Easy Statistics: Linear and Non-Linear Regression

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Three courses combined. Linear and Non-Linear Regression and Regression Modelling.

Learning and applying new statistical techniques can often be a daunting experience.

“Easy Statistics” is designed to provide you with a compact, and easy to understand, course that focuses on the basic principles of statistical methodology.

This course will focus on the concept of linear regression, non-linear regression and regression modelling. Specifically Ordinary Least Squares, Logit and Probit Regression.

The first two parts will explain what regression is and how linear and non-liner regression works. It will examine how Ordinary Least Squares (OLS) works and how Logit and Probit models work. It will do this without any complicated equations or mathematics. The focus of this course is on application and interpretation of regression. The learning on this course is underpinned by animated graphics that demonstrate particular statistical concepts.

No prior knowledge is necessary and this course is for anyone who needs to engage with quantitative analysis.

The main learning outcomes are:

1. To learn and understand the basic statistical intuition behind Ordinary Least Squares
2. To be at ease with general regression terminology and the assumptions behind Ordinary Least Squares
3. To be able to comfortably interpret and analyze complicated linear regression output from Ordinary Least Squares
4. To learn tips and tricks around linear regression analysis
5. To learn and understand the basic statistical intuition behind non-linear regression
6. To learn and understand how Logit and Probit models work
7. To be able to comfortably interpret and analyze complicated regression output from Logit and Probit regression
8. To learn tips and tricks around non-linear Regression analysis

Specific topics that will be covered are:

• What kinds of regression analysis exist
• Correlation versus causation
• Parametric and non-parametric lines of best fit
• The least squares method
• R-squared
• Beta’s, standard errors
• T-statistics, p-values and confidence intervals
• Best Linear Unbiased Estimator
• The Gauss-Markov assumptions
• Bias versus efficiency
• Homoskedasticity
• Collinearity
• Functional form
• Zero conditional mean
• Regression in logs
• Practical model building
• Understanding regression output
• Presenting regression output

• What kinds of non-linear regression analysis exist
• How does non-linear regression work?
• Why is non-linear regression useful?
• What is Maximum Likelihood?
• The Linear Probability Model
• Logit and Probit regression
• Latent variables
• Marginal effects
• Dummy variables in Logit and Probit regression
• Goodness-of-fit statistics
• Odd-ratios for Logit models
• Practical Logit and Probit model building in Stata

The computer software Stata will be used to demonstrate practical examples.

Regression Modelling

The third part provides useful practical tips for regression modelling.

Understanding how regression analysis works is only half the battle. There are many pitfalls to avoid and tricks to learn when modelling data in a regression setting. Often, it takes years of experience to accumulate these. In these sessions, we will examine some of the most common modelling issues. What is the theory behind them, what do they do and how can we deal with them? Each topic has a practical demonstration in Stata. Themes include:

• Fundamental of Regression Modelling – What is the Philosophy?
• Functional Form – How to Model Non-Linear Relationships in a Linear Regression
• Interaction Effects – How to Use and Interpret Interaction Effects
• Using Time – Exploring Dynamics Relationships with Time Information
• Categorical Explanatory Variables – How to Code, Use and Interpret them
• Dealing with Multicollinearity – Excluding and Transforming Collinear Variables
• Dealing with Missing Data – How to See the Unseen