library(readxl)
library(ggpubr)

## Loading required package: ggplot2

A5Q1 <- read_excel("C:/Assignment 5/A5Q1.xlsx")

ggscatter(
  A5Q1,
  x = "age",
  y = "education",
  add = "reg.line",
  xlab = "age",
  ylab = "education"
)

# The relationship is linear.
# The relationship is positive.
# There are outliers.
# I fixed the comment that Incorrectly mentioned that there were no outliers.

mean(A5Q1$age)

## [1] 35.32634

sd(A5Q1$age)

## [1] 11.45344

median(A5Q1$age)

## [1] 35.79811

mean(A5Q1$education)

## [1] 13.82705

sd(A5Q1$education)

## [1] 2.595901

median(A5Q1$education)

## [1] 14.02915

hist(A5Q1$age,
     main = "Age",
     breaks = 20,
     col = "lightblue",
     border = "white")

hist(A5Q1$education,
     main = "Education",
     breaks = 20,
     col = "lightcoral",
     border = "white")

# Variable 1: age
# The variable looks normally distributed.
# The data is symmetrical.
# The data has a proper bell curve.

# Variable 2: education
# The variable looks normally distributed.
# The data is symmetrical.
# The data has a proper bell curve.
# I fixed the comment that Incorrectly mentioned that the data is positively skewed.

shapiro.test(A5Q1$age)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q1$age
## W = 0.99194, p-value = 0.5581

shapiro.test(A5Q1$education)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q1$education
## W = 0.9908, p-value = 0.4385

# Variable 1: Age
# The variable is normally distributed (p > .05).

# Variable 2: Education
# The variable is normally distributed (p > .05).
# I fixed the misinterpreted variable 2 which was mentioned as abnormally distributed.

cor.test(
  A5Q1$age,
  A5Q1$education,
  method = "pearson"
)

## 
##  Pearson's product-moment correlation
## 
## data:  A5Q1$age and A5Q1$education
## t = 7.4066, df = 148, p-value = 9.113e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3924728 0.6279534
## sample estimates:
##       cor 
## 0.5200256

# A Pearson correlation was conducted to test the relationship between age (M = 35.33, SD = 11.45)
# and education (M = 13.83, SD = 2.60).
# There was a statistically significant relationship between the two variables, r(148) = .52, p < .001.
# The relationship was positive and strong.
# As age increased, income increased.