Linear Regression on Whiteside data

Packages installation and loading (again)

We will use the following packages. If needed, we install them.

Code

to_be_loaded <- c("tidyverse", 
                  "broom",
                  "magrittr",
                  "lobstr",
                  "ggforce",
#                  "cowplot",
                  "patchwork", 
                  "glue",
                  "DT", 
                  "viridis")

for (pck in to_be_loaded) {
  if (!require(pck, character.only = T)) {
    install.packages(pck, repos="http://cran.rstudio.com/")
    stopifnot(require(pck, character.only = T))
  }  
}

Dataset

Code

whiteside <- MASS::whiteside # no need to load the whole package

cur_dataset <- str_to_title(as.character(substitute(whiteside)))
 
# ?whiteside

Mr Derek Whiteside of the UK Building Research Station recorded the weekly gas consumption and average external temperature at his own house in south-east England for two heating seasons, one of 26 weeks before, and one of 30 weeks after cavity-wall insulation was installed. The object of the exercise was to assess the effect of the insulation on gas consumption.

Code

whiteside %>% 
  glimpse

Rows: 56
Columns: 3
$ Insul <fct> Before, Before, Before, Before, Before, Before, Before, Before, …
$ Temp  <dbl> -0.8, -0.7, 0.4, 2.5, 2.9, 3.2, 3.6, 3.9, 4.2, 4.3, 5.4, 6.0, 6.…
$ Gas   <dbl> 7.2, 6.9, 6.4, 6.0, 5.8, 5.8, 5.6, 4.7, 5.8, 5.2, 4.9, 4.9, 4.3,…

Start with columnwise and pairwise exploration

Code

C <- whiteside %>% 
  select(where(is.numeric)) %>% 
  cov()

# Covariance between Gas and Temp

mu_n <- whiteside %>% 
  select(where(is.numeric)) %>% 
  colMeans()

# mu_n # Mean vector

\[ C_n = \begin{bmatrix} 7.56 & -2.19\\ -2.19 & 1.36 \end{bmatrix} \qquad \mu_n = \begin{bmatrix} 4.88\\ 4.07 \end{bmatrix} \]

Use skimr::skim() to write univariate reports

Solution

Code

sk <- whiteside %>% 
  skimr::skim() %>% 
  select(-n_missing, - complete_rate)

skimr::yank(sk, "factor")

Variable type: factor

skim_variable	ordered	n_unique	top_counts
Insul	FALSE	2	Aft: 30, Bef: 26

Code

skimr::yank(sk, "numeric")

Variable type: numeric

skim_variable	mean	sd	p0	p25	p50	p75	p100	hist
Temp	4.88	2.75	-0.8	3.05	4.90	7.12	10.2	▃▅▇▇▃
Gas	4.07	1.17	1.3	3.50	3.95	4.62	7.2	▁▆▇▂▁

Build a scatterplot of the Whiteside dataset

Solution

Code

p <- whiteside %>% 
  ggplot() +
  aes(x=Temp, y=Gas) +
  geom_point(aes(shape=Insul)) +
  xlab("Average Weekly Temperature Celsius") +
  ylab("Average Weekly Gas Consumption 1000 cube feet")

p + 
  ggtitle(glue("{cur_dataset} data"))

Build boxplots of Temp and Gas versus Insul

Solution

Code

q <- whiteside %>% 
  ggplot() +
  aes(x=Insul)

qt <- q + 
  geom_boxplot(aes(y=Temp))

qg <- q + 
  geom_boxplot(aes(y=Gas))

(qt + qg) +
  patchwork::plot_annotation(title = glue("{cur_dataset} data"))

Build violine plots of Temp and Gas versus Insul

Solution

Code

(q + 
  geom_violin(aes(y=Temp))) +
(q + 
  geom_violin(aes(y=Gas))) +
  patchwork::plot_annotation(title = glue("{cur_dataset} data"))