Introduction to REGRESSION! | SSE, SSR, SST | R-squared | Errors (ε vs. e)
Why Cross Validated Stack Exchange recommends it
Stats Stack Exchange (Cross Validated) answerers point people to it for a plain-language explanation of R-squared, the sums of squares and the error term notation.
Recommended by 2 people across 2 different months, 2015 to 2018.
What it is
An introductory video on regression from zedstatistics, the first in a five-part series. It covers the fitted line, sample versus population error terms, why errors are squared, the SSE/SSR/SST decomposition and R-squared. The presenter notes the video has an updated 2023 version.
What people said
Recommends user3796494 · 2015-03 · Cross Validated Stack Exchange · on “difference between R square and rmse in linear regression”
Both indicate the goodness of the fit. R-squared is conveniently scaled between 0 and 1, whereas RMSE is not scaled to any particular values. This can be good or bad; obviously R-squared can be more easily interpreted, but with RMSE we explicitly know how much our predictions deviate, on average, from the actual values in the dataset. So in a way, RMSE tells you more. I also found this video [this video] really helpful.
Recommends Maddenker · 2015-08 · Cross Validated Stack Exchange · on “Learning material for regression analysis”
I suggest entering your list of topics in YouTube. I have found the videos there to be very useful in learning the techniques, although more so for the general public as opposed to a Math major. One example: [this video]
Cites Father Fan · 2018-04 · Cross Validated Stack Exchange · on “Difference between SSM and SSR”
Actually, it is typical to label $\sum(y_i - \hat y_i)^2 = SSE$ while $\sum(\hat y_i - \bar y)^2$ is labeled either $SSR$ or $SSM$. Most sources use $\sum(y_i - \bar y)^2 = SST$, so that the decomposition of variance is generally either $SST = SSE + SSM$ or $SST = SSE + SSR$. See, for example, [LINK] or [this video] So, the answer to your question is that $SSR$ and $SSM$ are just two common notations for the same quantity.