Assignment 4 Question 1

library(ggpubr) A4Q1 <- read_excel(“A4Q1.xlsx”)``` ## Research Question

Is there a relationship between age and years of education?

Scatterplot

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

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

Pearson Correlation Test

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

``` ## Interpretation

The scatterplot shows a positive relationship between age and years of education because the regression line slopes upward from left to right.

The Shapiro-Wilk tests showed that both variables were normally distributed (p > .05), so a Pearson correlation was appropriate.

The Pearson correlation showed a statistically significant positive relationship between age and years of education (r = 0.52, p < .001). This indicates that older individuals tended to have slightly more years of education.