18 Least-squares linear regression

Tutorial learning objectives

• Learn about using least-squares linear regression (“LSR”, also called “Model-1 regression”) to model the relationship between two numeric variables, and to make predictions
  
• Learn the assumptions of LSR, and how to test whether these assumptions are met
• Learn that the implied statistical null hypothesis for a LSR is that the slope of the relationship is equal to zero
• Learn how to interpret regression analysis output
• Learn about the “coefficient of determination”, \(R^2\), represents the fraction of variation in the response variable that is accounted for by the regression model
• Learn how to make predictions using LRS
• Learn how to implement and report the findings of LSR