Thread: Help with a simple regression model proof

1. 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.

2. 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 $\displaystyle R^2=1$.