library(readxl)
library(ggpubr)

## Loading required package: ggplot2

A5Q2 <- read_excel("C:/Users/giuli/OneDrive - Saint Louis University/AA 5221/Assignment 5/A5Q2.xlsx")
View(A5Q2)
ggscatter(
  A5Q2,
  x = "sleep",
  y = "phone",
  add = "reg.line",
  xlab = "sleep",
  ylab = "phone"
)

# The relationship is linear.
# The relationship is negative.
# There are no outliers.
mean(A5Q2$sleep)

## [1] 7.559076

sd(A5Q2$sleep)

## [1] 1.208797

median(A5Q2$sleep)

## [1] 7.524099

mean(A5Q2$phone)

## [1] 3.804609

sd(A5Q2$phone)

## [1] 2.661866

median(A5Q2$phone)

## [1] 3.270839

hist(A5Q2$sleep,
     main = "sleep",
     breaks = 20,
     col = "lightblue",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

hist(A5Q2$phone,
     main = "phone",
     breaks = 20,
     col = "lightcoral",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

# Variable 1: sleep
# The variable looks normally distributed.
# The data is positively skewed].
# The data has a proper bell curve.

# Variable 2: phone
# The variable looks abnormally distributed.
# The data is negatively skewed.
# The data does not have a proper bell curve.
shapiro.test(A5Q2$sleep)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q2$sleep
## W = 0.91407, p-value = 8.964e-08

shapiro.test(A5Q2$phone)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q2$phone
## W = 0.89755, p-value = 9.641e-09

# Variable 1: sleep
# The variable is abnormally distributed (p = 8.96e-08).

# Variable 2: phone
# The variable is bnormally distributed (p = 9.64e-09).
cor.test(
  A5Q2$sleep,
  A5Q2$phone,
  method = "spearman"
)

## 
##  Spearman's rank correlation rho
## 
## data:  A5Q2$sleep and A5Q2$phone
## S = 908390, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.6149873

# A Spearman correlation was conducted to test the relationship between Variable 1 (Mdn = 7.52) and Variable 2 (Mdn = 3.27).

# There  was not a statistically significant relationship between the two variables, ρ = 8.96e-08, p = 9.64e-09.

# As the independent variable increased, the dependent variable decreased.