Using a scatter plot graph to investigate the relationship between the X values of 7,2,4,5,1,6 and 3 combined with relative Y values of 5, 26, 20, 15, 30, 12 and 25 reveals some easily observable conditions.
The first condition to note is that on the traditional X and Y axis scatter graph, the points when plotted give an overwhelming downward trend, with the lower X values of 1, 2 and 3 correlating to the higher Y values of 30, 26 and 25.
That relationship is then confirmed with the middle values of X of 4 and 5, which correspond to Y values of 20 and 15 - finally the last two values of X 6 and 7, provide Y values of 12 and 5.
Arranging the series of numbers along the X axis, with the highest number first, with the corresponding Y axis number shown in brackets confirms that overriding pattern.
X axis (Y axis) - 1 (30), 2 (26), 3 (25), 4 (20), 5 (15), 6 (12), 7 (5)
When represented in scattergraph form, these coordinates show an approximately negative linear relationship. Indeed, the correlation co-efficient for this group of numbers is -.987, which is a relatively high correlation between two otherwise unrelated groups of numbers.
Despite this fact, if you are viewing the group of numbers as evidence of an absolute relationship, the fact that the correlation coefficient is not -1 means it has to be considered to be a negative nonlinear relationship, as not all numbers follow a clearly defined, mathematically logical relationship.
In essence, the difference between the two depends less on the numbers and more on the definitions of the terminology used. If you are happy to work in general terms then the relationship can be described as negative linear in general terms. However, if you are working to absolute terms, the fact that the points do not lie on one continuous line means that it has to be described as a negative nonlinear relationship.
The first condition to note is that on the traditional X and Y axis scatter graph, the points when plotted give an overwhelming downward trend, with the lower X values of 1, 2 and 3 correlating to the higher Y values of 30, 26 and 25.
That relationship is then confirmed with the middle values of X of 4 and 5, which correspond to Y values of 20 and 15 - finally the last two values of X 6 and 7, provide Y values of 12 and 5.
Arranging the series of numbers along the X axis, with the highest number first, with the corresponding Y axis number shown in brackets confirms that overriding pattern.
X axis (Y axis) - 1 (30), 2 (26), 3 (25), 4 (20), 5 (15), 6 (12), 7 (5)
When represented in scattergraph form, these coordinates show an approximately negative linear relationship. Indeed, the correlation co-efficient for this group of numbers is -.987, which is a relatively high correlation between two otherwise unrelated groups of numbers.
Despite this fact, if you are viewing the group of numbers as evidence of an absolute relationship, the fact that the correlation coefficient is not -1 means it has to be considered to be a negative nonlinear relationship, as not all numbers follow a clearly defined, mathematically logical relationship.
In essence, the difference between the two depends less on the numbers and more on the definitions of the terminology used. If you are happy to work in general terms then the relationship can be described as negative linear in general terms. However, if you are working to absolute terms, the fact that the points do not lie on one continuous line means that it has to be described as a negative nonlinear relationship.
