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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
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 |