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