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Regression Paper

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Regression Paper
Team
RES/342 Research and Evaluation
Teacher
Date

The Hypothesis
Team C’s hypothesis is that the more years of education one receives the more a person can potentially earn in salary. The team will use the process of linear regression analysis to explain how the information is used and conduct a five-step test to see if the hypothesis proves true or false.
Linear Regression Analysis Team C’s purpose of this research paper is to use a linear regression analysis test to determine if a significant linear relationship exists between an independent variable which is X, level or years of education, and a dependent variable Y, salaries earned or potentially earned. “It is used to determine the extent to which there is a linear relationship between a dependent variable and one or more independent variables,” (Statistically Significant Consulting, 2010, para. 1). Learning Team C will use the salary and education levels from the Wages and Wage Earners Data Set collected through access to the e-source link of University of Phoenix. For this test the dependent variable, Y, will represent the salary of the 100 participants and the independent variable, X, will represent the education of the 100 participants.
How the Information is used
This information will be used in a linear regression test to see if there is enough evidence to reject the null hypothesis that a higher education does not equal a difference in salary. This test will research and analyze the earnings of workers based on the years of education they have received to see if the slope equals zero. If the slope equals zero, then Team C will not be able to reject the null hypothesis. This week, Learning Team C will use linear regression to determine if a significant linear relationship between the two variables actually does exist. The Five Step Hypothesis Test
With the information provided from the data, Learning Team C will use the data set and execute the five step hypothesis test to draw a conclusion regarding the study of whether more years of education one receives relates to the more a person can potentially earn in salary.
The null hypothesis for this research paper is that higher education equals no difference in salary or salary potential. The alternate hypothesis is that the higher education attained will determine the higher salary that an individual might earn.
Step 1

H0 : B 1 = 0 (The slope equals zero/there is no linear evidence that the independent variable, education level an individual has, affects the dependent variable, salary earned)
Ha : B 1  0 (The slope does not equal zero/there is linear evidence that the independent variable, education level an individual has, affects the dependent variable, salary earned)

Step 2

In order for Team C to accept the idea that correlation exists between education and salary, the r2 should be least .95 for there to be a very good fit. Anything below that number would not be accepted.
Step 3

This sample was separated into the following variables: (X) independent variable: education (Y) dependent variable: salary. The sample size was 100, consisting of 47 females and 53 males. Educational years varied as does salary earned.
Step 4

Using the critical value at α = .05, rejection in the one-tailed test requires t >1.860. This week’s test resulted in a t value of 4.425. This means that there is a substantial amount of evidence to reject the null hypothesis, which is equal to zero. In addition, the r2 value is 0.167, which is less than .95 and shows that there is not a very good fit.
Step 5

The results of the hypothesis test show rejection on the null hypothesis because the data does not equal zero. The t-statistic of 4.425 is greater than the critical value of 1.860 and allows the rejection of the hypothesis. Below are the results of the Regression Analysis using MegaStat in Excel®.

Regression Analysis r² 0.167 n 100 r 0.408 k 1 Std. Error 15550.444 Dep. Var. Wage ANOVA table
Source SS df MS F p-value
Regression 4,735,209,494.9482 1 4,735,209,494.9482 19.58 2.50E-05
Residual 3,697,996,987.8918 98 241,816,295.7948
Total 28,433,206,482.8400 99 Regression Output
Variables Coefficients Std. Error
Intercept -699.9501 7,293.67
Yrs. Education 2,477.09 559.7779

Confidence Interval t (df=98) p-value 95% lower 95% upper
-0.096 0.9237 -15,174.00 13,774.10
4.425 2.50E-05 1,366.23 3,587.96

Analysis Results
Linear regression attempts to display two variables and their relationship by aligning a linear equation with observed data. In essence one variable is an explanatory variable whereas; the other represents a dependent variable as shown in the results of Team C’s regression analysis. The analysis revealed a relationship and the result of wages to the years of education, as if the information of the two given variables had a correlation. When trying to fit a linear regression model with the observed data, Team C must first determine if a relationship between variables of interest exist. It does not particularly matters if one variable causes the other. The Team C looked at the existence of two significant associations between two variables, giving off the idea that the scattered plot does not indicate any increasing or decreasing trends. In this case, fitting a linear regression model to the data may not be useful. A valuable numerical value of association between the wages and years of education represents the correlation coefficient, which is a value between -1 and 1 indicating the strength of the association of observed data relating to the two variables. In the team's analysis, a linear regression line has an equation of Y=a + bX, where X represents the explanatory variable and Y represents the dependent variable. The line slope is denoted by b, and a represents the intercept (the value of y when x = 0).
Conclusion
The regression analysis of this data set demonstrates very little correlation between education and wages. The data shows that the variance can only be explained by this model around 16.7% of the time. This means that the research does not correspond with regression analysis test. The level of education does not necessarily determine the amount of wages that may be earned or potentially earned for an individual. This results in a rejection of the null hypothesis.

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