
Reciprocal Transformation
12
Joint Hypothesis Tests
12.1
Simple versus Joint Hypothesis Tests
Application
12.2
Conducting a Joint Hypothesis Test
1. Estimate an Unrestricted Model
2. Estimate a Restricted Model
3. Construct a test statistic under the null
4. Determine a P-value and Conclude
12.3
Applications
Application 1: A wage application
Application 2: Constant Returns to Scale
12.4
A Concluding Application
Published with bookdown
Course Companion for MBA 8370 and MBA 8380
Course Companion for MBA 8370 and MBA 8380
Scott Dressler
2024-08-22