Respiratory Therapy

Respiratory Therapy Name Institution Introduction Various studies always depend on the relationships between two independent variables to make informed decisions on problem statements. Such relationships could be linear or nonlinear relationships, and univariate or multivariate relationships. In a linear relationship, two independent variables tend to have a relationship that can be plotted on a straight line. Thus, establishing whether independent variables are related is important to scholars and professionals in different fields. Consider the following example; in determining the effect of advertising on the number of sales, an analyst from company A plotted a graph of sales against the number of adverts. The output of the graph was a straight line indicating that an increase in the number of adverts leads to an increase in the number of sales. This reveals that identifying the relationship between two variables is an important statistical technique. One way of identifying a linear relationship involving two variables is through using the correlation coefficient(Clayton, Miller, and Peng, 2008). This paper examines the use of the correlation coefficient as an important technique for establishing linear relationships by citing evidence from previous publications. At this point, it is clear that the correlation coefficient is an important mathematical technique used to establish relationships between variables. To begin with, the term correlation could be elucidated as the process of determining whether two variables have a significant relationship. It is notable that multiple tools could be used to identify the correlation between two variables. For instance, plotting graphs helps in identifying the trend between two variables, hence the correlation. What is the correlation coefficient? Rubin (2013) defines the correlation coefficient as the magnitude of a straight line, or the linear association between two independent variables. In short using the correlation coefficient, which is denoted by r could help a researcher define the magnitude of association between two variables. How Correlation Coefficient Applies to a Real World Scenario The correlation analysis is a prominent statistical method used in summarizing scientific and medical research data. It does not only apply to making academic decisions, but also aids in making business decisions. This is proven by the fact that the example illustrated above can help in making business decisions. That is, a company intending to increase the number of sales can increase the number of adverts because it has been shown that the two variables have a positive linear relationship. Rubin (2013) notes that identifying the relationship involving two variables, and the magnitude of their relationship is important. The author further asserts that the correlation coefficient is also known as the Pearson`s product coefficient. This coefficient requires both the direction and the magnitude owing to the following two reasons. The magnitude defines the intensity of the relationship, while the direction defines whether the relationship has a positive or negative correlation. The correlation coefficient may only take values between 1 and -1; where the values are no dimensional, absolute, and with no units required. The correlation coefficient has characteristics that always help in interpreting its outcome. The first trait is interpreted when r is equal to zero and implies that the two variables under analysis are not correlated (Clayton, Miller, and Peng, 2008). If the value of r is close to -1 or 1, then there is a strong relationship between the two variables. What is the significance of the direction of r? A positive correlation variables, say Y and X indicates that an increase in the value of the independent variable X will lead to an increase in the value of the dependent variable Y. On the contrary, a negative correlation in variables; say W and Z indicates that an increase in the value of Z (predictor variable) will lead to a decrease in the value of Y (the predicted variable). The correlation coefficient r may be insignificant unless a scale is attached to the outcome of the coefficient. Consequently, absolute values between 0 and 0.367 indicate a weak relationship, 0.367 to 0.687 indicate a moderate relationship, and 0.688 to 1 indicate a strong positive association. However, describing the correlation coefficient as a weak, moderate, or strong relationship is not enough. Thus, the idea of the level of significance is important when determining the importance of r. Rubin (2013) defines the statistical significance as the random probability of observing r when correlation is zero. Therefore, the use of statistical tables can help in identifying whether the output r is statistically significant. It is notable that the level of significance varies depending on the size of the sample size used for the correlational analysis. The final element used in validating the efficiency of r is the r2 statistic (the r-squared residuals). It is defined as the variation of values in Y that are explained by the variations in the independent variable X. Worked Examples This section provides a manual direction for calculating the correlation coefficient. It also provides an example of the same data using Microsoft office excel so that scholars can appreciate the value of the elements used for testing. To begin with, the correlation for the correlation coefficient can be determined using the following formula. r=X-meanx*(y-(mean(y))X-meanx2*(y-meany2 Consider the following data for sales and adverts: Adverts Sales 0.29 42.00 0.92 77.00 0.52 58.00 0.55 47.00 0.40 48.00 0.66 55.00 ...