Correlation and Regression Analysis Assignment Coursework (Coursework Sample)

Correlation and Regression
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Institution
Correlation and Regression Analysis
The relationship between the salary of an officer and their experience is being investigated to determine whether there exists any correlation between the two variables. This analysis will be done using both regression analysis and correlation analysis.
Regression analysis is used to calculate the relationship between different variables (Bobko, 2001); it is also used to forecast change between the dependent and the independent variable. In this case, the salary given is dependent on the years of experience an employee has; therefore, the experience is the independent variable while the salary is the dependent variable. Based on the data provided, the summary output of the regression analysis is indicated below:
From the regression analysis above, the R Square equals 0.3172, which is not a very good fit because the closer the variable is to 1, the better the regression. Hence, in this case, the fit to the data is not very good with only 31.72% of the lines falling on the regression line. The significant value F was also less than 0.05, which is good and shows the set of variables were reliable. The regression line intercept stood at 17.4262 with the salary at 0.0804. This statistic indicates that for each unit increase in the experience of the employee, the salary increases by 0.0804 units; this is represented in the equation below:
y=mX + b
y=slope* + intercept.
Therefore, the equation representing the salaries for a pilot of 18 years is represented by
y= 0.0804x + 17.426
The correlation coefficient is often used to show how strongly two variables are related to one another (Bobko, 2001). The research tests the linear relationship between years of experience of the employee and their salaries.
As indicated above, the correlation coefficient between the salary and the years of experience is 0.5632. A value that stands between -1 and +1 shows how strongly two variables are interdependent on one another. In addition, a correlation coefficient of +1 shows that the variables have a perfect positive correlation. This statistic means, as experience increases, so does the income and vice versa. However, a negative coefficient indicates a negative correlation; this means, as variable V increases, variable Y decreases. In this case, the salaries and the experience are positively correlated (0.5633). When the data was filtered and the correlation was repeated based on the ranks of the officers, the following results were obtained for the Captains and the First Officers:
From the analysis, the correlation coefficient between the salaries and the experience in the Captains stood at (0.6278) while for the First Officers the correlation coefficient stood at (0.5369). These figures indicate that the Captain’s experience had a strong positive linear relationship with their salaries while the First Officers had a moderate positive linear relationship. The regression analysis for the Firs...