On Monday, we will finish up Chapter 4 of the course packet by talking about correlation among the predictors in a regression model (collinearity). We will then cover Chapter 5 of the course packet. Key topics:

  • sampling distributions and standard errors
  • bootstrapping
  • confidence intervals
  • the normal linear regression model

In class, we will practice bootstrapping in a regression model by revisiting two recent homework problems: finishing times in a ten-mile road race, and economic growth versus life expectancy in three different groups of countries.

On Wednesday, we will start Chapter 6 of the course packet on multiple regression. The key idea here is that of a partial relationship between two variables in a multiple-regression model.

Software

Outside of class, complete the following R walkthroughs.

For Wednesday of this week:

  • The wage gap: an introduction to multiple regression; quantifying uncertainty in a multiple regression model by bootstrapping.

For Monday of next week:

  • Current population survey: the affect of collinearity on the estimated coefficients and ANOVA table in a multiple regression model.

Readings

If you haven’t yet finished reading Chapter 5, then please do so. Then read Chapter 6 of the course packet: through page 135 by Wednesday (reading until the section on “Using multiple regression to address real-world questions”), and the rest of the chapter by next Monday. Note that in order to complete your homework, you’ll need some of the ideas from the latter half of Chapter 6 (i.e. the part you should have read by next Monday), particularly the use of the bootstrap to quantify uncertainty in a multiple regression model.

Videos

For Wednesday:

  • Partial relationships: using multiple regression to estimate a partial relationship between two variables, holding another variable constant.
    For Monday of next week:
  • Using multiple regression: a real-world application of multiple regression to answer some questions about the real-estate market in Saratoga, NY.

Exercises

Exercises 4 this week are about quantifying uncertainty in regression modeling. They are due in class on February 20.