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Use the least squares method to calculate an equation for a best fit line that describes the relationship between a continuous explanatory and continuous response variable |
Calculate and interpret estimates for the intercept and slope of regression models |
Use the regression equation to predict new values for Y given values of X |
Calculate and interpret confidence and prediction intervals for the slope value |
Visually assess assumptions of regression models |
Fit a linear regression model with multiple predictors and interpret the coefficients |
Interpret the regression coefficient for binary, and categorical predictors |
Fit a model with a log transformed, or binary outcome and interpret the results |
Choose the best fitting model among several candidates using metrics like R2, AIC, BIC and Accuracy |
Introduction to Regression modeling
Everything is a linear model
Learning Path
Where we’ve been
Learning how to statistically assess the relationship between two variables.
Where we’re at
Learning the fundamentals of linear regression, a foundational method of modeling for many types of analyses. We’ll start with simple linear regression, a model that describes the relationship between two quantitative variables as a straight line.
Then we’ll expand that model to include multiple predictors of varying types.
And then we’ll make it even more generalizable by transforming the response variable \(y\) and modeling a log transformed outcome, and a binary outcome using the same regression modeling framework.
Objectives
Learning Materials
This section uses the the Lung function dataset and the following packages:
- Plotting: ggplot2, ggdist, sjPlot,gridExtra
- Presenting results: broom, gtsummary
- Assumption checking: performance
See PMA6 Appendix for more details about the Lung data.
Note: Regression is such a big deal, there are MANY functions in MANY packages that help you get out the relevant information out of the model, and display it in many different ways. I will show several in the slides.
Slides (Will open in full screen. Right click to open in a new tab)
📚 Reading
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PMA6 Ch 8 |
PMA6 Ch 12 |
ASCN 10.2.1, ASCN 10.4 Intro, ASCN 10.3 |
PMA6 Ch 7 |
ASCN Ch 9 |