# SC504 Quantitative Methods

## Question:

Utilizing the Lazarsfeldian equation framework, hypothesize possible relationships between variables in the dataset. Create a path diagram to illustrate these.

The netearn23 final outcome variable and all other variables from the dataset should be shown in the diagram.

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A sequence of three regression models can be fitted, each with netearn23 being the dependent variable. This will allow you to estimate the parameters and evaluate the path model.

It is likely that you will have to recode variables.

You must present your model results in publication-quality tables and not raw Stata output.

Also, create tables in Word that can be pasted into your report.

Interpret the coefficients, how they change in successive models and any other statistics that would be helpful to the reader in understanding the meaning of the results.

If they are helpful in understanding, you can also use a small number of charts.

Introduction

There has been curiosity about the factors that determine the pay of an employee since the dawn of industrialization.

Zabel (2015) conducted a salary survey to discover what factors affect salaries.

The study results showed that the hardest-to-fill job attracted a higher salary than one whose market was saturated.

A second research done in the late 1990s revealed that there was a gap in male and female salaries (Aizer, 2010,). This suggests that sex could also play a role in causing a difference in salary.

This study is designed to:

Check out whether tall people earn more than the rest

How does one’s ability and social status (read, sex, parental, etc.) affect earnings?

Therefore, the goal of the research is to determine the factors that impact earnings.

“Is there an association between salary and factors such sex, height, ability to read, social class, and sex?”

The following questions should be answered at the conclusion of our research.

Is height a factor in determining an individual’s net income?

Is there a correlation between reading ability, sexuality, and parental social classes?

Is there a relationship among reading ability, sex and parental social class?

Literature Review

The British began to classify their population according to occupation or industry in the middle of the industrialization period, which was around 1851 in Britain.

In general, the population was divided into these classes:

Professions

Managerial, technical and managerial occupations

Skilled occupations (i.e.

“Nonmanual” and “Manual”

Partly skilled occupations

Unskilled occupations

Accordingly, the classification of workers according to social classes was established and has been used as a basis for stratification in societal classes.

Erola & Lehti (2016), in their social paper about social stratification and movement argue that “…despite relative high degrees of equality of opportunity for most of the developed nations, family background still influences inheritanceof social classes.” So, different socioeconomic statuses tend to influence one another, i.e.

Education, class, income (Crowford und Erve 2015).

Ruel (2013) and Hauser (2013) discovered that there is a clear income gap between males and females in their research on gender and income disparities.

In particular, the wealth accumulation gap between married couples and men is large. This can be attributed both to investment strategies as well as selection effects.

Furthermore, households with a single parent have less wealth than those with two parents.

The married (Schmidt, Sevak and 2005).

Gregory conducted a 1960s study that found there was little preference for shorter people than for shorter men.

Pinsker (2015) asserts that “an additional inch correlates with an estimated \$800 per year in increased earnings.” This could be due to the fallacy, that tall men especially (gender disparity as it is) are stronger and are chosen to do the most demanding tasks.

The Atlantic post notes that men whose heights are between 5’4′” and 5’6 have the highest earnings.

Tyrrell (2016) says that height and socioeconomic standing are directly related.

As we mentioned earlier, socioeconomic status is heavily determined by one’s income. This can be used as a basis for social stratification.

The result is that males and girls seem to be different in height. Women are on average shorter than men.

The figure below shows the hypothetical relationship of the research variables with net income as the outcome variable. The underlying assumptions also state that each person is influenced and influenced by a certain parental social status.

Methodology

The data for this research was obtained from the UK Data Service.

It contains seven variables:

It includes 7 variables:

During data cleaning and administration, the sex variables are renamed to gender. The redundant nature of the female variable, i.e.

Both the gender and male variables serve the same purpose so that they both indicate whether the respondent is male/female.

The intmth11 variable is removed from our dataset as it is not relevant for data analysis.

Also, netearn23 has been renamed Net earnings and height23 to Height. The read11 variable is now Read.

Gender variables are coded as 1-Male, 2-Female.

The codes for parental social classes start at 1:6. 1 is the highest social class, while 6 is the lowest. This code is renamed Class from class16.

Regression

Our primary interest is to establish the relationship between net income and other predictor variable variables.

Based on these three research questions, three regression models were constructed. The response variables to net earnings and the predictor variable for height in the 1st equation were net earnings.

The predictor variables for the 2nd regression equation are reading ability and sex. However, the last equation has all variables except net earnings. These variables are independent variables, as shown in the equations below.

