Stat 21 Week 8 Worksheet

Load relevant packages and create the predictor.

library(tidyverse)

## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.4.0      ✔ purrr   1.0.1 
## ✔ tibble  3.1.8      ✔ dplyr   1.0.10
## ✔ tidyr   1.2.1      ✔ stringr 1.5.0 
## ✔ readr   2.1.3      ✔ forcats 0.5.2 
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()

n <- 100 
x <- seq(-5, 50, length = n)

Create the response as a linear function of the predictor plus some random error.

## Error with constant variance, Normally distributed 
y <- 3*x -1 + rnorm(n, mean = 0, sd = 2)

## Error with constant variance, not Normally distributed 
#y <- 3*x -1 + ? 

## Error with non-constant variance, Normally distributed 
#y1 <- 3*x -1 + ? 
#y2 <- 3*x -1 + ?  
#y <- c(y1, y2)

## Error with non-constant variance , not Normally distributed 
#y1 <- 3*x -1 + ?
#y2 <- 3*x -1 + ?
#y <- c(y1, y2)

Fit a SLR model and look at the residuals

regmod <- lm(y~x)
my_data <- tibble(response = y, predictor = x, resids = regmod$residuals, fits = regmod$fitted.values)

ggplot(my_data, aes(x=fits, y=resids)) + 
  geom_point() + 
  labs(title="Residual plot", subtitle="Normal/non-Normal error with constant/non-constant variance") ## Edit the subtitle accordingly 

ggplot(my_data, aes(sample=resids)) + 
  geom_qq() +
  geom_qq_line() + 
  labs(title="Normal quantile plot of residuals", subtitle="Normal/non-Normal error with constant/non-constant variance") ## Edit the subtitle accordingly