Lecture 20: Regression (part 2) and correlation
April 14, 2026Simple linear regression
In this second lecture on regression, we will explore inferences related to regression models, including confidence bands for regression lines, prediction intervals for single observations, and statistical hypothesis testing. We will introduce diagnostic tools to evaluate whether a regression model can be trusted for prediction. Additionally, we will discuss the assumptions underlying regression models and the importance of proper sampling when using regression analysis.
Correlation, assessing normality and non-parametric statistical hypothesis testing
In this lecture, we cover Pearson’s correlation, a statistic used to measure the degree of covariation between two continuous variables. Following this, we explore a visual method for assessing normality: the QQ plot. The video below provides an excellent explanation of these plots and how they are used to evaluate normality.
Finally, we discuss an example of a non-parametric test, which can be used when the assumption of normality is violated. Non-parametric tests are a diverse group of methods, and a comprehensive discussion would require about half a semester. While traditional parametric tests, which assume normality, are the most widely used and are the focus of this course, it is crucial to be aware of these alternative methods.
In Lecture 22, we will delve further into these alternatives.
Normal Quantile-Quantile Plots, by JBStatistics.
“An introduction to normal quantile-quantile (QQ) plots (a graphical method for assessing whether a set of observations is approximately normally distributed). The author discusses the motivation for the plot, the construction of the plot, then look at several examples. In the examples they look at what a normal quantile-quantile plot looks like when sampling from various other distributions. They then illustrate what normal QQ plots look like when sampling from a normal distribution by simulating several samples, for two different sample sizes.”
Lecture
Slides will be posted here prior to each lecture.