Assignment 5 Question 1

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

A5Q1 <- read_excel("C:/Users/nehab/OneDrive/A5221/Assignment 5/A5Q1.xlsx")
ggscatter(
  A5Q1,
  x = "age",
  y = "education",
  add = "reg.line",
  xlab = "Age",
  ylab = "Years of Education Completed"
)

# The relationship is linear.
# The relationship is positive.
# There are no meaningful 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 = "Distribution of Age",
  xlab = "Age"
)

hist(
  A5Q1$education,
  main = "Distribution of Education",
  xlab = "Years of Education Completed"
)

# Age looks approximately normally distributed.
# The age distribution is reasonably symmetrical.
# Education looks approximately normally distributed.
# The education distribution is reasonably symmetrical.

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

# Age is normally distributed because p = .558.
# Education is normally distributed because p = .439.
# Both p-values are greater than .05.
# Therefore, a Pearson correlation will be used.

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 examine the relationship
# between age and years of education completed.
# There was a statistically significant positive relationship,
# r(148) = .52, p < .001.
# The relationship was strong.
# As age increased, years of education completed tended to increase.