Week 2

Review of Regression

Week Learning Objectives

By the end of this module, you will be able to

• Describe the statistical model for regression
• Write out the model equations
• Simulate data based on a regression model
• Plot interactions

Task Lists

1. If you have questions, attend the Tuesday Q&A session
2. Complete the assigned readings
   • Gelman et al. ch 1.1, 1.2, 1.4
   • Gelman et al. ch 4.1, 4.2, 4.4, 4.5
   • 10 quick tips to improve your regression modeling
3. Attend the Thursday session and participate in the class exercise
4. Complete Homework 2

Lecture

Slides

You can view and download the slides here: HTML PDF

Statistical Model

Check your learning: In the example in the video, why do we need a random component?

Because there is only one predictor
Because the relation between the variables is linear
Because people who spend the same amount of time studying do not always have the same mastery level

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Import Data

Check your learning: What is the coding for the sex variable?

1 = male, 2 = female
2 = male, 1 = female
0 = female, 1 = male
0 = male, 1 = female

Take a pause and look at the scatterplot matrix. Ask yourself the following:

• How does the distribution of salary look?
• Are there more males or females in the data?
• How would you describe the relationship between number of publications and salary?

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Linear Regression

Sample regression line

Check your learning: How would you translate the regression line \(y = \beta_0 + \beta_1 \text{predictor1}\) into R?

y ~ 0 + predictor1
predictor1 ~ 1 + y
y ~ predictor1

Centering

Check your learning: The mean of the pub variable is 18.2. If we call the mean-centered version of it as pub_c, what should be the value of pub_c for someone with 10 publications?

8.2 1.8 -8.2 1.82

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Categorical Predictor

Check your learning: In a regression analysis, assume that there is a binary predictor that indicates whether a school is public (coded as 0) or private (coded as 1). If the coefficient for that predictor is 1.5, which category has a higher predicted score?

private public

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Multiple Regression

Think more: the coefficient of pub_c becomes smaller after adding time into the equation. Why do you think that is the case?

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Interaction

Pratice yourself: from the interaction model obtain the regression line when pub = 50.