Module 5 Linear Regression

This module introduces students to the fundamentals of linear regression, a powerful statistical tool for modeling relationships between two numerical variables. Students begin by exploring scatter plots to visually assess linear associations and then progress to fitting a simple linear regression model of the form \(\hat{y}=b_0+b_1x\) using the least squares method.

Key concepts include:

Interpreting slope and intercept in context.

Understanding residuals and how they measure model error.

Calculating and interpreting the correlation coefficient \((R)\) and the coefficient of determination \((R^2)\) to assess model strength and predictive power.

Evaluating model assumptions through visual inspection of residuals and scatter plots.

Students apply these ideas to real-world data, including a study on how professor appearance may influence course evaluations. Through worked examples and exercises, they learn to build, interpret, and assess regression models, gaining insight into both the mechanics and implications of statistical modeling.