Correlation and Regression Explorations

Author

Arvind V

Packages

library(tidyverse)
library(mosaic)
library(broom)
library(ggformula)
ggplot2::theme_set(new = theme_classic())

Intro

I will work through and “unify” at least two things:

Hadley Wickham’s chapter on modelling and his analysis of the linear model for the diamonds dataset
The diagnostic aspects of Linear Regression as detailed in Crawley’s book

Explorations into Diagnostic Plots

Let us create dependent y* variables with different sorts of errors:

x <- 0:300
en <- rnorm(301, mean = 0, sd = 5)
eu <- (runif(n = 301) - 0.5) * 20
eb <- rnbinom(n = 301, prob = 0.3, size = 2)
eg <- rgamma(n = 301, shape = 1, rate = 1 / x)
yn <- x + 10 + en
yu <- x + 10 + eu
yb <- x + 10 + eb
yg <- x + 10 + eg
data <- tibble(x, yn, yu, yb, yg)
data

ABCDEFGHIJ0123456789

x <int>	yn <dbl>	yu <dbl>	yb <dbl>	yg <dbl>
0	7.496430	8.639245	12	10.00000
1	12.561495	2.192567	30	11.76559
2	16.235447	2.567936	13	13.58764
3	4.098073	21.782213	15	15.74643
4	9.527473	12.403828	18	17.80034
5	15.769124	12.176289	26	22.22576
6	19.913854	12.971213	30	19.61077
7	12.033571	8.704312	19	17.77735
8	21.603782	11.689667	18	26.96920
9	20.422105	20.747138	23	23.20453

Normal Errors

lm_norm_aug <- lm(yn ~ x, data = data) %>%
  augment()
lm_norm_aug %>% gf_point(.resid ~ .fitted)

lm_norm_aug %>%
  gf_qq(~.resid) %>%
  gf_qqline()

Uniform Errors

lm_unif_aug <- lm(yu ~ x, data = data) %>%
  augment()
lm_unif_aug %>% gf_point(.resid ~ .fitted)

lm_unif_aug %>%
  gf_qq(~.resid, distribution = stats::qnorm) %>%
  gf_qqline()

Negative Binom Errors

lm_nbinom_aug <- lm(yb ~ x, data = data) %>%
  augment()
lm_nbinom_aug %>% gf_point(.resid ~ .fitted)

lm_nbinom_aug %>%
  gf_qq(~.resid, distribution = stats::qnorm) %>%
  gf_qqline()

Gamma Errors

lm_gamm_aug <- lm(yg ~ x, data = data) %>%
  augment()
lm_gamm_aug %>% gf_point(.resid ~ .fitted)

lm_gamm_aug %>%
  gf_qq(~.resid, distribution = stats::qnorm) %>%
  gf_qqline()