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When no possible relationship between the two variables in question is statistically significant.
Usually the expression is employed in the context of the relationship between a dependent variable and another variable. The latter may or may not be independent: often it is time but that is not necessary. In some cases there is some indication that that there is a linear relationship between the two variables and that relationship is referred to as a trend.Note that a trend is not the same as causation. There may appear to be a strong linear trend between two variables but the variables may not be directly related at all: they may both be related to a third variable. Also, the absence of linear trends does not imply that the variables are unrelated: there may be non-linear relationships.
Directly proportional means that both variables increase or decrease at the same time.
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