Hi GD_ ....There are subtle differences - and they are all technical - or should I say STATISTICAL - because that's what these indicators really are.
( How much I miss Jim!)
QUOTE :The fidelity chart plots a moving linear regression - LR that appears similiar to an Simple Moving Average.)

All these indicators are essentially Statistical estimators ie guesses of the future data point

(1) SMA is just that - takes all the points in the lookback time period and puts a dot at the average of those points as the best guess
(2) A Linear Regression takes all those points and "fits" a line to them. Hence it has 1 degree higher assumption than the Average.

For all practical purposes - the LR is a dynamic adjustment to the Average ( Simple Linear Model theory states that the Regression is the Mean ie Average + Slope*Design Matrix)

A Moving Linear Regression as plotted on Charts is just that "ending point estimate" and moving ie dynamic ie endpoint now, endpoint as it was yesterday and so on ....

So if the Index is having a trend and it can be approximated by a line ( more or less linear visually) - MLR will beat the SMA - by construction. Since its a better parametrized model. But NOT ALWAYS!

EXCEPT THAT :SMA just has a time series assumption and doesnt have the linear one - so its better approximation in a heavily undulating non-linear series.

As you can surmise from the above- NONE of that is related to SLOPE :)

The concept of the SLOPE is also embedded in Statistical theory - to determine CIT ie Change In Trend.

Its actually precisely to check for that phenomenon I mentioned above ie undulation. If one goes with the assumption that the underlying undulating index can be approximated by a PIECE-WISE Linear graph by setting the approximate periodicity ( ie lookback) THEN the CHANGE in the SLOPE helps in establishing CIT.

NET MESSAGE: What works better- Unfortunately you have to run a Backtest thru something like GTR to establish that.

Jim's original method vs Yours to determine. They are both VALID indicators and pretty darn good .... but optimality cant be guaranteed a-priori.

Best