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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.

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  • $\begingroup$ 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. $\endgroup$
    – Quinton.Quagliano
    Commented Oct 17, 2023 at 3:20
  • $\begingroup$ stats.stackexchange.com/questions/354803/… is closely related $\endgroup$
    – Christoph Hanck
    Commented Oct 17, 2023 at 13:00
  • $\begingroup$ Thank you for the comments. It has given me a rough idea of how to approach it. $\endgroup$
    – user377597
    Commented Oct 17, 2023 at 14:06

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