library(readxl)
library(ggpubr)

## Loading required package: ggplot2

A5Q2 <- read_excel("C:/Users/peter/Desktop/SLU/AA 5221 Applied Analytics & Methods/Week 5/Assignment 5/A5Q2.xlsx")

ggscatter(
  A5Q2,
  x = "sleep",
  y = "phone",
  add = "reg.line",
  xlab = "Sleep",
  ylab = "Phone"
)

# The relationship is linear.
# The relationship is negative.
# There are 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 = "Independent Variable",
     breaks = 20,
     col = "lightblue",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

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

# Variable 1: Sleep
# The variable looks abnormally distributed.
# The data is negatively skewed.
# The data does not have a proper bell curve.

# Variable 2: Phone
# The variable looks abnormally distributed.
# The data is positively 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 = 9.0e-08).

# Variable 2: Phone
# The variable is abnormally distributed (p = 9.6e-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 Sleep (Mdn = 7.5) and Phone (Mdn = 3.3).

# There was a statistically significant relationship between the two variables, ρ < .001, p < .001.

# The relationship was negative and strong.

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