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Math Help - Help with a simple regression model proof

  1. #1
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    Help with a simple regression model proof

    Suppose we have only two data points: (X1, Y1) and (X2, Y2). Consider the case where we estimate
    the following simple regression model:
    Yi = α + βXi + ui, i= 1, 2. (i is supposed to be in subscript form)
    Show that R^2 = 1.


    Anyone have an idea how to solve this?

    I'd appreciate any help.

    Thanks.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Since you only have TWO points and your model is a line, i.e., TWO parameters you have a perfect fit.
    There is no statistics here.
    Just connect the dots and you have your line.
    Hence there is no error (SSE=0) and R^2=1.
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