library(readxl)
library(ggpubr)

## Loading required package: ggplot2

A5Q1_Sheet1_<- read_excel("C:/Users/USER/OneDrive - Saint Louis University/AA 5221/Assignment 5/A5Q1(Sheet1).xlsx")
View(A5Q1_Sheet1_)

#plot

ggscatter(
  A5Q1_Sheet1_,
  x = "age", 
  y = "education",
  add = "reg.line",
  xlab = "age",
  ylab = "education"
)

#Interpretations 

# The relationship is linear.
# The relationship is positive.
# There are outliers.

mean (A5Q1_Sheet1_ $age)

## [1] 35.32634

sd (A5Q1_Sheet1_ $age)

## [1] 11.45344

median (A5Q1_Sheet1_ $age)

## [1] 35.79811

mean (A5Q1_Sheet1_ $education)

## [1] 13.82705

sd (A5Q1_Sheet1_ $education)

## [1] 2.595901

median (A5Q1_Sheet1_ $education)

## [1] 14.02915

#Histogram

hist(A5Q1_Sheet1_$age,
     main = "age",
     breaks = 20,
     col = "lightblue",
     border = "white",
     cex.main = 1, 
     cex.axis = 1, 
     cex.lab = 1)

hist(A5Q1_Sheet1_ $education,
     main = "education",
     breaks = 20,
     col = "lightcoral",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

#Interpretations

# 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.

#Shapiro Wilk test

shapiro.test(A5Q1_Sheet1_ $age)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q1_Sheet1_$age
## W = 0.99194, p-value = 0.5581

shapiro.test(A5Q1_Sheet1_ $education)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q1_Sheet1_$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).

# using Pearson Correlation
# We use Pearson Correlation because both our histograms appear to be normal and also both Shapiro-wilk tsts indicate normality. 

cor.test(
  A5Q1_Sheet1_$age,
  A5Q1_Sheet1_$education,
  method = "pearson"
)

## 
##  Pearson's product-moment correlation
## 
## data:  A5Q1_Sheet1_$age and A5Q1_Sheet1_$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 = 2.61).

# There was a statistically significant relationship between the two variables, r(148) = .52, p < .001

# The relationship was positive  and strong.

# As age increased, education increased.