Does an Education Imply a Sustainable Income?

An investigation into if a longer education provides a platform for earning more money long term

Zack Seath (s3843672)

Last updated: 28 May, 2023

RPubs Link

This Presentation can be found on RPubs at the following address https://rpubs.com/ZackS116/1046473

Introduction

Education no matter what form is a vital stage of everyone’s lives.
It can be essential in providing a starting point for careers and future ambitions.
However, is there a certain threshold to where a certain number of years education results in peak income once entering the workforce.
Or does the levels of income increase in tandem with the increase of years of education of a person.

Problem Statement

The aim of this investigation is to observe whether more years spent in the education system implies higher income once working.
In order to do so, the data will be explored to identify if there is a correlation between an increase in years spent in the education system and overall composite hourly wage for these people.

Data Description

The data set for this investigation was sourced from Kaggle, an Open Data Repository for Machine Learning and Data Science
This data was collected in a 1994 survey of Canadian Labor and Income Dynamic conducted in Ontario.
The data set consists of 7425 observations with 5 variables.
Those variables include the following:
Wages: Composite hourly wages from all jobs in Canadian Dollars.
Education: Amount of schooling in Years.
Age: in Years.
Sex: Factor Variable with levels of Male and Female.
Language: Factor Variable with levels of English, French or Other.

Data Preprocessing

# Import the data
Slid <- read.csv("SLID.csv", header = TRUE)

# Check the data
names(Slid)

# Drop the 1st column as it is just the index
Slid <- Slid[-c(1)]

# Check summary statistics
summary(Slid)

# Remove observations with wages as NA
Slid2 <- na.omit(Slid)

# Make sure the two factor variables are factors
Slid2$sex <- as.factor(Slid2$sex)
Slid2$language <- as.factor(Slid2$language)

# Final Check of Summary Statistics
summary(Slid2)

Data Preprocessing Explained

The two main important variables for this investigation are wages and education.
In looking at the summary of the data set a large proportion of the wages data set contained NA values.
This isn’t ideal due to the importance of the variable but given such a large proportion of the observations contain NA values a method such as imputing the mean of the column would lead to inaccurate results.
As such the only method in this situation was to remove any NA values from the data set and explore the data from a smaller subset of the data without any NAs.
This smaller subset turned out to contain 3987 observations.
Other than that the data is now cleaned and ready for investigation.

Descriptive Statistics

sumtable(Slid2)

Summary Statistics
Variable	N	Mean	Std. Dev.	Min	Pctl. 25	Pctl. 75	Max
wages	3987	16	7.9	2.3	9.2	20	50
education	3987	13	3	0	12	15	20
age	3987	37	12	16	28	46	69
sex	3987
… Female	2001	50%
… Male	1986	50%
language	3987
… English	3244	81%
… French	259	6%
… Other	484	12%

Descriptive Statistics Explained

Looking into the descriptive statistics of the subset we can see the average wages being $16 per hour with a minimum of $2.30 per hour and a maximum of $50 per hour from the individuals surveyed.
On average, participants completed the typical 13 years of education while the responses ranged from no education at all to 20 years of education.
The individuals surveyed were typically 37 years of age however they ranged from 16 to 69 years old.
There is also essentially a pretty even split of males and females interviewed.
Finally, a majority of the people questioned were English (81%), however, there was also 12% classed as other and 6% French.

Wages and Education Visualisation

p1 <- plot(Slid2$education, Slid2$wages, xlab = "Education", ylab = "Wages")
p1 <- abline(lm(Slid2$wages ~ Slid2$education))

Visualisation Explained

From the visualisation plotting the wages and education there is evidence to assist the assumption that more years spent in education does lead to higher wages.
However, it is definitely not a strong correlation at first glance and assisted through the line of best fit.
Here there is still a significant portion of people who have spent a large number of years in the education system but still are only earning a fairly small hourly wage.
Although one important thing to note that supports the investigation is that there are almost no people with a small number of years in the education system and a large hourly wage.

Hypothesis Testing

To begin with we have the following Hypotheses put into place for the investigation.
The null hypothesis being that the p-value is equal to 0 and there is no significant linear relationship between the two variables.
The alternative hypothesis being that the p-value is not equal to 0 and there is indeed a significant linear relationship between the two variables.

\[H_0: p = 0 \]

\[H_A: p \ne 0\]

Hypothesis Testing Continued

hyptest <- lm(Slid2$wages ~ Slid2$education, data = Slid2)
hyptest %>% summary()

## 
## Call:
## lm(formula = Slid2$wages ~ Slid2$education, data = Slid2)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -17.688  -5.822  -1.039   4.148  34.190 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      4.97169    0.53429   9.305   <2e-16 ***
## Slid2$education  0.79231    0.03906  20.284   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.492 on 3985 degrees of freedom
## Multiple R-squared:  0.09359,    Adjusted R-squared:  0.09336 
## F-statistic: 411.4 on 1 and 3985 DF,  p-value: < 2.2e-16

Hypothesis Testing Explained

As can be derived from this test an drastically small p-value less than the the value of alpha and one that is not equal to 0 as implied in the null hypothesis would indicate that the relationship between education and wages is statistically significant.
As such the null hypothesis should be rejected in favour of the alternative hypothesis.
It is however very important to still recognise the adjusted r-squared value.
At 0.09336, this implies there is not a strong linear relationship between the two variables.

Discussion - Limitations

It should be noted though that this is also quite a small sample size as well as it unfortunately had to be subsetted due to the large number of missing values within the wages column of the original data set.
As such this is just a depiction of whether or not education is vital for income from residents surveyed in Canada and there could indeed be different results in countries all around the world.

Discussion - Findings and Conclusion

This investigation has highlighted the importance of education when it comes to earning a decent income in the workforce.
Demonstrated through the fact that within the plot, next to none of the participants surveyed with less than say 8 years of education were earning any sort of substantial hourly wages.
However, it is important to acknowledge that having a significant amount of years within the education system won’t automatically imply a large hourly wage.
The adjusted r-squared value in the hypothesis testing backs this up. Portraying that there is indeed a relationship between more years of education and a larger hourly wage but most definitely not a significant one.
Ultimately, education is something that is vital for making a decent living once in the workforce, but it shouldn’t be expected that with a long time in the education system people can just walk into earning a subtantial hourly rate without any effort.

References

Singh, U., 2023, Survey of Labour and Income Dynamics, Kaggle, Viewed on 27 May 2023, https://www.kaggle.com/datasets/utkarshx27/survey-of-labour-and-income-dynamics?resource=download

Fox, J. (2016) Applied Regression Analysis and Generalized Linear Models, Third Edition. Sage.

Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition, Sage.