STAA57 - WorkSheet 15

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Goal: Practice multiple regression using factor variables.

You will work with the fuel consumption data for new cars in 2018 & 2019, and examine combined fuel consumption (COMB) vs other variables.

rm(list=ls())
library(tidyverse)
fcr = read_csv("../data/2018 Fuel Consumption Ratings.csv") %>% 
  filter( FUEL %in% c("X", "Z") ) %>% 
  mutate( FUEL = factor( FUEL, levels = c("X", "Z", "D", "E", "N"), 
         labels = c("Regular", "Premium", "Diesel", "Ethanol", "Nat Gas")) )
new_fcr = read_csv("../data/2019 Fuel Consumption Ratings.csv") %>%
  filter( FUEL %in% c("X", "Z") ) %>% 
  mutate( FUEL = factor( FUEL, levels = c("X", "Z", "D", "E", "N"), 
         labels = c("Regular", "Premium", "Diesel", "Ethanol", "Nat Gas")) )

1. The variable CLASS describes the car category (“COMPACT”, “SUV - SMALL”, etc.). Sort the categories by the number of new car models (2018 data only).

2. Fit a regression model for COMB (in L/100km) with ENGINE_SIZE, CYLINDERS, and CLASS as explanatory variables, and no intercept or interactions. Based on your results, rank the categories from most to least fuel-efficient.

3. Plot the residuals vs the fitted values of the model. What is the standard deviation of the residuals (use broom::glance)?

4. Use the previous model to predict the fuel consumption of the 2019 models (data-frame new_fcr). Plot the actual (y-axis) vs fitted (x-axis) values, and calculate the standard deviation of the prediction errors.

5. Use fct_lump() to keep the top 5 categories & combine the rest in “Other” (2018 data). Fit a regression model for COMB with ENGINE_SIZE and CLASS as explanatory variables with interaction, and report the resulting parameter estimates.

6. Based on your previous model, write down the linear function formula for the FULL-SIZE car class, including the actual values of the coefficients.