Install Packages

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

Import Data

A5Q1 <- read_excel("~/Library/CloudStorage/OneDrive-SaintLouisUniversity/AA-5221-12/Assignment 5/A5Q1/A5Q1.xlsx")

Create a Scatterplot

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

## Interpret the Scatterplot

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

Calculate Descriptive Statistics

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

Create Histograms

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

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

## Interpret the Histograms

# 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.

Run the Shapiro-Wilk Tests

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

Interpret the Shapiro-Wilk Tests

# Variable 1: age
# The variable is normally distributed (p = .56).

# Variable 2: education
# The variable is normally distributed (p = .44).

Conduct the Pearson Correlation

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 = 35.32, SD = 11.45) and education (M = 13.82, SD = 2.59).
# There was a statistically significant relationship between the two variables, r(148) = .52, p <.001.
# The relationship was positive and moderate.
# As age increased, education increased.