Is this true or false when there are no identifable trends in a graph it most likely means that there is no relationship between the two variables?
It is false. There may appear to be no relationship for several reasons:The most likely is that there is a third variable which is hiding the trend. To take a couple of crude examples, consider the relationship between age and earnings. If you look at the overall population it will be quite a wide scatter and there may be little trend - if any. The reason is that you have not included occupation. Once you have adjusted for occupation you will get a much better trend in the relationship.Similarly, if you have temperature measurements for your hometown, taken at various times of the day and night, you may see no trend. This is because you are not controlling for the time of day. In addition to the daily variations, there is also a longer term cycle - the seasonal variations (and then cycles over geological periods).With some regular time-series data, you may find "aliasing", which will give a completely wrong relationship (if you find one). If your data are collected at regular intervals, but ones which are out of synch with the periodicity of the variable, you may find that the effects of the asynchronicity are greater than the trend.The data set may have gone beyond the range of one relationship and into a different relationship. For example, take a spring and hang an increasing amount of mass from it. As the mass increases the spring will get stretched in direct proportion to the mass. However, keep adding mass and the spring will enter a phase of inelastic extension (until it breaks). If you mix data from the elastic and inelastic phase, you will not find a proper relationship.
