Assignment 4, Question 1

Load Packages

library(readxl)

## Warning: package 'readxl' was built under R version 4.6.1

library(ggpubr)

## Warning: package 'ggpubr' was built under R version 4.6.1

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 4.6.1

library(rmarkdown)

Import Dataset

A4Q1 <-read_excel("C:/Users/rteno/OneDrive - Saint Louis University/AA 5221-11_Assignment 4/A4Q1.xlsx")

Create scartterplot

ggscatter(
  A4Q1,
  x = "age",
  y = "education",
  add = "reg.line",
  xlab = "Age",
  ylab = "Education",)

#The relationship appears linear.
#The relationship is positive.
#The relationship is moderate.
#There are no outliers.

Calculate descriptive statistics

mean(A4Q1$age)

## [1] 35.32634

sd(A4Q1$age)

## [1] 11.45344

median(A4Q1$age)

## [1] 35.79811

mean(A4Q1$education)

## [1] 13.82705

sd(A4Q1$education)

## [1] 2.595901

median(A4Q1$education)

## [1] 14.02915

Create histogram for age

hist(
  A4Q1$age,
  main = "Age",
  breaks=20,
  col = "lightblue",
  border = "white",
  cex.main = 1,
  cex.axis= 1,
  cex.lab= 1)

# Age is normally distributed. 
# It is symmetrical. 
# It has a proper bell curve.

Create histogram for education

hist(
  A4Q1$education,
  main = "Education",
  breaks = 20,
  col = "lightcoral",
  border = "white",
  cex.main= 1,
  cex.axis= 1,
  cex.lab= 1)

# Education is normally distributed. 
# It is symmetrical. 
# It has a proper bell curve.

Normality Tests

shapiro.test(A4Q1$age)

## 
##  Shapiro-Wilk normality test
## 
## data:  A4Q1$age
## W = 0.99194, p-value = 0.5581

shapiro.test(A4Q1$education)

## 
##  Shapiro-Wilk normality test
## 
## data:  A4Q1$education
## W = 0.9908, p-value = 0.4385

# Age is normal.
# Education is normal

Conduct inferential test (pearson correlation)

cor.test(
  A4Q1$age,
  A4Q1$education,
  method = "pearson")

## 
##  Pearson's product-moment correlation
## 
## data:  A4Q1$age and A4Q1$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, education increased.