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Res 342 - Regression Hypothesis Testing Paper

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Regression Hypothesis Testing Paper

Regression Paper

In a competitive world, candidates searching for employment are seeking top wages. The study team has performed several hypothesis tests concerning wage and wage earners. A one-sample hypothesis test shows to gain the higher paying positions the individual will need to have current and up-to-date skills. College is a place where a person can reinvent him or herself by learning the latest programs and methods of communication. Whereas research proves that many factors contribute to individuals earning a higher wage, including race, age, ethnicity and work experience, education tends to be the driving force behind employers paying higher wages in the workforce. As more individuals obtain a college degree, the wage scale should begin to tip toward more groups achieving higher wages in correlation with his or her education.

Expanding the study using the two-sample hypothesis testing to determine if gender has an impact on obtaining a higher paying position, the team identifies that trailing in the wages earned between men and women. The study of 57 men out of 100 people polled reveals 33% of the men exceed $40,000 whereas the 43 women out of the 100 people polled only two percent of women exceed $40,000 in the same year. The study team proves through a nonparametric method that males are currently dominating the workforce with higher wages than females and the level of education does not determine the cause of this matter.

Purpose of the Study

Considering the amount of money people spend on earning a higher education, the individual may further his or her career by simply working up the corporate ladder if age is the determining factor. If a person makes more money simply because of his or her years of experience there would be no incentive to further his or her college education. The study team is awaiting the answer to know if the individuals polled in this study can clearly reflect the statement that age is its own reward. As the individuals age, an amount of experience accompanies him or her on the career path. Experience is a non-purchasable commodity, which individuals have to earn in time.

The study team will shift its focus to the age of candidates to see if there is any correlation between the age of an individual and the amount of money, he or she makes on an annual basis. Our focus will be to perform a thorough analysis to determine if age plays a factor in wages earned on an annual basis by conducting a linear regression analysis using the data provided in the Wage and Wage Earners Data Set. "Correlation coefficients and scatter plots provide clues about relationships among variables and may suffice for some purposes. But often, the analyst would like to model the relationship for prediction purposes (Doane & Seward, p. 496, 2007)." For this purpose, the study team has created a hypothesis to help explain the correlation between age and wages.

Hypothesis Statement Formulated

Our hypothesis statement is to determine if the relationship between wages and age are significantly linearly by conducting a test for the significance of the correlation coefficient. Computations are from the Pearson correlation r and the calculations are as follows:

From here, the study team will test for the significance of the correlation coefficient. The following null and alternate hypothesis will be used in the testing process:

The study team will use the t-test for testing the null hypothesis as shown below:

Finally, two-tailed p-value for this test, the computation is:

Since this means the team fails to reject the null hypothesis H0. Hence, the study team does not have enough evidence to support the claim that the correlation between Wage and Age is significantly different from zero. In observing the attached scatter plot (See Appendix B), there is little to no degree of linear association in the study team's comparison of age versus wages.


The study team can interpret the results of the regression hypothesis test as rejected. The information gathered shows there are 20 individuals polled making more than 44,000 per year range in age from 27 to 61. The information reveals two individuals aging from 21 to 30 making over $40,000 during the year polled. One individual over the age of 60 making over $40,000 during the year polled. The other 17 individuals range in age from 31 to 57. The team can identify six in the age group for 30's, five in the age group for 40's and six in the age group for 50's during the study process. The team was hypothesizing the older an individual became the more money he or she would earn.

The information used in the study reflects the three individuals earning the most income in this study varied in age. One person is 28, the second person is 53, and the person making the most money is 41. The wage earned by the different individuals does not have any bearing on the age of the person. The only thing that the top three individuals had in common was that each of the individuals had extended the years on his or her education. Two of the individuals had 17 years of education and one of the individuals had 18 years of education.

After reviewing the information from the study, the final test results reveal there is no significant increase in income for individuals in the age group of 21 to 30. The study reveals individuals within age groups of 31 to 40 and 51 to 60 are earning higher wages. A person can hypothesize that the reason individuals ranging from 31 to 40 and from 51 to 60 are making more money is that there is a driving force within, encouraging the individual to achieve this goal. People in the age group 31 to 40 are starting families and have a strong motivation for his or her family. This motivation is a strong reason behind why there is an increase in wage at those ages. The people in the age group 51 to 60 are planning for the upcoming retirement of his or her career. This may contribute to the individual's choice to increase his or her annual income to ensure a comfortable retirement. The truth is there has not been any defendant reason to why the individuals in this study make what



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