---

title: “question1” author: “sree” date: “2026-04-10” output: html_document

library(readxl) 

## Warning: package 'readxl' was built under R version 4.5.3

library(ggpubr)

## Warning: package 'ggpubr' was built under R version 4.5.3

## Loading required package: ggplot2

DatasetZ <- read_excel("C:\\Users\\sahit\\Downloads\\A4Q1.xlsx")

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

# The relationship is linear.
# The relationship is positive.
# The relationship is weak.
# There no outliers.

mean(DatasetZ$age)

## [1] 35.32634

sd(DatasetZ$age)

## [1] 11.45344

median(DatasetZ$age)

## [1] 35.79811

mean(DatasetZ$education)

## [1] 13.82705

sd(DatasetZ$education)

## [1] 2.595901

median(DatasetZ$education)

## [1] 14.02915

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

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

# Variable 1: age
# The first variable looks normally distributed.
# The data is symmetrical.
# The data has a proper bell curve.


# Variable 2: education
# The second variable looks normally distributed.
# The data is symmetrical.
# The data has a proper bell curve.

shapiro.test(DatasetZ$age)

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

shapiro.test(DatasetZ$education)

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

# Variable 1: age
# The first variable is normally distributed (p = .55).

# Variable 2: education
# The second variable is normally distributed (p = .43)

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

## 
##  Pearson's product-moment correlation
## 
## data:  DatasetZ$age and DatasetZ$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 a person's age in years (M = 35.32, SD = 11.45) and Variable 2 (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 strong.
# As age increased, education increased.