Weighted G.M. of relative formula and Time Reversal Test:

Weighted G.M. of relative formula is a statistical formula used to determine the average relationship between two variables by taking into account the weight of each variable. On the other hand, Time Reversal Test is a statistical methodology used to test whether a given time series is time-reversible or not.

The Weighted G.M. of relative formula satisfies the Time Reversal Test because of the following reasons:

- Time Reversal Test is based on the property of time-reversibility, which means that the statistical properties of a time series should remain unchanged if the time direction is reversed. In other words, if a time series is time-reversible, it should exhibit the same statistical behavior whether we analyze it forward or backward in time.
- The Weighted G.M. of relative formula is a mathematical formula that calculates the average relationship between two variables. It takes into account the weight of each variable, which means that it is sensitive to the magnitude of each variable.
- Since the Weighted G.M. of relative formula is based on the relationship between two variables, it is not affected by the direction of time. Whether we analyze the relationship forward or backward in time, the formula will yield the same result.
- Therefore, the Weighted G.M. of relative formula satisfies the Time Reversal Test because it is insensitive to the direction of time and yields the same result whether we analyze the relationship forward or backward in time.

Conclusion:

In conclusion, the Weighted G.M. of relative formula satisfies the Time Reversal Test because it is insensitive to the direction of time and yields the same result whether we analyze the relationship forward or backward in time.