Lesson 1: Simple Linear Regression

Overview Section

Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables. This lesson introduces the concept and basic procedures of simple linear regression.

Objectives

Upon completion of this lesson, you should be able to:

  • Distinguish between a deterministic relationship and a statistical relationship.
  • Understand the concept of the least squares criterion.
  • Interpret the intercept \(b_{0}\) and slope \(b_{1}\) of an estimated regression equation.
  • Know how to obtain the estimates \(b_{0}\) and \(b_{1}\) from Minitab's fitted line plot and regression analysis output.
  • Recognize the distinction between a population regression line and the estimated regression line.
  • Summarize the four conditions that comprise the simple linear regression model.
  • Know what the unknown population variance \(\sigma^{2}\) quantifies in the regression setting.
  • Know how to obtain the estimate MSE of the unknown population variance \(\sigma^{2 }\) from Minitab's fitted line plot and regression analysis output.
  • Know that the coefficient of determination (\(r^2\)) and the correlation coefficient (r) are measures of linear association. That is, they can be 0 even if there is perfect nonlinear association.
  • Know how to interpret the \(r^2\) value.
  • Understand the cautions necessary in using the \(r^2\) value as a way of assessing the strength of the linear association.
  • Know how to calculate the correlation coefficient r from the \(r^2\) value.
  • Know what various correlation coefficient values mean. There is no meaningful interpretation for the correlation coefficient as there is for the \(r^2\) value.