Unit VII Essay. Explain the correlation of the data points to the equations

Correlation Coefficient
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Correlation Coefficient
The Pearson coefficient is the method applied in measuring the relationship between 2 variables, X and Y, which have a Gaussian distribution and no exceptional values. In the case of such conditions not being verified as is in most cases, using the Pearson coefficient may result in drawing wrong conclusions on the P of a relationship between the values. However, the fact that there is no linear relationship between the coefficients does not imply that no relation can be established to exist between the traits under study. This analysis takes this principle approach to explain the correlation of the data points to the equations in Fig. 4.3 on page 119 and the assumptions shown in Figures 4.4A, 4.4B, and 4.4C on page 120.
Correlation Coefficient: Explanation
Interpreting the linear correlation of coefficients is not as straightforward and easy as most people tend to believe; if the coefficient tends closer to 1 or -1, the points also tend closer to a straight line. In the case of p=± 1, the points are thus strictly aligned. Notably, a statistical table is used to help in specifying a value from where the coefficient is considered to be close to 1 or -1. When 0 is used, the correlation coefficients obtained are very close to 1, such as 0.95, usually on nonlinear data. If the data is linked by an exact nonlinear correlation, then the correlation coefficients that are obtained are null (Tofani, Candeloro, Sabbadini, Lucibello, Figura, Fabbrini, & Castelli, 2020). However, a statistical relationship that is established through a graph or coefficient fails to show the causal relationship that exists between the two variables. Causality is only established from a non-statistical data analysis approach.
When the appropriate coefficients are used in the upstream of any measure of correlation, then the shape of the possible relationship that exists between two characters should be defined through the appropriate graphical representation (Portney, 2020). Further, depending on the relation that is observed between the two variables, the hypotheses formulated are not the same and the measurement tools used are not the same. The correlation coefficients obtained from such scenarios are used measure the intensity of the relation between the two characters and interpreting its meaning if the relation is monotone. Further, the Pearson correlation coefficient enables the use to analyze the linear relations and obtaining the correlation coefficient of Spearman in the case of monotonic nonlinear relations.
There are also other coefficient that are used to represent non-monotonic and non-linear relations. Such coefficients are used for determining whether or not there is a linear relation between two continuous quantitative characters. The coefficient is computed by first computing the covariance (Ghauri, Grшnhaug, , & Strange, 2020). Covariance is defined as the mean of the deviations of the product from the mean. Computing the covariance marks the first step towards the analysis of the relationship between characters. It is considered an exp...