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

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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

Learning Materials

This section uses the the Lung function dataset and the following packages:

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)

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lec08
lec08b

📚 Reading

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Topic Overview
PMA6 Ch 7 (p98-103 Sec 7.8- 7.9 robustness, AND Section 7.13)
Additional reference: IMS Ch 24

Assignments

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HW08

Assessment

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Quiz 09
Project Phase 4