Add linearRegression!

[mbostock]

Examples: https://observablehq.com/@data-workflows/plot-linear-regression

I also folded offsetRange into the range helper method. The linearRegression mark is a little interesting in that I lazily populate the channel values during the transform to avoid materializing extra copies.

[mbostock]

To be slightly more forward-looking, we could use Plot.regression as the name, and then default to type = "linear". Then we could support other types of regressions in the future. (Note that these other types of regressions would likely need to use Plot.line or a custom mark type instead of building on top of Plot.link.)

[Fil]

Agree with "regression" as a name (or even "trend" or "trendline"), and switching to a line mark rather than a link would make sense—it's more a line than a link.

I love the way it works with z (or in the example, stroke=species), as this is something I'm still finding a bit difficult to do in my experiments (see e.g. this comment).

While I don't dispute its usefulness in many cases, I think there's a risk it raises a lot of questions, in particular if we want to make this a first-class element of Plot.

First remark is that a linear regression is primarily a statistical analysis and modelling technique, and it's unfortunate if we can't get the model back from plot. In particular, we would like to get the significance of the correlation back, not only the trend. Currently if the correlation is too weak to be meaningful, Plot will happily display a line, which might be the wrong thing to do. We'd also want to get the "predict" function back, in most cases.

Second remark: there's more than one way to create trendlines (we might want to base it only the most recent data, or do an exponential fit, etc), so I'd imagine that an open system where linear regression could be plugged-in would be more versatile than a specific mark.

The third question I have is when we have different scale types, to define what we're correlating: reading the code I'm under the impression that we're doing a correlation of the "raw" values, but if I were to do a log-log plot I'd probably want the analysis to be done on the logarithm of the values. This can be done by passing a transform before the linear regression, but then the scales with type:"log" wouldn't apply.

[mbostock]

Good feedback. I agree that showing the significance of the correlation is important for understanding the analysis. And decoupling visualization from data processing, like we do with transforms, is more conducive to inspection and extensibility. So I’d like to think more about how we’d expose regression functions. Perhaps we should just integrate with d3-regression as you have already prototyped. It’s pretty awesome that already you can just use a d3-regression function as a transform and it “just works”…

[Fil]

Yes I think having d3-regression as an example of a transform that's easy to plug-in makes more sense than having it "built-in". I can imagine a Fourier example also, following a similar same pattern, and with configurable low-pass filters.