Yi = b0+b1X1+ + PSI. Where: b0is your regression coefficient

b1 refers to the coefficient of predictor variable X1’s height

PSi is the term for random errors

Yi is the response variable in net earnings

Yi=b0+b1X1+b2X2+b3X3+PSI.

b1 refers to the coefficient of predictor variable, X1 reading capability

X2 is the predictor variable. The coefficient of prediction variable b2 (or b2) is b2.

b3 refers to the coefficient of predictor variable, X3 Parental social status

PSi is the term for random errors

Yi is the variable that responds to net earnings

Yi=b0+b1X1+b2X2+b3X3+b4X4+PSI.

b1 refers to the coefficient of predictor variable, X1 reading capability

X2 is the predictor variable. The coefficient of prediction variable b2 (b2) is 0.

b3 refers to the coefficient of predictor variable, X3 Parental social status

b4 refers to the coefficient of predictor variable height X4.

PSi is the term for random errors

Yi is the response variable in net earnings

Three sets of hypotheses were created to answer research questions.

Null hypothesis

Taller persons make the same income as any other person

Alternative hypotheses

The earnings of taller people are higher than those of other people, i.e.

There is a relationship between height, net earnings and other factors.

Null Hypothesis

The ability to read, the parental social status or sex of an individual does not impact their net earnings.

Alternative hypotheses

The ability to read, parental social standing and sex are all important factors in determining an individual’s net income.

Null hypothesis

There is no relationship among all predictor variables (e.g.

There is no relationship between all the predictor variables i.e. height, sex and parental social class, as well one’s ability read and net earnings

Alternative hypotheses

There is substantial evidence to show that all of the predictor variables (e.g.

Height, height, parental social classes, and one’s ability read and net earnings are some of the predictor variables.

Results and discussion

Table 1 shows that F-statistic’s p-value is 0.000, which is lower than 522.14’s computed F value. This indicates that height plays a significant role in predicting net earnings. The coefficient of regression, however, is -85.0305, while the coefficient for height is 92.34439.

Additionally, the adjusted R-squared is 0.1056. This is used to measure efficiency when new variables are added to the regression model.

The regression diagnostics are used to determine:

Yi = -85.0305 + 92.343939X1, X1 height in cm. Random errors are not included as they do not impact the expectation.

An individual’s height is projected to rise by \$7 for every one cm of increase.

The p value for the tstatistic is 0.0000.05 with 95% confidence interval. We reject the null hypothesis of height not affecting net earnings and conclude there is substantial evidence that height has an effect on net earnings. Pinsker (2015) is correct.

Regression Equation 2.

Table 2 shows that the p value of the t statistic is 0.000 in sex and reading, and 0.048 in parental social classes. These variables are all less than 0.05 at 95% confidence interval.

The null hypothesis of no interaction between response and predictor variables is rejected. Instead, we conclude that one’s parental socio class, ability read, and sex influence one’s net earning potential.

An increase in the parental social class level by \$98.2 increases an individual’s net earnings. A female worker, however, earns \$76.6 more than a male worker.

Negative relationship between net earnings and ability to read is found where, assuming all other factors remain constant, one earns about \$99.2 more than someone who cannot read.

3. Regression Equation

The regression diagnostics shown in table 3 show that the adjusted R squared statistic increases upon the inclusion of height into the regression models. This indicates that the model’s accuracy is improved.

Furthermore, the Sex, Read, Height and Parental Social Class variables have significant impact on net earnings prediction. Their p-values are less than 0.0.05 for tstatistic, while they have p values of 0.104>0.05 at 95% confidence interval.

The intercept of the regression coefficients is 61.30585 and the coefficient of Read variable 0.468691. While the coefficient of Sex variable -19.2853 is, we assume that the parental category variable is not significant while that for height variable is 19.43205.

Therefore, we get a regression equation that is the following:

It is evident that the equation above shows a positive correlation between height and ability to read variables and net earnings. Conversely, net earnings are negatively correlated with sex.

Conclusion

The net earnings of an individual are affected by many factors.

Our results show that sex is an important factor in determining one’s net income.

There is an income gap that is defined by gender, where men and women earn different incomes.

The other side is that height increases have a positive effect on income. However when we examine the third regression result, we see that not all factors are equally important in predicting an individual’s net income.

The 2nd regression results show that parental social status had a significant impact on individual net earnings in the absence or inclusion of the height variable. However, the effect of parental social status on net earnings is diminished when the height variable has been introduced.

It is safe to conclude that taller individuals earn on average higher wages and that there is a correlation between one’s sexual ability and net earnings.

Recommendations for Further Research

After this research is completed, it is recommended to conduct research into the causes of income disparity between males/females in order to identify the underlying causes.

References

(2010) Domestic Violence and The Gender Wage Gap.

American economic review 100(4), pp.

Higher education leveling the playing field?

Education sciences, 5(4).

Parents’ education, class and income during the early years and children’s achievement.

Research in Social Stratification & Mobilization, 44(6), pp.

The Financial Perks to Being Tall.

Official Social Classifications of the UK

Explaining the Gender Wealth Gap.

Gender, Marriage and Asset Accumulation in the United States.

Working papers, 39(3), pp.

Mendelian randomization Study at UK Biobank. Height, Body Mass Index and Socioeconomic Status.

Results of the 2016 survey: A profession that needs change.

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