Simple Linear Regression

By the end of this module, you should be able to:

• Describe the purpose of linear regression and how a regression line is estimated,
• Demonstrate appropriate use of the vocabulary and notation of linear regression,
• Use linear regression to describe the relationship between an independent and dependent variable,
• Interpret the regression line,
• Connect the estimated regression line to the corresponding scatterplot and correlation,
• Apply appropriate inferential methods for the slope of the line to determine whether a linear relationship exists,
• Use graphical displays, including residual plots, to assess whether a regression line is appropriate to describe the relationship between two quantitative variables, and whether related inferential methods are appropriate,
• Identify situations in which a log transformation is appropriate and interpret results of a linear regression in which the data have been log transformed.

Topics covered in this module

Learning resources:

1. Data Used in this Module
2. The Regression Line (video)
3. Simple Linear Regression: Some Cautions (video)
4. R², The Coefficient of Determination (video)
5. Inference for the Slope (video)
6. Checking the Conditions for Linear Regression (video)
7. Transformations in Linear Regression (video)
8. Optional: Guide to carrying out the analysis in this module using R (pdf)