Purpose
The present report assesses the relationship between wage (hourly earnings) and number of years of education. The objective of the study is how well does the number of years of education impact wage of a person.The association between the two variables is necessary from economic point of view.
Education and wage have a causal relationship. In the modern society the wellbeing of a person is dependent not only capital and labour but also on the level of education. The attainment of education has been found to be positively associated with healthy lifestyles (Michalos 2017). A higher level of education symbolizes secure jobs with high pay and benefits. With the attainment of right level of education and proper training a person may have a higher wage.However,ifproper training is not provided to the person then even with higher level of education a person may not derive benefits (Lee and Sabharwal 2016).
Wage differences exist in our society (Leuze and Strauß 2014). Wage differences are not only based on the level of education but also gender. Gender inequality in wages can be attributed to gender stereotyped enrolment in academic subjects.According to research higher percentage of women attain education in social sciences, humanities and education, while subjects like engineering and natural sciences are overrepresented by men (Ochsenfeld 2014).Thus by the choice of the subject of education differences in wages are created.
Mismatch in wage and level of education is defined according to “assignment theory.” Underutilization or overutilization of skills creates wage disparity (BadilloAmador and Vila 2013). However, research shows that the attainment of skill is based on education and learning ability of a person. Persons with same level of education may have different skill levels as a result of learning ability, opportunity and demands of the present job (Pecoraro 2016).Thus, individuals with higher skill sets is bound to garner higher wage and vice versa.
To assess the relationship between the two variables a random sample of 100 observations was collected.Initially we examine the descriptive statistics of the variable. We have examined the central tendency, dispersion and spread of the collected sample data. The sampled data is represented graphically to examine the rate of change of the variables. The association between the variables is tested with the use of regression equation. The regression equation is used to predict the hourly earnings of a person’s having 12 and 14 years of education. The rate of change in hourly earnings is also evaluated.
Background
A
Table 1: Descriptive Statistics
Statistics 
Wage 
Educ 
Mean 
22.31 
13.76 
Standard Deviation 
14.02 
2.73 
Minimum 
4.33 
6.00 
Maximum 
76.39 
21.00 
Median 
19.39 
13.00 
1st Quartile 
12.02 
12.00 
3rd Quartile 
27.10 
16.00 
IQR 
15.08 
4.00 
The above table provides a descriptive analysis of the earnings per hour (Wage) and Years of Education (Educ).
From the above table we find that the minimum and maximum wages of the sample of 100 observations is 4.33 and 76.39 respectively. The average wage of the sample data is 22.31. The average wages of the sample data has a variation of 14.02. From the sample of 100, half the number of people get a wage of less than equal to 19.39. 25% of the sampled people have a wage of less than 12.02. In addition, 25% of the people have a wage of more than or equal to 27.10. Half the number of people sampled get a wage in the range of 15.08.
From the above table we find that the minimum and maximum education of the sample of 100 observations is 6.00 and 21.00 years respectively. The average numbers of years of education for the sample data is 13.76 years. There is a variation of 2.73 years in the number of years of education. Half the number of people sampled have an education of less than or equal to 13 years. 25% of the sampled people have less than 12.00 years of education. In addition, 25% of the people have more than or equal to 16.00 years of education. Half the number people sampled have an education in the range of 4.00 years.
Figure 1: Relation of Education and Wage
The scatter plot shows the relation between the number of years of education and wages of the sampled population. From the scatter plot it can be inferred that the wages do not have a linear increase with the number of years of education. The sampled population shows that people with a fixed level of years of education may have different wages. There is no proportionate increase in wages with the number of years of education.
Table 2: Regression statistics
Regression Statistics 

Multiple R 
0.4131 
R Square 
0.1706 
Adjusted R Square 
0.1621 
Standard Error 
12.8344 
Observations 
100 
ANOVA 

df 
SS 
MS 
F 
Significance F 

Regression 
1 
3320.69 
3320.69 
20.159 
0.000 
Residual 
98 
16142.78 
164.72 

Total 
99 
19463.47 
Coefficients 
Standard Error 
t Stat 
Pvalue 

Intercept 
6.9148 
6.6339 
1.0423 
0.2998 
educ 
2.1238 
0.4730 
4.4899 
0.0000 
The regression equation that can be used to interpret the relationship between number of years of education and wages can be depicted as:
 Wages = 2.1238*educ – 6.9148
From the above equation it is found that the coefficient of education is 2.1238. Hence it can be said that for each year increase in education the wage increases by 2.1238.
To test for the association between the number of years of education and wages the pvalue for the sloe coefficient is judged. The pvalue for the slope coefficient is 0.0000. Hence it can be inferred that at 0.05 level of significance there is a statistically significant association between education and wages.
Method
Regression studies shows that the correlation between number of years of education and wages is 0.4131. Thus, it can be said that the two variables have positive, moderate correlation. Moreover, from the sampled data 17.06% of the variability in wages can be predicted from the number of years of education. Since the predictability of the model is only 17.06% hence the model is not a good fit.
The regression equation for the relation between education and wage is
 Wages = 2.1238*educ – 6.9148
For a person having 12 years of education
 Wages = 2.1238*12 – 6.9148 = 25.4856 – 6.9148 = 18.5708
Hence, the earning per hour for a person having 12 years of education is 18.5708.
For a person having 14 years of education
 Wages = 2.1238*14 – 6.9148 = 29.7332 – 6.9148 = 22.8184
Hence, the earning per hour for a person having 14 years of education is 22.8184.
Thus, the difference in hourly wage rate for a person having 14 and 12 years of education is 22.8184 – 18.5708 = 4.2476
Thus the increase in hourly wage rate is 2.1238.
The analysis of the data shows that the wage of sample of the population is skewed to the right. However, the variable education is normally distributed. In addition, from the scatter plot it is found that wage does not have a linear growth with years of education. different levels of hourly earnings are got by persons having same level of education.
Moreover, the predictability of variation in wage from education is also poor although there is a significant association between wage and years of education.
From the study on the association it would be prudent to say that more research should be done to investigate the differences in wage pattern and education. Previous research suggests that there is a disparity in education between gender. Thus it can be recommended that government should investigate and reduce gender gap in different subjects of education.
References
BadilloAmador, L. and Vila, L.E., 2013. Education and skill mismatches: wage and job satisfaction consequences. International Journal of Manpower, 34(5), pp.416428.
Lee, Y.J. and Sabharwal, M., 2016. Education–job match, salary, and job satisfaction across the public, nonprofit, and forprofit sectors: Survey of recent college graduates. Public Management Review, 18(1), pp.4064.
Leuze, K. and Strauß, S., 2014. Femaletypical subjects and their effect on wage inequalities among higher education graduates in Germany. European Societies, 16(2), pp.275298.
Michalos, A.C., 2017. Education, happiness and wellbeing. In Connecting the Quality of Life Theory to Health, Wellbeing and Education (pp. 277299). Springer, Cham.
Ochsenfeld, F., 2014. Why do women’s fields of study pay less? A test of devaluation, human capital, and gender role theory. European Sociological Review, 30(4), pp.536548.
Pecoraro, M., 2016. The incidence and wage effects of overeducation using the vertical and horizontal mismatch in skills: Evidence from Switzerland. International Journal of Manpower, 37(3), pp.536555.