Correlation Assignment - Essay Example

Correlation Correlation is one of the most common and important statistical analysis used today. A correlation is a single value that defines the extent of linear relationship between any two variables (Cohen et al. 8). For instance, we might be interested in assessing whether the number of hours students spend watching television is related to their performance in school. In such a case, we will interview a few students selected randomly from the student population regarding their television watching patterns, then compare these values with their GPA scores using appropriate correlation tests.

Generally, we expect a negative correlation between the two variables since GPA scores are seen to be low among students who spend more hours watching television and vice versa. A positive correlation would imply that as one variable increases in magnitude, the second variable also increases correspondingly. For instance, age and weight among children is observed to be exhibit positive correlation, i.e. as a child grows taller, the weight increases correspondingly. As observed, correlation can be either positive or negative.

Another aspect of correlation that needs mention is that the value arising from calculation of correlation is known as correlation coefficient, or “r”. It ranges between -1.00 and +1.00. The more the value is close to +1 or -1, the greater the relation between the two variables. A value of “r” close to 0 implies a lack of relation between the variables. A negative value or “r” implies negative correlation while a positive one implies positive correlation. Although correlation values can be used to make important decisions, squaring it makes more sense (Spiegel 42).

The square of the correlation coefficient, known as “R2” denotes the proportion of variation in one variable that is related to the variation in the other. For instance, an “r” value of 0.6 indicates that 36% of the variation is related (0.6 * 0.6). Calculation of Correlation Coefficient My case study will focus on the relation between educational attainment and synthetic work-life earnings. The earnings represent expected earnings over a 40-year time period for the population aged 25–64 who maintain full-time jobs throughout the year (Julian 1).

Since academic qualification is non-numeric, it will be ranked from a scale of 1 to 9 (1 refers to the lowest level of education and 9 for the highest) to make analysis possible. Data used for this analysis was sourced from the US Census Bureau, 2011 American Community Survey and is as shown below. Educational Level Rank Synthetic Work Life Earnings ($) None to 8th grade 1 936,000 9th to 12th grade 2 1,099,000 Some college 3 1,371,000 Associate’s degree 4 1,632,000 Associate’s degree 5 1,813,000 Bachelor’s degree 6 2,422,000 Master’s degree 7 2,834,000 Professional degree 8 4,159,000 Doctorate degree 9 3,525,000 The scatterplot is shown below: From the shape of the scatterplot, we observe that the two variables increase correspondingly, i.e. as educational attainment increases, synthetic work life earnings also increase.

Therefore, we expect a high positive correlation between the two variables. Correlation Coefficient From the analysis, we obtain a correlation coefficient of +0.949. This value implies a very high positive correlation and the result can be interpreted to mean that as one’s educational attainment increases, synthetic work life earnings increases correspondingly. The shape of the scatterplot is consistent with the value obtained for the correlation coefficient as it shows a linear positive relation between the two variables.

To a large extent, we can conclude that the higher the educational attainment, the higher a person earns over his/her lifetime. Conclusion Numerous factors affect the amount a person earns over his or her career. This summary data from the US Census data shows that educational attainment is just one of them. People with doctorate qualifications have the highest synthetic work life earnings while those with a maximum of an 8th grade have the lowest synthetic work life earnings. As one’s academic attainment improves, they become specialists in their own fields and are able to attract higher paying jobs.

Besides, they are more likely to get promotions resulting into salary hikes. Ultimately, persons with higher academic credentials not only earn more than their counterparts with fewer qualifications, but they are also more likely to get employed as well. This accounts for high synthetic work life earnings among the former. This relation is supported by numerous studies and is not due to chance. Apart from educational attainment, other factors can affect one’s synthetic work life earnings. These include college major and occupation.

For instance, a person who majors in medicine or engineering at university is likely to earn significantly higher salaries that graduates in other fields. Works Cited Cohen, Jacob, Patricia Cohen, Stephen West, & Leona S. Aiken. Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). NY: Psychology Press, 2002. Print. Julian, Tiffany. Work-Life Earnings by Field of Degree and Occupation for People With a Bachelor’s Degree: 2011. US Census Bureau. October 2012. Web. 9 November 2012.

Spiegel, Murray R. Theory and Problems of Probability and Statistics, 2nd ed. New York: McGraw-Hill, 1992. Print.