HW 03: Multiple Linear Regression

due Friday, July 16 at 11:59p

Clone assignment repo + start new project

library(usethis)
usethis::use_git_config(user.name = "github username", user.email = "your email")

Data

In Lab 08, we considered simple linear regression models where we estimated the average life_expectancy of each country using each one of the following variables: the number of years of schooling, adult_mortality, and average BMI category (BMI_cat). In this homework, we will now fit multiple linear regression models for life_expectancy. The data were modified from this Kaggle dataset, and are available in Sakai. Upload the data just like you did in Lab 08. Once you have done so, you can run the following code to load the packages and data to get started.

library(tidyverse)
library(broom)
life_expect <- read_csv("data/life_expectancy.csv")

Codebook

Variable name Description
country Country
year Year (2000-2015)
status Developed or Developing country status
life_expectancy life expentancy in age
adult_mortality Adult Mortality Rates of both sexes (probability of dying between 15 and 60 years per 1000 population)
infant_deaths Number of Infant Deaths per 1000 population
alcohol Alcohol, recorded per capita (15+) consumption (in litres of pure alcohol)
percentage_expenditure Expenditure on health as a percentage of Gross Domestic Product per capita (%)
hepB Hepatitis B immunization coverage among 1-year-olds (%)
measles Number of reported cases of Measles per 1000 population
BMI Average Body Mass Index (BMI) of entire population
under_five_deaths Number of under-five deaths per 1000 population
polio Polio immunization coverage among 1-year-olds (%)
total expenditure General government expenditure on health as a percentage of total government expenditure (%)
diphtheria Diphtheria tetanus toxoid and pertussis immunization coverage among 1-year-olds (%)
HIV_AIDS Deaths per 1000 live births HIV/AIDS (0-4 years)
GDP Gross Domestic Product per capita (in USD)
population Population of the country
thinness_10_19 Prevalence of thinness among children and adolescents for Age 10 to 19 (% )
thinness_5_9 Prevalence of thinness among children for Age 5 to 9(%)
income_composition Human Development Index in terms of income composition of resources (index ranging from 0 to 1)
schooling Number of years of schooling

Exercises

Part 1: Data Manipulation

  1. Identical to Lab 08, we will be focusing on a single year of data. Filter the data to only retain observations from 2015. Additionally, create the following new variable:

Once you have created these variable, createa new dataset that retains only the following variables: country, life_expectancy, schooling, adult_mortality, BMI_cat, and status. Then omit all NAs. This is the dataset you will use for the remainder of the exercises.

Part 2: Exploratory Data Analysis

  1. Visualize the relationship between the number of years of schooling, life_expectancy, and the BMI_cat of each country. Describe what you see.

Part 3: Multiple linear regression

  1. Fit a linear main effects model to predict average life expectancy using the following variables: schooling, status, BMI_cat, adult_morality. Write out the equation of the fitted model, and interpret all the coefficients.

  2. Obtain and interpet the \(R^2\) for the main effects model.

  3. Fit a linear model to predict average life expectancy using the same main effects as above, but now with the addition of an interaction between BMI_cat and schooling. Write out the equation of the fitted model.

  4. Write the regression equations for each level of BMI_cat.

  5. Compare the adjusted \(R^2\) for both models. Which model do you prefer and why?

Part 4: Inference

  1. Use the model you ultimately selected in Exercise 7 for the remainder of this section. Examine if the conditions to perform inference on the regression coefficients are satisfied.

  2. Conduct a hypothesis test evaluating whether or not adult_mortality is associated with life_expectancy.

  3. Compute the mean adult mortality for each BMI category. Replace the dashes in the following code with the mean adult mortality for each respective BMI_cat. This code creates a new data frame to predict average life expectancy for hypothetical countries with the corresponding values for the explanatory variables.

Hint: Remember, we use the augment() function to predict from a fitted model. You can use augment(<model>, newdata = <data_frame_for_prediction>) to obtain predictions.

What are the predicted life expectancies for these hypothetical countries?