Lab 1: Linear regression

Author

General Instructions

Labs will begin with loading necessary packages (for R users). If this is the first time using these packages, they will need to be installed prior to being loaded.

Lab instructions follow in numbered steps. In general, you will need to add code (Insert… Code Cell… R), run it to obtain output, and provide an interpretation of the results. It is not enough to provide output without interpretation.

We will cover Parts 1 and 2 in one day. Part 3 will be revisited after we have covered more of the simple linear regression notes.

Learning objectives

Be able to fit and interpret frequentist and Bayesian simple linear regression models
Compare the results to those that would be obtained using a 2-sample t-test
Compare the results of robust versus classical standard error estimates for the frequentist approach

Load R packages

Load the following packages for use in this lab.

library(rms)

Loading required package: Hmisc


Attaching package: 'Hmisc'

The following objects are masked from 'package:base':

    format.pval, units

library(rstanarm)

Loading required package: Rcpp

This is rstanarm version 2.32.1

- See https://mc-stan.org/rstanarm/articles/priors for changes to default priors!

- Default priors may change, so it's safest to specify priors, even if equivalent to the defaults.

- For execution on a local, multicore CPU with excess RAM we recommend calling

  options(mc.cores = parallel::detectCores())

1. Read in dataset

We will be using the inflammation dataset. Full documentation is available

The data is available as tab delimited or Stata format

2. Perform basic descriptive statistics for variables of interest

We will only be considering the three variables: age, male, and bmi

Male is coded as 0 for female and 1 for male. Create a factor variable (R) or label (Stata) this variable accordingly

Part 1: BMI and gender (classical standard error estimate)

1. Create and describe a plot of BMI by gender

2. Fit a simple linear regression model of BMI (outcome) on gender (predictor) using a frequentist approach.

3. Conduct an (equal-variance) t-test of BMI by gender. Compare to the output of the linear regression model

4. Fit a Bayesian linear regression model of BMI (outcome) on gender (predictor). Use the default priors. Compare the results.

Part 2: BMI and age

1. Create and describe a plot of BMI by age

2. Fit a simple linear regression model of BMI (outcome) on age (predictor) using a frequentist approach

3. Interpret the slope and corresponding 95% confidence interval

4. What is the estimate association for a 5-year increase in age? A 10-year increase in age? Give the confidence interval for each.

5. Fit a similar Bayesian linear regression model and interpret the results.

Part 3: BMI and gender, robust standard error

We will complete this part after covering robust standard errors in the notes

1. Fit a regression using the robust standard error estimate. Compare the results from this regression model to a t-test assuming unequal variance between group.