Week 10: Simple Linear Regression, Multiple Linear Regression

Slides

Available closer to date.

Performance Outcomes

You should feel confident to perform the following outcomes:

Multiple linear regression

• Explain the purpose and basic concepts of simple linear regression
• Identify the variables involved and write the regression equation
• Interpret the slope and intercept in the context of real data
• Describe the assumptions underlying simple linear regression
• Fit a simple linear regression model using statistical software
• Interpret regression output, including coefficients, R-squared, and p-values
• Use the model to make predictions based on new data
• Evaluate the model fit using residuals and diagnostic plots
• Write the general form of a multiple linear regression equation and define its components
• Identify the key assumptions underlying multiple linear regression models, including linearity, independence, homoscedasticity, normality of errors, and absence of multicollinearity
• Fit a multiple linear regression model to a dataset using R
• Interpret the coefficients, R-squared, adjusted R-squared, and significance values from a multiple linear regression output.
• Evaluate model assumptions and use diagnostic plots to detect potential violations.
• Use the regression model to make predictions and interpret these predictions in the context of the study.
• Communicate the results and implications of a multiple linear regression analysis effectively.

Resources

If you don’t feel yet confident after going through the teaching materials or would like further resources, then you are also encouraged to go through the following materials.

• Statistical Inference via Data Science: A ModernDive into R and the Tidyverse (2nd Edition)
  • Chapter 10: Inference for Regression
• OpenIntro Statistics (4th Edition)
  • Chapter 8: Introduction to linear regression

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