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"In regression analysis, when you use the first independent variable to indicate two groups (with values 0 and 1), the test statistic for the slope in regression is the same as the test statistic used in a two-sample t-test."

I intuitively understand what the concept is, but it is difficult to prove it mathematically, so please help.

user377597
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  • I don't have a great mathematical proof but I can tell you that this is related to the fact that the t-test and linear regression both have the underlying General Linear Model. If you are looking for a stronger mathematical understanding of why these are the same, that is probably a good starting place. – Quinton.Quagliano Oct 17 '23 at 03:20
  • https://stats.stackexchange.com/questions/354803/fitted-values-of-a-simple-regression-with-intercept-and-dummy is closely related – Christoph Hanck Oct 17 '23 at 13:00
  • Thank you for the comments. It has given me a rough idea of how to approach it. – user377597 Oct 17 '23 at 14:06

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