q1 assignment 4

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(ggplot2)

A4Q1 <- read_excel("A4Q1.xlsx")
ggscatter(
  A4Q1,
  x = "age",
  y = "education",
  add = "reg.line",
  xlab = "age",
  ylab = "education"
)

# The relationship is linear.

# The relationship is positive.

# The relationship is weak.

# There are no outliers

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

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

hist(A4Q1$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 not proper bell curve.


# Variable 2: education
# The second variable looks normally distributed.
# The data is negative skew.
# The data has not proper bell curve.

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

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

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

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

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

## 
##  Spearman's rank correlation rho
## 
## data:  A4Q1$age and A4Q1$education
## S = 267492, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.5244375

# A Pearson correlation was conducted to test the relationship between a person's age in years (M = 35.79, SD = 2.59) and Variable 2 (M = 14.02, SD = 2.59).
# There was a statistically significant relationship between the two variables, r(148) = .52, p = .113.
# The relationship was positive and strong.
# As age increased,  education increased.


# A Spearman correlation was conducted to test the relationship between Variable 1 (Mdn = 35.79) and Variable 2 (Mdn = 14.02 ).
# There was a statistically significant relationship between the two variables, ρ = 267492, p < 2.2.
# The relationship was positive and strong.
# As age increased,  education increased.