Linear Regression: Understanding Quantitative Relationships

This lecture introduces linear regression, a statistical method used to assess the impact of quantitative variables on an outcome. It covers the process of developing a research question, designing an experiment, and collecting data to answer the research question. The lecture explains the concept of independent and dependent variables, using examples such as predicting learning gains based on student interactions. It also demonstrates how to compute regression coefficients manually and using the lm() function in R. The lecture discusses the interpretation of R-squared as the proportion of variance explained by the model and the significance of adding predictors to improve the model. Additionally, it explores the assumptions of regression analysis, the decomposition of sums of squares, and the application of multiple regression to incorporate multiple predictors.