# Report on Linear regression analysis of Education Vs Wage

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## Question

In your role as an economic analyst you have been asked the following question

How much does education affect wage rates?

The Excel data file (wage) contains 100 observations for each of the following variables:

**Variables**

wage Earnings per hour

ln_wage The log of earnings per hour

educ Years of education

educ2 Years of education squared

Conduct a simple linear regression analysis to examine the relationship between ‘education’ (the independent variable) and ‘wage’ (the dependent variable). Using the Excel data file, prepare a 2000 word report using the following structure:

- Purpose
- Background
- Method
- Results
- Discussion
- Recommendations

In preparing your report you must address the following questions:

**(a)** Obtain summary statistics and histograms for the variables WAGE and EDUC. Discuss the data characteristics.

**(b)** Estimate the linear regression WAGE = β1 + β2EDUC + ε and interpret the slope.

**(c)** Calculate the residuals and plot them against EDUC. Are any patterns evident and, if so, what does this mean?

**(d)** Estimate the quadratic regression WAGE = α1 + α2EDUC2+ ε and interpret the results. Estimate the marginal effect of another year of education on wage for a person with 12 years of education, and for a person with 14 years of education. Compare these values to the estimated marginal effect of education from the linear regression in part (b).

**(e)** Construct a histogram of ln (WAGE). Compare the shape of this histogram to that for WAGE from part (a). Which appears to be more symmetric and bell-shaped?

**(f)** Estimate the log-linear regression ln (WAGE) = γ1 + γ2EDUC + ε and interpret the slope. Estimate the marginal effect of another year of education on wage for a person with 12 years of education, and for a person with 14 years of education. Compare these values to the estimated marginal effects of education from the linear regression in part (b) and quadratic in part (d)

## Solution

### Purpose

The nexus between wage and education has been a matter of interest for researchers in the field of labor economics for a stint period (Newman, Couturier, & Scurry, 2010). With graduation of time, the labor force for any organization has been started to be considered as another form of capital, i.e. human capital (Machlup, 2014). Now productivity of a capital comes from its applicability, and in the case of human capital, applicability, suitability, and skill come with the level of education. If we move up the value chain of any organizations, it can be easily seen that the level of skill required for performing an operation rises, and so as the decision making power. Without having adequate education, a perfect mix of skill can never be attained, and this is a factor, which decides one’s position in an organization, and so as the wage level (Autor, Katz, & Kearney, 2008). Therefore, there is a possible nexus between education and wage.

The purpose of this study is to investigate the impact of education on wage. In order to study this impact, we intend to perform three different regressions on the aforesaid parameters. For estimating these regression models, we have taken earnings per hour and years of education as the proxies of wage and education. Based on the results of the three regression models, we have been able to comment on the association between wage and education.

### Background

Considering the developmental objective of any nation, focus on education plays a major role. Educational attainment can be divided into three major parts, namely primary education, secondary education, and tertiary education (Barro & Lee, 2013). From the perspective of job creation, these three levels of education play significant roles in ascertaining the job creation and the level of wages. Looking at the least developed countries, it can be seen that the attainment of primary level education is reflected in the mechanical jobs, which are comparatively lower in terms of wage rate (Cuesta & Salverda, 2009).

When we move towards the developing and developed countries, then we can see a comparatively clear divide in terms of wage (Balán, Browning, & Jelin, 2014), which is generated out of level of educational attainment, i.e. the high level of educational attainment causes wage to rise (Goldin & Katz, 2009).

However, inequality in wage has been an age-old problem in the field of labor economics (Acemoglu, 1998). Several researchers have investigated about this in diverse contexts, and the majority of them found the level of educational attainment as one of the major reasons behind this issue. With the technological evolution, it has become an unwritten mandate for the organizations to hire skilled labor force, so that they can be able to handle the technology with efficiency. Owing to this reason, the term ‘*Human Capital*’ came into existence (Becker, 2009). In view of this, it is not hard to assume that the level of education plays a major role in determining the wage level for labor.

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