Assignment 4 Question 1

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

 ds1 <- read_excel("~/Downloads/ds1.xlsx")
 ggscatter(
     ds1,
     x = "age",
     y = "education",
     add = "reg.line",
     xlab = "age",
     ylab = "education"
)

The relationship is linear. The relationship is positive. The relationship is moderate or weak. There are no outliers.

mean(ds1$age)

## [1] 35.32634

sd(ds1$age)

## [1] 11.45344

median(ds1$age)

## [1] 35.79811

mean(ds1$education)

## [1] 13.82705

sd(ds1$education)

## [1] 2.595901

median(ds1$education)

## [1] 14.02915

 hist(ds1$age,
      main = "age",
      breaks = 20,
      col = "lightblue",
      border = "white",
      cex.main = 1,
      cex.axis = 1,
      cex.lab = 1)

 hist(ds1$education,
      main = "USD",
      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: USD The second variable looks normally distributed. The data is symmetrical. The data has a proper bell curve.

 shapiro.test(ds1$age)

## 
##  Shapiro-Wilk normality test
## 
## data:  ds1$age
## W = 0.99194, p-value = 0.5581

 shapiro.test(ds1$education)

## 
##  Shapiro-Wilk normality test
## 
## data:  ds1$education
## W = 0.9908, p-value = 0.4385

Variable 1: age The first variable is normally distributed (p = .5581). Variable 2: education The second variable is normally distributed (p = .4385).

cor.test(ds1$age, ds1$education, method = "pearson")

## 
##  Pearson's product-moment correlation
## 
## data:  ds1$age and ds1$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 = 35.33, SD = 11.45) and a person’s education in years (M = 13.83, SD = 2.60). There was a statistically significant relationship between the two variables, r(148) = .52, p > .05. The relationship was positive and strong. As age increased, education increased.